well control problems associated with gas solubility in

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1988

Well Control Problems Associated With GasSolubility in Oil-Based Drilling Fluids.Patrick Leon O'bryanLouisiana State University and Agricultural & Mechanical College

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Well control problems associated w ith gas solubility in oil-based drilling fluids

O’Bryan, Patrick Leon, Ph.D.

The Louisiana State University and Âgricnltnral and Mechanical CoL, 1988

C opyrigh t © 1989 by O ’B ry a n , P a trick Leon. A ll rights reserved.

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WELL CONTROL PROBLEMS ASSOCIATED WITH GAS SOLUBILITY IN OIL-BASED DRILLING FLUIDS

A Dissertation

Submitted to the Graduate Faculty of the Louisiana State University and

Agricultural and Mechanical College in partial fulfillment of the

requirements for the degree of Doctor of Philosophy

in

The Department of Petroleum Engineering

by

Patrick L. O'Bryan B.S., Mississippi State University, 1983 M.S., Louisiana State University, 1985

May 1988


©1989

PATRICK LEON O',BRYAN

All Rights Reserved


ACKNOWLEDGMENT

The author wishes to thank Dr. A.T. Bourgoyne, Jr., under whose

guidance this work was conducted, for his encouragement and sug

gestions, and the many opportunities he provided this student through

out the course of his graduate career.

A special thanks goes to Drs. Teresa Monger, Zaki Bassiouni, Bill

Holden, Rex Pilger, and Ahmed El-Amawy for serving on the examining

committee.

The financial assistance provided by Amoco, Arco, British

Petroleum, Chevron, Cities Service, Conoco, Exxon, Tenneco, and Union

oil companies for this project is greatly appreciated.

The author would like to thank Debra Kopsco for her assistance in

completing the phase behavior study, Allen Kelly for his assistance in

completing the full-scale well experiments, and Jan Easley for typing

this document.

The author thanks the good Lord for making all of this possible

and blessing the author and his family with so much.

To his wife Pam and son Taylor, the author would like to say thank

you for the love and support you provided him during the course of this

study and his graduate career. We made it!

Finally, the author is indebted to his parents for providing the

opportunity to attend graduate school and always being very supportive.

In particular, the author thanks his father for teaching him early in

life how to use his head for something other than a hat rack and would

like to dedicate this work to him.

ii


TABLE OF CONTENTS

Page

ACKNOWLEDGMENT............................................. li

LIST OF TABLES............................................. v

LIST OF FIGURES............................................ vii

ABSTRACT................................................... x

CHAPTER I INTRODUCTION............................ 1

CHAPTER II LITERATURE REVIEW....................... 9

CHAPTER III AN EXPERIMENTAL AND THEORETICAL STUDY OF METHANESOLUBILITY IN OIL-BASED DRILLING FLUIDS.... 15

3.1 Purpose of Study................... 15

3.2 Experimental Apparatus and Procedure 15

3.3 Experimental Results..... 27

3.4 Equation of State Modeling......... 28

CHAPTER IV ADDITIONAL GAS SOLUBILITY DATA......... 33

4.1 Experimental Apparatus and Procedure.... 33

4.2 Experimental Results.............. 33

4.3 Solubility of Other Gases......... 41

CHAPTER V GAS SOLUBILITY APPROXIMATION........... 44

5.1 Solubility of Gas in Base Oil. 45

5.2 Solubility of Gas in Water.... 47

5.3 Solubility of Gas in Oil-Based DrillingFluids............................ 53

5.4 Experimental Verification of the Correlation....................... 53

CHAPTER VI GAS MISCIBILITY......................... 55

6.1 First Contact Miscibility......... 55

6.2 Methane Miscibility with No. 2 Diesel Oil 55

iii


3 Effects of Other Gases on MethaneMiscibility............................ 61

6.4 Field Application...................... 61

CHAPTER VII SWELLING OF OIL-BASED DRILLING FLUIDS DUE TODISSOLVED GAS............................... 65

7.1 Oil Swelling Calculations.............. 65

7.2 Pit Gain Calculations................. 66

7.3 Field Application..................... 71

7.4 Example Calculations.................. 77

7.5 Drilling Fluid Density Calculations 81

CHAPTER VIII HANDLING DRILLED-GAS IN OIL-BASED DRILLINGFLUIDS...................................... 83

8.1 Drilled-Gas Concentration............. 83

8.2 Circulating Time to Gas Evolution..... 84

8.3 Calculation of the Decrease in BottomholePressure Due to Gas Evolution.......... 87

8.4 Drilling Fluid Expelled Due to GasEvolution and Surface Gas Rate......... 92

8.5 Experimental Verification of CalculationProcedure .......................... 92

8.6 Evaluation of Field Procedures........ 94

CHAPTER IX CONCLUSIONS................................. 108

CHAPTER X RECOMMENDATIONS.............................. 110

CHAPTER XI REFERENCES................................... Ill

APPENDIX A PENG-ROBINSON EQUATION OF STATE............. 113

APPENDIX B FULL SCALE EXPERIMENTS...................... 117

APPENDIX C GAS FREE DRILLING FLUID PRESSURE CALCULATIONS 125

APPENDIX D TWO-PHASE PRESSURE GRADIENT CALCULATIONS 129

VITA....................................................... 131

iv


LIST OF TABLES

Page

TABLE 2.1 Methane Solubility in No. 2 Diesel Oil atT = 100®F (Thomas, Lea, and Turek).......... 10

TABLE 2.2 Methane Solubility in Unweighted Oil-BasedDrilling Fluid at T = 100°F (Thomas, Lea, and Turek).................................. 10

TABLE 3.1 Base Oil Molar Compositions.................. 17

TABLE 3.2 Composition of 13 Ibm/gal Oil-Based DrillingFluid (Salisbury)........................... 18

TABLE 3.3 Experimentally Measured Versus PREOS PredictedMethane Solubility in Mentor 28 Oil......... 29

TABLE 3.4 Experimentally Measured Versus PREOS PredictedMethane Solubility in 13 Ibm/gal Oil-Based Drilling Fluid.............................. 31

TABLE 4.1 Natural Gas Composition........ 34

TABLE 5.1 Empirical Correlation Constants.............. 46

TABLE 5.2 Gas Solubility in Water Curve Fits........... 52

TABLE 5.3 Experimentally Measured Versus PredictedBubble Point Pressure for Natural Gas/13-lbm/gal Oil-Based Drilling Fluid......... 54

TABLE 6.1 API Average Bottomhole Circulating Temperature 62

TABLE 7.1 Base Oil Critical Properties................. 67

TABLE 7.2 Comparison of Experimentally Measured andComputed Values of Volume Factor, Bo, for Methane in No. 2 Diesel Oil at 100°F........ 68

TABLE 7.3 Comparison of Experimentally Measured andPredicted Pit Gains in 6000 ft. ExperimentalWell........................................ 72

TABLE 8.1 Comparison of Experimental Observations andTheoretical Predictions..................... 93

TABLE 8.2 Volume of Drilling Fluid Expelled Due to GasEvolution................................... 100

TABLE A.1 Peng-Robinson Equation of State BinaryInteraction Coefficients.................... 116

V


TABLE B.l

TABLE B.2

TABLE B.3

Full Scale Experimental Gas Composition.

Full Scale Experimental Conditions.....

Full Scale Experimental Measurements....

Page

119

120

121

Vi


LIST OF FIGURES

FIGURE 1.1

FIGURE 1.2

FIGURE 1.3

FIGURE 1.4

FIGURE 2.1

FIGURE 2.2

FIGURE 3.1

FIGURE 3.2

FIGURE 3.3

FIGURE 3.4

FIGURE 3.5

FIGURE 3.6

FIGURE 3.7

FIGURE 3.8

FIGURE 3.9

FIGURE 4.1

FIGURE 4.2

FIGURE 4.3

FIGURE 4.4

Gas Kick Versus Drilled-Gas.

Gas Kick Detection In Water-Versus Oil-Based Drilling Fluids............ .................

Drilled-Gas Contamination of Water-Based Drilling Fluids.........................

Drilled-Gas Contamination of Oil-Based Drilling Fluids.......................

Methane Solubility in No. 2 Diesel Oil (Thomas, Lea, and Turek)..............

Carbon Dioxide, Hydrogen Sulfide, and Methane Solubility in No. 2 Diesel Oil (Matthews)....

Experimental Apparatus......................

Sample Experimental Pressure Versus Volume Plot

Experimental Procedure Verification.........

Methane Solubility in Mentor 28 Oil.........

Methane Solubility in Emulsifier............

Methane Solubility in 13 Ibm/gal Oil-Based Drilling Fluid..............................

Methane Solubility in Mentor 28 Oil, Emulsifier, and Brine (T = 100°F)....

Methane Solubility in No. 2 Diesel, Mentor 28, and Conoco LVT Base Oils (T = 100°F)........

Pressure Versus Density for Methane/13-blm/gal Oil-Based Drilling Fluid Mixture..

Ethane Solubility in Mentor 28 Base Oil.

Ethane Solubility in 13 Ibm/gal Oil-Based Drilling Fluid...........................

Carbon Dioxide Solubility in Mentor 28 Base Oil...............................

Carbon Dioxide Solubility in 13 Ibm/gal Oil-Based Drilling Fluid...............

Page

2

12

13

19

20 21

22

23

24

25

26

32

35

36

37

38

v ix


FIGURE 4.5 Natural Gas Mixture Solubility in Mentor 28Base Oil....................................

FIGURE 4.6 Natural Gas Mixture Solubility in 13 Ibm/galOil-Based Drilling Fluid....................

FIGURE 4.7 Gas Solubility in Mentor 28 Base Oil(T = 100°F).................................

FIGURE 5.1 Methane Solubility in Pure Water (McCain)....

FIGURE 5.2 Carbon Dioxide Solubility in Pure Water(Crawford, et. al.).........................

FIGURE 5.3 Water Salinity Correction for MethaneSolubility in Water (McCain)................

FIGURE 5.4 Water Salinity Correction for Carbon DioxideSolubility in Water (Crawford, et. al.).....

FIGURE 6.1 Pressure-Composition Diagram................

FIGURE 6.2 Methane/No. 2 Diesel Oil Miscibility PressuresVersus Temperature..........................

FIGURE 6.3 Locus of Cricondenbars for Methane and No. 2Diesel Oil..................................

FIGURE 6.4 Pit Gain Per 1000 SCF Méthane Kick in Oil- andWater-Based Drilling Fluids.................

FIGURE 6.5 Methane Miscibility Depth Versus No. 2 DieselOil-Based Drilling Fluid Density...... ......

FIGURE 7.1 Gas/Oil-Based Drilling Fluid Downhole Mixing.

FIGURE 7.2 No. 2 Diesel Oil Swelling Due to DissolvedMethane (T = 100°F).........................

FIGURE 7.3 No. 2 Diesel Oil Swelling Due to DissolvedMethane (T = 200°F) ........................



FIGURE 7.6 Downhole Oil-Based Drilling Fluid DensityChanges Due to Dissolved Methane............

viii

Page

39

40

42

48

49

50

51

56

58

59

60

64

70

73

74

75

76

82


Page

FIGURE 8.1 Circulating Gas Contaminated Drilling Fluid Out of Well................................. 85

FIGURE 8.2 Annular Velocity Profiles Due to Laminar Flow and Hole Eccentricity....................... 88

FIGURE 8.3 Computer Model Wellbore Geometry............ 89

FIGURE 8.4 Effect of Penetration Rate and Drilling Fluid Density on Drilled-Gas Concentration (D = 8000 Feet)....................................... 95

FIGURE 8.5 Effect of Penetration Rate and Drilling Fluid Density on Drilled-Gas Concentration (D = 15000 Feet)................. ■..................... 96

FIGURE 8.6 Effect of Drilled-Gas Concentration on Circulation Time to Gas Evolution........... 97

FIGURE 8.7 Effect of Penetration Rate and Gas Sand Thickness on Bottomhole Pressure Reduction... 99

FIGURE 8.8 Effect of Gas Send Thickness on Gas Volume in Well........................................ 101

FIGURE 8.9 Effect of Pump Rate and Drilled-Gas Concentration on Peak Surface Gas Rate...... 102

FIGURE 8.10 Rotating Head - Separator Flow Arrangement for No Free Gas in Wellbore................. 104

FIGURE 8.11 Rotating Head Pressure Rating Required to Keep Gas in Solution............ ........... 105

FIGURE 8.12 Rotating Head - Separator Flow Arrangement with Free Gas in Wellbore................... 106

FIGURE B.l Full Scale Experimental Test Well........... 118

FIGURE B.2 Experiment No. 1 Measured Data.............. 122



FIGURE C.l Friction Factors for Frictional Pressure Loss

Ix


ABSTRACT

Gas contamination of an oil-based drilling fluid during drilling

operations, whether it be by the flow of formation gas into the

wellbore (gas kick) or by the drilling of gas-bearing formations

(drilled-gas), poses a potential hazard to the drilling equipment,

environment, and personnel. This danger is the greatest when

bottomhole conditions are such that the gas will completely dissolve

into the drilling fluid and rapidly evolve as the gas-cut drilling

fluid is circulated up the well.

This work summarizes a study of well control problems associated

with gas solubility in oil-based drilling fluids. The solubilities of

various gases (i.e., methane, ethane, carbon dioxide, etc.) in base

oils used in oil-based drilling fluid preparation as well as an

oil-based drilling fluid over a range of pressures and temperatures

were measured and a method for predicting the solubility of a gas

mixture containing methane, ethane, and carbon dioxide in an oil-based

drilling fluid is pesented. In addition, methods for predicting the

pit gain to be expected for a given gas kick taken while drilling with

an oil-based drilling fluid and for predicting the annular behavior to

be expected when drilled-gas contaminates an oil-based drilling fluid

during drilling were developed. Both methods were verified using data

measured during experiments conducted in a 6000 ft test well.


CHAPTER I

INTRODUCTION

Oil-based drilling fluids, or muds as they are often referred to by

drilling personnel, are an alternative to the standard water-based

drilling fluids commonly used in the petroleum industry. Several

factors including reduced formation damage, better lubricity of both

surface and subsurface drilling equipment, better borehole stability,

and better drilling fluid stability at high pressures and temperatures

have led some companies to use oil-based drilling fluids exclusively

when drilling water sensitive production formations and/or deep, hot

wells. However, the use of oil-based drilling fluids have presented

several problems with respect to well control when the drilling fluid is

contaminated by gas.

Figure 1.1 illustrates how a drilling fluid can become contaminated

by formation gas. In Figure 1.1a the gas sand pressure is greater than

the circulating bottomhole pressure in the wellbore resulting in gas

flow from the sand into the well. This flow of formation gas is often

referred to as a "gas kick". Also notice in Figure 1.1a that the gas in

the wellbore displaces drilling fluid from the well resulting in an

increase in the volume of drilling fluid in the surface tanks or pits.

This is referred to as a "pit gain" and is the most commonly used and

most reliable method for detecting a kick in the well.

Figure 1.1b shows another way by which gas contaminates the

drilling fluid. In this case no gas flows from the sand because the

circulating bottomhole pressure in the well is greater than the gas sand

pressure. However, the gas contained in the pore space of the sand

1


Mud Inj

0Bottom Hole Pressure Less thtn 6aa Sand Formation Pressure

@)Gas Flows into Wellbore

@ Gas Kick in Wellbore

0)6as Kick Displaces Mud from Wellbore (P it Gain)

(§)Gos Send

(a ) GAS KICK

Mud In

rk

•

(D Bottom Hole Pressure Greater than Gas Sand Formation Pressure

©Me Gas Flow into Wellbore

©Dispersed Gas Bubbles from Gas Sand Destroyed by Bit in Wellbore

® No Mud Displaced from Wellbore

® Gas Sand

(b ) DRILLED GAS

Figure 1.1 - Gas Kick Versus Drilled-Gas.


destroyed by the bit will mix with the drilling fluid. This gas is

referred to as "drilled-gas".

When a gas kick is taken while drilling, it is imperative that the

kick be detected early enough to allow the proper well control

procedures to be implemented in order to reduce the risk of damage to

the environment, equipment, and personnel due to a "blowout", which is

the uncontrolled flow of formation fluids into the wellbore. As

previously mentioned, the most reliable indicator of a gas kick in the

wellbore is the surface pit gain. However, the pit gain observed for a

given gas kick size will be a function of several variables, one of

which is the type of drilling fluid being used (i.e., water- or

oil-based). Figure 1.2 schematically shows the difference between the

observed pit gain for a gas kick taken while drilling with water- and

oil-based drilling fluids.

When the gas kick enters the wellbore while drilling with a

water-based drilling fluid (Figure 1.2a), the volume of drilling fluid

displaced from the wellbore is proportional to the volume the gas kick

occupies at the pressures and temperatures existing in the well.

However if the gas kick is taken in an oil-based drilling fluid (Figure

1.2b), the volume of drilling fluid displaced from the well is much

less due to gas being more soluble in oil-based drilling fluids than in

water-based drilling fluids. The volume of drilling fluid displaced

from the well in this case is a function of the volume of gas dissolved

in the oil-based drilling fluid and tha swelling of the drilling fluid

due to the dissolved gas at wellbore pressures and temperatures.

As with gas kicks the well response associated with drilled-gas

contamination of the drilling fluid is a function of the drilling fluid


Mud In

riS

I

m 90 Gas Flows Into Wellbore

(§)G&t Kick exists as Free Gas

d) Pit Gain Equal to Gas Kick Volume at Bottomhole Pressure and Temperature

Gos Sand

(a ) GAS KICK IN W ATER-BASED MUD

Mud InI

0 Gas Flows into Wellbore

0 Gas Dissolves into Oil Mud No initial Free Gas in Wellbore

0 Pit Gain Equal to Swelling of Oil Mud Due to Dissolved Gas

Gos Sond

(b) GAS KICK IN OIL-BASED MUD

Figure 1.2 - Gas Kick Detection In Water-Versus Oil-Based Drilling Fluids.


type being used. For drilled-gas in water-based drilling fluids (Figure

1.3), the buoyancy of the gas bubbles and the relative insolubility of

the gas in the water causes the gas to migrate up the wellbore. This

migration of the gas causes the concentration of gas per volume of

water-based drilling fluid to be very low and in most cases has no

adverse effect on the drilling process.

For the case where drilled-gas contaminates an oil-based drilling

fluid (Figure 1.4), the solubility of the gas in the drilling fluid

causes the gas to remain concentrated as the gas/oil drilling fluid

mixture is circulated up the well. Once the bubble point depth of the

gas/drilling fluid mixture is reached in the well, the gas will evolve

from the drilling fluid usually very close to the surface. The bubble

point depth is defined as the depth at which the wellbore pressure and

temperature are such that the first bubble of gas appears. A

significant amount of gas and drilling fluid will be spewed out of the

well exposing the drilling rig personnel to hazardous conditions and a

reduction of the bottomhole pressure will occur due to the removal of

drilling fluid from the well which could possibly allow formation fluids

to flow from exposed subsurface formations.

Currently in the petroleum industry, computer models are used to

train field personnel in the proper well control procedures to be used

in the eve-t a gas contaminates the drilling fluid while drilling and

how the well will behave. However, these models are greatly simplified

and in most cases only model gas kicks taken while drilling with

water-based drilling fluids. It is the purpose of this study to extend

existing published data for the solubility of various gases in oils used


CD■DOQ.CgQ.

■DCD

C/)C/)

DRILLED GAS IN W ATER-BASED MUDS

8■D

CD

3.3"CD

CD■DOQ.CaO3"Oo

CDQ.

■DCD

Mud In

Ir-q

i-

Mud In

\

X D

Gas Send

0 Drilled Gas Enters Well as Bubbles and Migrates up Wsllbore«

Gos Sond

0 Drilled Gae Concentration Substantially Reduced by Bubble Migration.

(D L ittle or No Bottom Hole Pressure Rsduetlsn*

C/)(/)

Figure 1.3 - Drilled-Gas Contamination of Water-Based Drilling Fluids.os

CD"OOQ.CsQ.

"OCDC/)o'3O

8"O(O'

3.3"CD

O"OOQ.CaO3■DO

CDQ.

■DCD(/)(/)

Mud In

t

DRILLED GAS IN O IL-B ASED MUDS

Mud In

1Mud in

i

Gas Sand

0 Drilled Gaa Enters Well and Dissolves Into Oil Mud.

Gas Sand

No Migration.

rc%

*v *

Gas Sand

0 Violant Gao Expanolon noar Surfaea* 0 Bottomhole Prooouro Rodvctlonf

Figure 1.4 - Drilled-Gas Contamination of Oil-Based Drilling Fluids.

in oil-based drilling fluid preparation and an oil-based drilling fluid.

This data will be used to develop models that will allow the expected

well behavior to be predicted when gas contaminates an oil-based

drilling fluid during the drilling process. Models developed will focus

on gas kick detection in oil-based drilling fluids as well as the

effects of drilled-gas dissolved in oil-based drilling fluids on well

behavior.


CHAPTER II

LITERATURE REVIEW

In 1981, O'Brien first reported the results of a study of well

control problems caused by gas solubility in oil-based drilling fluids.

Although the author made no experimental measurements, he concluded that

at the same pressure and temperature, the solubility of gas in an

oil-based drilling fluid would be 10 to 100 times greater than the

solubility in water-based fluids.

O'Brien also stated that the use of a drilling fluid-gas separator

at the surface where any dissolved gas in an oil-based drilling fluid

could be removed from the drilling fluid would reduce the hazard of any

gas being released on the drilling rig floor. No design criteria as to

the size of the separator required was presented.

In 1984, Thomas, Lea, and Turek presented nine experimentally

measured data points for methane solubility in No. 2 Diesel oil and

three for methane solubility in an unweighted oil-based drilling fluid

all at 100°F. The units used to express gas solubility are standard

cubic feet (SCF) per surface barrel (STB). A summary of the data

presented by the authors is shown in Tables 2.1 and 2.2. In this study

it was shown that methane solubility in the oil-based drilling fluid was

less than the solubility of methane in pure No. 2 Diesel oil. It was

stated that this difference in methane solubilities in the two liquids

was caused by the presence of brine, emulsifier, and solids in the

drilling fluid. Also presented were curves from computer predictions

using the Redlich-Kwong equation of state for methane solubility in No.

2 Diesel oil over a range of temperatures (i.e., 100 to 600°F). These


10

Table 2.1 - Methane Solubility in No. 2 Diesel Oil at T = 100°F (Thomas, Lea, and Turek)

Pressure, psia Methane Solubility, SCF/STB

805 1261000 1691682 2802065 3442405 4273635 6384820 8505790 1066

Table 2.2 - Methane Solubility in Unweighted Oil-Based Drilling Fluid at T = 100°F (Thomas, Lea, and Turek)

Pressure, psia Methane Solubility, SCF/STB

1555 1672570 3353585 502

Composition of oil-based drilling fluid used:Component Weight Percent

No. 2 Diesel Oil 51.31Calcium-Based Surfactant 2.17Lignite 2.61Slaked Lime 2.61Burite 10.17Kengel (Oil-wetting Bentonite) 0.52NaCl Saturated Brine 30.61

Z = 100.00

Density of oil-based drilling fluid at 14.7 psia and 78°F = 1.0985 gm/cm^.


11

curves are shown in Figure 2.1. No experimental data was presented

pertaining to the swelling of the base oil or drilling fluid due to the

dissolved methane.

In addition, Thomas, Lea, and Turek addressed the surface responses

(i.e., annular flow rate and pit gain) due to a gas kick taken while

drilling with an oil-based drilling fluid. They did this study with the

aid of a proprietary computer model and concluded that pit gain was the

most reliable indicator of a gas kick m both oil- and water-based

drilling fluids. It is interesting to note that to predict the swelling

of the oil-based drilling fluid due to dissolved gas, the authors used

the Standing correlation which was developed for gas dissolved in

California crude oils.

In a follow-up paper, Thomas and Lea provided further computer

simulation studies for gas kicks taken in both oil- and water-based

drilling fluids. They stated that the well response to a gas kick in an

oil-based drilling fluid is dampened by the solubility of gas in the

drilling fluid. The authors recommended that a consistent procedure for

kick detection based on pit gain measurements be developed.

In 1984, Matthews presented solubility curves for methane, carbon

dioxide, and hydrogen sulfide in No. 2 Diesel oil at 250° F. For

equivalent volumes of the three gases in a mixture at some temperature,

the author concluded that as pressure is decreased, methane would come

out of solution first followed by carbon dioxide and then hydrogen

sulfide. This is to say that hydrogen sulfide is the most soluble gas

of the three gases studied with methane being the least soluble in No. 2

diesel oil. The curves presented in this work are shown in Figure 2.2.


12

10

8 -

10PRESSURE (MPa)

20 30 40TT - r T

CVICD lOCO lO

B BIL ILo 0o oo o(0 in

îc09r:N

IOCNÎ

50 60T Tiq o>g 2ro lO

ÜJ O

1.81.6

5.4

1.2

I0.80.60 .4

0.2

W

§ = !ë °to -Jë S

w Ul s o

ro ro E Ed 0: H y en û-

2 0 0 0 4 0 0 0 6 0 0 0PRESSURE (psic)

8 0 0 0

Figure 2.1 - Methane Solubility In No. 2 Diesel Oil (Thomas, Lea, and Turek).


13

PRESSURE (MPa) 20 30 5040

T = 250*F (l2rC)

üJ _l _ILÜ men3 ü J

CMCM

O

0.8 (j) omm 0.6

0.4

0.2

2000 4000 6000PRESSURE (psia)

8000

Figure 2.2 - Carbon Dioxide, Hydrogen Sulfide, and Methane Solubility In No. 2 Diesel Oil (Matthews).


14

Matthews also presented simplified curves for estimating the depth

at which methane, carbon dioxide, and hydrogen sulfide would break out

of solution for various drilling fluid weights. He also advocated the

use of a rotating head to divert gas contaminated drilling fluid from

the rig floor to a drilling fluid-gas separator although no design

criteria was presented.

In 1985, Ekrann and Rommetveit presented an outline for a simulator

for gas kicks in oil-based drilling fluids. Their work dealt primarily

with the numerical solution techniques used in their model and no

results pertaining to the effects of gas solubility in oil-based

drilling fluids on drilling operations were reported.


CHAPTER III

AN EXPERIMENTAL AND THEORETICAL STÜDY OF METHANE SOLUBILITY IN On.-BASED DRILLING FLUIDS

The author’s research work in the area of well control problems

associated with gas solubility in oil-based drilling fluids began during

the course of completing requirements for the Master of Science Degree

in Petroleum Engineering. This chapter summarizes that work.

3.1 Purpose of Study

The purpose of this study was to extend the existing data

pertaining to methane solubility in oil-based drilling fluids to a wider

range of pressures and temperatures and base oils used in oil-based

drilling fluid preparation than previously presented. More data about

methane solubility in oil-based drilling fluids was desired because it

is the most common gas encountered in the field.

In addition, it vas desired to apply an equation of state to

predict methane solubility in a specified oil-based drilling fluid at a

given pressure and temperature as well as the density of the oil-based

drilling fluid with dissolved methane. The ability to accurately

predict the solubility of methane in oil-based drilling fluids and the

resulting densities would allow models to be developed for predicting

the well behavior to be expected when methane contaminates an oil-based

drilling fluid during drilling.

3.2 Experimental Apparatus and Procedure

The base oils chosen for use in this study were No. 2 Diesel,

Mentor 28, and Conoco LVT oils. The composition of these three oils is

15


16

shown in Table 3.1. The composition shown for No. 2 Disel oil was

reported by Thomas, Lea, and Turek while the compositions for the Mentor

28 and Conoco LVT oils were obtained from chromatographic analysis. In

addition to the base oils, methane solubility was measured in an

emulsifier used in rll-based drilling fluid preparation and a 13

pound-per-gallon (Ibm/gal) oil-based drilling fluid having a composition

as shown in Tahle 3.2

To measure the solubility of methane in the base oils, emulsifier,

and oil-based drilling fluid, an experimental apparatus was constructed.

Figure 3.1 shows a diagram of the experimental apparatus used. The

system has a 250 cm^ positive displacement pump used to displace mercury

into a blind pressure-volume-temperature (PVT) cell. Mercury is used

for pressurizing the mixture being studied. Pressure is monitored using

a 10,000 psi bourdon tube gauge. The PVT cell is heated with a heating

mantle and heat losses to the atmosphere are minimized by the addition

of extra insulation. The temperature of the system is monitored using a

digital thermometer with a platinum resistance probe placed between the

PVT cell and heating mantle. The PVT cell is mounted on a stand that

allows rotation of the cell during experiments which facilitates

mechanical mixing of the fluids being studied.

After each experiment, a commercial computer model was then used to

calibrate the raw experimental data. The model takes into account the

expansion and compressibility of the PVT cell, pump manifold, and

mercury due to changes in temperature and pressure. The calibrated data

was then plotted as pressure versus volume as shown in Figure 3.2. The

break in the isotherm indicates the bubble point pressure of the


17

Table 3.1 - Base Oil Molar Compositions

Mole PercentCarbon Number

8 9

10

11

12

13

14

15

16

17

18

19

20 21

22

23

24

Z =

No. 2 Diesel

0.22 0.88 3.79

10.68

13.45

13.73

16.01

15.18

9.10

8.53

4.19

2.40

1.16

0.42

0.12 0.11

+ 0.03

100.00

Mentor 28

1.4187

2.2240

6.0817

10.6920

9.4953

31.8370

28.1870

+ 10.0710

Conoco LVT

1.1736

11.2037

24.1092

16.5396

11.8951

17.6742

15.2455

1.4253

+ 0.7333

100.0000 100.0000

Molecular Weight (Ib/lb-mole)

Density @ 60°F (Ibm/gal)

199.0

6.932

252.0

7.117

177.4


18

Table 3.2 - Composition of 13 Ibm/gal Oil—Based Drilling Fluid (Salisbury)

Component Volume, cc Weight, gm

Mentor 28 225 -

Lime — 4.5

Primary Emulsifier 12 -

Filtration Agent - 5

Water 50 -

Gelling Agent - 4.5

Secondary Emulsifier 6 -

Calcium Chloride - 23

Barite - 292


CD"OOQ .CgQ.

"OCD

C/)C/)

8"O

CD

3.3"CD

CD"OOQ.CaO3"OO

CDQ.

"OCD

BURRET

SAMPLEBOTTLES

TEMPERATURE CONTROLLER- + PROBE HIGH

PRESSUREBOTTLESPVT CELL

VACUUMPUMP

MERCURY PUMP

C/)C/)

Figure 3.1 - Experimental Apparatus.

20

2500

2000

COo

s. 1500LÜ(T3COCOLÜg 1000

rm

0 ^

BUBBLE ^ “ POINT PRESSUR500

300 400 500 600SAMPLE VOLUME, cc

Figure 3.2 - Sample Experimental Pressure Versus Volume Plot.


CD"OOQ.CgQ.

"OCD

</)C/)

CD

8"O( O '

CD"OOQ.CaO3"OO

CDQ.

"OCD

(/)(/)

5 1200 jO S.t>*

600

CD 400 3O(/)

wz<XHLÜS

200 -

1000 -O-JUJwWS 800 -aCM6zz

>-

Pressurepsia Thomos et. ol.CurrentStudy

720 130605 126 -

1000 169 -

1220 - 2331475 - 2581682 280 .

2065 3442405 427 -

2545 4673635 6383795 - 6954080 - 8214820 850 -

5790 1066 -

□ Currant Study O Thomos et.ol. T= lOO'F

1000 50002000 3000 4000PRESSURE, psia

Figure 3.3 - Experimental Procedure Verification.

6000

N>

22

500 Pressurepsia

Temperature Methane Solubility degree F s c f/b b i

j O

S 400

COOJ

trO 300 -

LÜs

*-_i 200m3Ow

LÜZ<XI -LÜ

775 100 1261200 100 1901985 too 3172315 100 3712825 too 4 4 3

670 200 851340 200 1751950 200 2652325 2 00 3212660 2 00 377

980 300 1121315 300 1551780 3 00 2132190 300 2732670 300 341

D T = ! 00®FO T = 2 0 0 ‘»FA T =300®F

100 -

1000 2000 PRESSURE , psiG

3 0 0 0

Figure 3.4 - Methane Solubility In Mentor 28 Oil.


23

400 r Pressure Temperature Methane Sal.psia degree F set/bbl

.o 900 100 83JO I8 6 0 100 188

2 8 0 0 100 315

u 770 200 73(0 1725 2 0 0 159

3215 2 0 0 315Œ 300 7 5 0 3 0 0 63UJ 1745 3 0 0 159ÛZ 3 2 0 0 3 0 0 267

CO D T= IOO®FO 7= 2 00® F

3 A T = 3 0 0 « F

UJ

2 200>K

ffi3w 100wz<UJ

1000 2000PRESSURE, psia

3000 4000

Figure 3.5 - Methane Solubility In Emulsifier.


24

600 r Pressure Temperature psio degree F

Methane Sol. scf/bbi

500 -jb

o <0O 3sd 400 o

1360 100 1583250 100 3794575 100 5441660 200 1562595 200 2684160 200 4032660 300 2 6 03325 300 3004700 30 0 396

O T = IOO*F0 T = 2 0 0 “ F6 T =300°F

lO

>I -

CD3_lO(0UJz<XI -w

300 -

200 -

<00 -

1000 2 00 0 3000P R E S S U R E , psio

4000 5000

Figure 3.6 - Methane Solubility In 13 Ibm/gal Oil-Based Drilling Fluid.


25

500 r

400

tu 200

UJ

o MENTOR 28 OIL O 300.000 PPM BRINE A EMULSIFIER

100

40003000200010000P R E S S U R E , psio

Figure 3.7 - Methane Solubility In Mentor 28 Oil, Emulsifier, and Brine (T = 100°F).


26

500

400

300

aa

oz>I -

CO3_l 200LÜZ<I►-111z

100

METHANE SOLUBILITY, SCF/bbl Pressure No. 2 Diesel Conoco Mentor 28

psio LVT

395 720 775 875 1200 1220

1345 1475 1985

2 0 8 0 2315 2545 2825

□ MENTOR 28 OIL O DIESEL OIL A CONOCO LVT OIL

233

258

67 -

126166 —

- 190

258 -

3174 5 3 —

- 371

443

1000 2000 PRESSURE, psio

3000J

4000

Figure 3.8 - Methane Solubility In No. 2 Diesel, Mentor 28, and Conoco LVT Base Oils (T = 100°F).


27

mixture. Above the bubble point the mixture is all liquid and below the

bubble point the mixture is both gas and liquid.

Figure 3.3 shows a plot of methane solubility in No. 2 Diesel oil

versus pressure at 100°F for data obtained using the experimental

apparatus and procedures described previously and data published by

Thomas, Lea, and Turek. Note tht both sets of data lay along the same

trend indicating that the experimental procedures of the current study

were correct.

3.3 Experimental Results

Figures 3.4-3.6 summarize the solubility data obtained for methane

dissolved in Mentor 28 oil, emulsifier, and the 13 Ibm/gal oil-based

drilling fluid at 100, 200, and 300°F. Notice that in all figures,

methane solubility in the experimental liquid decreases with increasing

temperature for the range of pressures studied. Also notice that at a

given pressure and temperature, methane is more soluble in the Mentor 28

oil than in the emulsifier and 13 Ibm/gal oil-based drilling fluid.

Figure 3.7 shows a plot of methane solubility in Mentor 28 oil,

emulsifier, and brine which are the only components of an oil-based

drilling fluid in which a gas can dissolve. The solubility of methane

in brine was determined from correlations presented by McCain. Notice

that methane is the most soluble in the Mentor 28 oil followed by

emulsifier and brine. It was concluded, as it was in the study of

Thomas, Lea, and Turek, that brine, emulsifier, and solids in the

drilling fluid reduce the solubility of methane in the drilling fluid by

diluting the base oil volume in a give volume of drilling fluid.


28

Figure 3.8 shows the solubility of methane in the three base oils

studied at 100°F. Notice that at methane concentrations less than about

200 SCF/STB, methane solubility is not greatly effected by the base oil

type. However at methane concentrations greater than 200 SCF/STB, the

solubility of methane in the base oil is strongly effected by base oil

type.

3.4 Equation of State Modeling

It was shown in this study that methane solubility in an oil-based

drilling fluid is controlled by the volume fractions of base oil, brine,

and emulsifier in the drilling fluid. However, since the volume of

emulsifier in a drilling fluid is small and its volume fraction in the

drilling fluid difficult to determine, it can be neglected for the

purposes of calculating the solubility of methane in an oil-based

drilling fluid.

The solubility of methane in an oil-based drilling fluid can

accurately be determined at a given pressure and temperature by,

R = f R + f R .............................(3.1)sm o so w swwhere R is the solubility of methane in the drilling fluid, basesm,o,woil, and water in SCF/STB and f is the volume fraction of oil ando,wwater in the drilling fluid.

The Peng-Robinson equation of state (PREOS) was used to predict the

solubility of methane in the base oil Table 3.3 shows a comparison of

experimentally measured and predicted methane solubilities in Mentor 28

base oil at 100, 200, and 300®F. The solubility of methane in water was

determined from correlations presented by McCain.


29

Table 3.3 - Experimentally Measured Versus PREOS Predicted Methane Solubility in Mentor 28 Oil

Methane Solubility, SCF/STB Pressure, psia T = 100 F 200 F 300 F

775 126 (114)1200 190 (184)1985 317 (329)2315 371 (397)2825 443 (510)670 - 85 (78)1340 - 175 (167)1950 - 265 (260)2325 - 321 (324)2660 - 377 (386)980 - - 112 (107)1315 - - 155 (150)1780 - - 213 (214)2190 - - 273 (278)2670 - - 341 (363)

( ) - PREOS Predicted Methane Solubility


30

Table 3.4 shows a comparison of experimentally measured and

predicted methane solubilities in the 13 Ibm/gal oil-based drilling

fluid used in this study.

The PREOS was also used to predict the density of methane/oil-based

drilling fluid mixtures. Figure 3.9 shows a comparison of

experimentally measured versus predicted single— and two-phase densities

for a mixture of 379 SCF of methane and one STB of 13 Ibm/gal oil-based

drilling fluid. Notice that the PREOS predicts densities less than

those experimentally measured. This is commonly reported in the

literature when the PREOS is used.


31

TABLE 3.4 — Experimentally Measured Versus PREOS Predicted Methane Solubility in 13 Ibm/gal Oil-based Drilling Fluid

Methane Solubility, SCF/STB Pressure, psia T = 100°F 200°F 300°F

1360 158 (138)

3250 379 (398)

4575 544 (666)

1660 - 156 (140)

2595 - 258 (243)

4160 - 403 (485)

2660 - - 206 (234)

3325 - - 300 (325)

( ) - PREOS Predicted Methane Solubility


I32

6 0 0 0

5 0 0 0

4 0 0 0

<AO.w(r3COU)wccCL

3 0 0 0 -

2000

1000

3 79 SCF Methane/bbI Oil Mud = 13 lb/go!

T = IOO®F * — Bubble Point □ — Experimentol A — Computer Predicted ^ .

_L _L9 II

DENSITY, Ib/gol13

Figure 3.9 - Pressure Versus Density For Methane/13-lbm/gal Oil-Based Drilling Fluid Mixture.

rReproduced with permission of the copyright owner. Further reproduction prohibited without permission.

CHAPTER IV

The ultimate goal of this work is to study the effects of gas

solubility in oil-based drilling fluids on the drilling process.

Although methane is the most common gas encountered during drilling it

is not the only gas present. Further data is needed for the solubility

of other gases in base oils and oil-based drilling fluids before

definitve conclusions can be made. In this chapter, a summary of

additional measurements of the solubility of ethane, carbon dioxide, and

a natural gas mixture in Mentor 28 oil and a 13 Ibm/gal oil-based

drilling fluid will be presented.

4.1 Experimental Apparatus and Procedure

As mentioned previously, the base oil used was Mentor 28 oil. The

13 Ibm/gal oil-based drilling fluid had a composition as shown in Table

3.2. The composition of the natural gas used is shown in Table 4.1.

Measurements of gas solubility in the base oil and drilling fluid

were made at 100, 200, and 300°F using the apparatus and procedures

outlined in Chapter III.

4.2 Experimental Results

Figures 4.1-4.6 summarize the data obtained from these gas

solubility experiments. Notice that in all of the figures, as

pressure is increased the solubility of the gas in the oil and drilling

33


34

Table 4.1 - Natural Gas Composition

Component Mole Percent

Nitrogen 0.28

Carbon Dioxide 0.89

Methane 90.18

Ethane 4.84

Propane 2.05

i-Butane 0.49

n-Butane 0.53

i-Pentane 0.23

n-Pentane 0.15

Hexanes 0.14

Heptanes + 0.22

Z = 100.00

Natural Gas Specific Gravity = 0.62


35

6 0 0 r

Pressure Temperature Ethane Sol. psia degree F scf/bbi2 40 100 121360 100 2474 50 100 3 6 8575 100 5 0 56 10 100 681

2 05 200 794 5 0 2 00 1546 5 0 2 0 0 2357 0 0 2 0 0 331

1050 2 0 0 443

290 300 1037 3 0 300 154840 3 00 2 66

1055 300 3551180 3 0 0 4 3 3

-2 r = too®O T = 2 0 0 "A T = 300®

5 0 0 1000

PRESSURE, psIa1500

Figure 4.1 - Ethane Solubility In Mentor 28 Base Oil.


36

300 rjaJO

o(A

O3S

O 2 00 -ocr

fO

100 -

m

ocoUJ

<XHLÜ

Pressuri Ttmptrature Ethane Soi.psio degree F sef/bbi2 0 9 100 8 63 7 0 100 1755 5 5 100 2 8 3

2 4 3 2 0 0 754 0 3 2 0 0 1395 5 9 2 0 0 207

169 3 0 0 36362 3 0 0 85621 3 0 0 144

O T = IO O * F O T = 2 0 0 *F A T = 3 0 0 * F

5 0 0 1000

PRESSURE , psia1500

Figure 4.2 - Ethane Solubility In 13 Ibm/gal Oil-Based Drilling Fluid.


37

3000r Pressure Temperature Carbon Dioxide Sol.

- 2500

CO CMg 2000gzUJs

psio degree F s c f / l725 100 3 6 7

1030 100 7 8 91140 100 12971200 100 17941295 100 2839

270 200 1067 7 0 2 0 0 2 60

1080 2 00 4 2 51240 2 0 0 5 4 01420 200 7056 00 300 141

1140 3 0 0 3 031400 300 418I8 6 0 3 0 0 5 0 91910 3 0 0 659

c T = IOO»Fo T = 2 0 0 “ F4 T = 300®F

m3_JOC/5

1500 -

O 1000 §

Om(T<Ü 500 -

500 1000PRESSURE , psia

1500 2000

Figure 4.3 - Carbon Dioxide Solubility In Mentor 28 Base Oil.


38

400 r Pressure Tëmperefure Corbon Dioxide psia degree F Sol.,scf/bbl

aao(A

O3z-I 300 -

260 too 61585 100 162700 100 219430 200 68900 200 15 1

1100 200 245590 300 84900 300 139

1400 300 379

O T= IOO®FO T= 200 °FA T = 300°F

200 ->i—

003_jOWUJO 100Xo

zomoc<u

1000 2000 PRESSURE, psia

3000

Figure 4.4 - Carbon Dioxide Solubility In 13 Ibm/gal Oil-Based Drilling Fluid.


39

_ 800 A

o(0

Pressure Temperoture Noturol Gas Sol. psio degree F s c f/b b i

600 -O00CM

(rezUJ

— 400 >-

CD

3oCO

CO<CO

6 2 5 100 1161040 100 1881775 100 3092 7 5 0 100 4 9 737 1 0 100 698

810 200 1281440 200 2051990 200 3032500 200 4 3 33475 20 0 616

8 0 0 300 9 31580 300 1972310 3 0 0 3163 030 300 4613 8 0 0 30 0 6 3 2

D T = IOO»F0 T = 2 0 0 ° F4 T = 3 0 0 ° F

200

<a:3

1000 2000PRESSURE . psia

3000 4000

Figure 4.5 - Natural Gas Mixture Solubility In Mentor 28 Base Oil.


40

_ 4 0 0 r

o(A

O32UO"5

2ro

PressurepsioI I I O

2080 3115

Temperature degree F

100100!00

Noturol Gos Sol scf/bbl

3 0 0 -

1090 2001900 2002 6 0 0 200

1025 3001800 3002735 300

O T = :00»F o T = 200"F A T = 3 0 0 "F

Z 2 0 0 -

>-H_iCO3_jOV)CO<o

<oc3

1000 2000 PRESSURE, psio

3 0 0 0 4 0 0 0

Figure 4.6 - Natural Gas Mixture Solubility In 13 Ibm/gal Oil-Based Drilling Fluid.


41

fluid increases and as temperature is increased gas solubility decreases

at constant pressure.

Figure 4.7 shows a plot of gas solubility versus pressure for

methane, ethane, carbon dioxide, and the natural gas mixture dissolved

in Mentor 28 oil at 100*F. Notice that ethane is the most soluble while

methane is the least soluble in the base oil of the four gases. For

hydrocarbon gases the solubility of the gas increases with increasing

gas specific gravity. It can further be concluded that for a mixture of

equal parts of methane, ethane, and carbon dioxide dissolved in the base

oil at constant temperature, as the pressure is decreased, methane would

break out of solution first followed by carbon dioxide, and then ethane.

4.3 Solubility of Other Gases

From the results of the solubility experiments, it was concluded

that it would not be practical to measure the solubility of hydrocarbon

gases heavier than ethane (i.e., propane, n-butane, etc.) in base oil

and drilling fluid. This is because ethane is very soluble in base oils

and drilling fluids, and as previously shown an increase in hydrocarbon

specific gravity increases gas solubility at constant pressure and

temperature.

For most conditions existing in a wellbore, hydrocarbon gases

heavier than ethane will not breakout of solution, if at all, until the

gas contaminated drilling fluid has reached the surface. It can

therefore be reasonably assumed that the effects of hydrocarbon gases

heavier than ethane, in terms of existing in the well as a free gas

phase, is negligible and these gases can be assumed to exist as solution

gas.


42

800r

u(0_ J

GO

ITO&—ZbJZ 400 z

CD 3 200 C| (SPGR=.55)

N GAS(SPGR*.64) 02 (SPGR=I.058Î CO2 (SPGR= 1.518)

OV)CO<CD

40003000200010000PRESSURE, psio

Figure 4.7 - Gas Solubility In Mentor 28 Base Oil (T = 100“F).


43

Hydrogen sulfide solubility was not measured due to the high

toxicity of this gas. However, it is recommended that this gas be

studied, if the proper facilities are available, because this gas is

common in deep hot well.


CHAPTER V

GAS SOLUBIILTY APPROXIMATION

In Chapter III an equation of state model was outlined for

predicting the solubility of methane in an oil-based drilling fluid.

However, considerable computer time (1 computer processing unit minute

per 11 data points) is required to solve for methane solubility in a

drilling fluid at a given pressure and temperature. Any increase in the

number of components in the gas to be mixed with the oil-based drilling

fluid will increase the ratio of computer-time-required-to-solve-for-

the-gas-solubility-to-number-of-data-points. As pointed out previously,

it is the obj ective of this study to determine the effects of gas

contamination of an oil-based drilling fluid on the drilling process.

To satisfy this objective, a model requiring the calculation of the

solubility of a gas in an oil-based drilling fluid quickly and

accurately will be needed. Also, a method for predicting gas solubility

in an oil-based drilling fluid which is easy to use yet accurate will

aid in the training of field personnel as to how much gas could go into

solution for given well conditions.

It is the purpose of this chapter to summarize a method for

approximating the solubility of a gas mixture containing methane,

ethane, and carbon dioxide in an oil-based drilling fluid. The method

will allow quick, direct calculations of the solubility of a gas mixture

containing these components in an oil drilling fluid based on

experimental observations.

44


45

5.1 Solubility of Gas in Base Oil

From the results of the experimental studies previously discussed,

the following empirical equation for predicting the solubility of

methane, ethane, and carbon dioxide in a base oil was developed,

+ cl' « • »

where is the gas solubility in the base oil in SCF/STB, P is the

pressure in psia, T the temperature in °F, and a, b, c, and n constants

determined from Table 5.1.

Equation 5.1 also takes into account the variations of methane

solubility in base oil due. to base oil composition which was pointed out

in Chapter III. The trend observed for variations of methane solubility

in base oils of differing composition was used in accounting for

variations of ethane solubility in different base oil types since both

methane and ethane are hydrocarbon gases and no data existed for ethane

solubility in different base oils. No adjustment of carbon dioxide

solubility variation due to base oil composition was made since no such

data was generated and carbon dioxide is not a hydrocarbon gas.

Equation 5.1 is valid for carbon dioxide solubility in Mentor 28 base

oil only.

It should be pointed out that the inverse proportionality of

methane solubility to temperature is based on experimental observations

made over the range of pressures and temperatures studied. However,

the curves of Figure 2.1 presented by Thomas, Lea, and Turek indicate

that at high pressures this observation reverses and methane solubility

increases with increasing temperature. This behavior is calculated at

pressures near and above the cricondenbar in the single phase region


46

Table 5.1 - Empirical Correlation Constants.

Gas Type a b c______________________ n________Methane 1.922 0.2552 4.94 e(-00081P+.00177T) q .8922 y

o-.7521Ethane 0.033 0.8041 0 0.8878 y^

Dioxide 0.059 0.7134 0.3352e^’°^°^^“'°^^^'^ 1.0

where, T = temperature, “F

P = pressure, psia

y^ = base oil specific gravity


47

where methane and oil are miscible in all proportions. Equation 5.1

takes this phenomena into account.

To calculate the solubility of a gas mixture containing methane,

ethane, and carbon dioxide in a base oil, in SCF/STB, the following

equation is used,

so " ^sCg^Cg ^sCOg^COg.............

where f is the volume fraction of methane (Cj), ethane (Cg), and carbon

dioxide (COg) in the gas mixture and R^ for each gas component is

determined by equation 5.1.

5.2 Solubility of Gas in Water

For most cases, the solubility of gas in the internal water phase

of an oil-based drilling fluid can be neglected because of the small

contribution made to the overall solubility of a gas in the drilling

fluid. However, if it is desired to account for gas solubility in the

water phase, R ^ in SCF/STB, it can be calculated as,

^sw " \Cj^Cj ^sCg^Cg ^sC02^C02............

where f is the volume fraction of methane (C^), ethane (Cg) and carbon

dioxide (COg) in the gas mixture and R^ the solubility of each component

in water determined from Figures 5.1 and 5.2, and corrected for water

salinity using Figures 5,3 and 5.4. For convenience these figures have

been fitted to equations shown in Table 5.2.

A correlation of ethane solubility in water was not found in the

literature and since the solubility of a hydrocarbon gas in water is

small, it is assumed that the solubilities of methane and ethane in

water are equivalent.


48

teLJ 64

56UJ

48

-X

24U.

- 1,000

- 600- r 200 r

O 60 ICO 140 180 220 260 300 340TEMPERATURE (*F )

Figure 5.1 - Methane Solubility In Pure Water (McCain).


!(D

IOOZ;I

f5

awf,ord. et.

«sV)

50

UJZq:es

CO<o_J<(TIDH<l l

O

OS3OCO

w 1.00Q90 -0.80 -

0.70 -

020 -

O 0.15 CO 0 10 20 30TOTAL DISSOLVED SOLIDS (%)

Figure 5.3 - Water Salinity Correction For Methane Solubility In Water (McCain).


51

I O r

0.9

35,000 PPM

100,000 PPM

% 0.7

0.6

Uioc 0 5

2 0 0 ,0 0 0 PPM

0.4

0.370005 0 0 0 6 0 0 01000 2 0 0 0 3 0 0 0 4 0 0 0

PRESSURE, psio

Figure 5.4 - Water Salinity Correction For Carbon Dioxide Solubility In Water (Crawford, et. al.).


52

Table 5.2 - Gas Solubility In Water Curve Fits.

Carbon Dioxide:2 3Rsco = (A + BP + CP + DP ) X Salinity Correction

A = 95.08 - .931 + 2.28E - 03T^

B = 0.1626 - 4.025E - 04T + 2.5E - 07T^

C = -2.62E - 05 - 5.39E - 08T + 5.13E - lOT^

D = 1.39E - 09 + 5.94E - 12T - 3.61E - 141^

Salinity Correction = .92 - .0229 % Solids

Hydrocarbon Gas:

^sHC ~ (A + BT + CT^) X Salinity Correction

A = 5.5601 + 8.49E - 03P - 3.06E - 07P^

B = -0.03484 - 4.0E - 05P

C = 6.0E - 05 + 1.5102E - 07P

Salinity Correction = EXP[(-.06 + 6.69E - 05T)

X (% Solids)]

where, P = pressure, psia

T = temperature, ®F


53

P

5.3 Solubility of Gas in Oil-Based Drilling Fluids

For a given drilling fluid volume, the relative volumes of base oil

and water in the drilling fluid can be determined from a standard retort

analysis. Once the volume fractions of and the solubility of the gas in

the oil and water in the drilling fluid are known, the solubility of a

gas in the oil-based drilling fluid can be determined by Equation 3.1.

5.4 Experimental Verification of the Correlation

Using an iterative calculation procedure, the bubble point

pressures of the natural gas/13-lbm/gal oil-based drilling fluid mixture

studied in Chapter IV were predicted using the equations developed in

this chapter. The predicted bubble point pressures were compared with

the experimentally measured bubble point pressures. The results are

shown in Table 5.3. An average error of -0.5% was obtained indicating

good agreement between the predicted and measured bubble point pressures

for the data compared.


54

Table 5.3 - Experimentally Measured Versus Predicted Bubble Point Pressure For Natural Gas/13-lbm/gal Oil-Based Drilling Fluid.

Natural Gas Bubble Point Pressure, psiaSolubility, SCF/STB T, °F Measured Predicted Error, %

125 100 1110 1105 - .45248 100 2080 2187 +5.14346 100 3115 2968 -4.72

102 200 1090 1037 —4.86190 200 1900 1933 +1.74282 200 2600 2771 +6.58

84 300 1025 906 -13.13172 300 1800 1866 +3.67268 300 2735 2773 +1.39

Average % Error = -0.5


CHAPTER VI

GAS MISCIBILITY

In this chapter the concept of gas miscibility will be introduced

as it relates to the behavior of a gas kick taken while drilling with an

oil-based drilling fluid under certain well conditions. Although the

conclusions of this chapter are not based on the experimental

observations of this study, they will provide a basis from which further

studies into this complex phase behavior phenomena can be extrapolated.

For the purposes of this discussion methane and No. 2 Diesel oil will be

considered since published data in the miscible region exists for this

mixture.

6.1 First Contact Miscibility

Stalkup defines a fluid that is "first contact miscible" as being a

fluid that will mix directly with an oil in all proportions and that

their mixtures will remain single phase. For this to occur, the fluid

and oil mixture must be exposed to pressures above the cricondenbar, as

determined from a Pressure-Composition (P-X) diagram for the fluid and

oil mixture (Figure 6.1). Methane is a gas that is first contact

miscible with an oil.

6.2 Methane Miscibility with No. 2 Diesel Oil

From Figure 2.1, the miscibility pressure as a function of

temperature can be determined for methane and No. 2 Diesel oil. The

miscibility pressure is represented by the pressure at which the curves

of Figure 2.1 become vertical indicating infinite methane solubility in

55 ■


56

(OQ.

UJa:3COcoLUû:CL

Gos Miscible in Ail Proportions with Oil Cricondenbar

Pressure

Single- Phose Region

Ploit^ Point

Tw o-Phose Envelope

MOLE FRACTION OF GAS IN GAS-OIL MIXTURE

Figure 6.1 - Pressure-Composition Diagram.


57

No. 2 Diesel oil. Figure 6.2 shows a plot of miscibility pressure

versus temperature for this mixture as determined from Figure 2.1.

A better understanding of this phenomena as it relates to the

wellbore can be obtained from Figure 6.3 which shows the locus of

cricondenbars for a mixture of methane and No. 2 Diesel oil. If a

methane kick enters the wellbore at point (P^, T^), the methane will

exist as a gas and dissolve into a diesel oil-based drilling fluid.

However, if a methane kick enters the wellbore at point (P,, T^), the

methane will exist as a miscible fluid because the mixture is above the

cricondenbar pressure and will mix in all proportions with the drilling

fluid.

Figure 6.4 represents the pit gain to be expected per thousand

standard cubic feet (MSCF) of a methane kick versus depth for a well

having a depth of 15,000 feet. The drilling fluid is a 15.5 Ibm/gal,

diesel oil-based drilling fluid having an oil-water ratio of 80:20. A

comparison is made between the oil-based drilling fluid and a

water-based one. Point A represents the transition from a miscible

fluid to a gas for the oil-based drilling fluid case. Notice that at

depths greater than 10,000 feet the pit gain resulting from the methane

kick in the oil-based drilling fluid is essentially the same as a

methane kick in a water-based drilling fluid when little or no natural

mixing takes place. However, at depths less than 10,000 feet the

methane will go into solution and the pit gain in the oil-based drilling

fluid case is less than the water-based drilling fluid. If the methane

mixed with the oil-based drilling fluid to give a gas-drilling fluid

ratio of 1000 SCF/STB, the methane would break out of solution at point


58

I0 0 0 0 r

UJ 8000

6000

O 4000

2000

300 400 500TEMPERATURE, *F

600

Figure 6.2 - Methane/No. 2 Diesel Oil Miscibility Pressures Versus Temperature.


59

Locus of Cricondenbors * Critical Points10000r

8 0 0 0

Q. 6 0 0 0

W 4 0 0 0

2000

NO. 2 Diesel Oil^^y/^Nethone800200 4 0 0 6 0 00-200

TE M P E R A TU R E . »F

Figure 6.3 - Locus of Cricondenbars For Methane and No. 2 Diesel Oil.


CD■DOQ .CgQ .

’f

■DCD

C/)C/)

8■D

3.3"CD

CD■DOQ .CaO3"Oo

CDQ .

■DCD

C/)C/)

PIT GAIN PER MSCF OF METHANE KICK VOLUME, BBL

1 2 3 4

5000 -

XHO.uo

CIRCULATING TEMPERATURE,®F 0 100 200

10,000 -

OIL-BASED MUD WATER-BASED MUD

KICK SIZE : 1000 SCF ® 15.5 LB/GAL

♦ b a s e o il » No. 2 DIESEL OIL-WATER RATIO « 8 0 : 20 3 0 0 ,0 0 0 ppm CoClg BRINE

15,000*-

Figure 6.4 - Pit Gain Per 1000 SCF Methane Kick In Oil- and Water-Based Drilling Fluids. ONO

61

B. If on the other hand, the gas-drilling fluid ratio was only 100

SCF/STB, the methane would not break out of solution until point C was

reached.

6.3 Effects of Other Gases On Methane Miscibility

Stalkup states that hydrocarbon gases heavier than methane mixed

with oil will have a lower miscibility pressure than methane. It can be

concluded that any addition of hydrocarbon gases heavier than methane to

pure methane will lower the pressure at which the gas mixture will

become miscible with a diesel oil-based drilling fluid below the

miscibility pressure of mixtures of pure methane and diesel oil-based

drilling fluids.

6.4 Field Application

For field applications, the miscibility pressure for pure methane

and No. 2 Diesel oil-based drilling fluids will be the highest pressures

above which gas miscibility in a wellbore can exist. Using American

Petroleum Institute (API) charts (Western Engineers Handbook) for

estimating the average bottomhole circulating temperature as a function

of the geothermal gradient and assuming an incompressibile oil-based

drilling fluid, the maximum depth above which gas miscibility in a

wellbore as a function of diesel drilling fluid density can be

determined.

First, the depth at which an assumed circulating temperature exists

for a given geothermal gradient can be determined from the regression

equations for the API circulating temperature charts as shown in Table

6.1. Next, the methane/diesel miscibility pressure corresponding to the

assumed temperature is determined from Figure 6.2. The drilling fluid


62

Table 6.1 - API Average Bottomhole Circulating Temperature

SECT = A X EXP(B x D)

where, BHCT = Bottomhole Circulating Temperature, °F

D = Depth, ft

A = 109.28 - 40.44 + 11.83

B = 5.48E - 05

G^ = Geothermal Gradient, °F/100 feet


63

density corresponding to the depth and methane/diesel miscibility

pressure is calculated as,

- W - 0 5 2 0 ..................................where is the drilling fluid density in Ibm/gal, is the

methane/diesel miscibility pressure in psi, and D is the depth

corresponding to the assumed temperature in feet.

Figure 6.5 shows a plot of methane miscibility depth versus No. 2

Diesel oil-based drilling fluid density for a range of geothermal

gradients. These curves represent the upper limit above which gas

miscibility can exist in a wellbore.


64

15000

14000

12000

% 13000h~Q.W0>- H

müen2 II 0 0 0

UJz<1l- 10000 ÜJ

9000

8000 _L9 II 13 15 17 19NO. 2 DIESEL OIL-BASED DRILLING FLUID DENSITY

lb /gal

Figure 6.5 - Methane Miscibility Depth Versus No. 2 Diesel Oil-Based Drilling Fluid Density.


CHAPTER VII

SWELLING OF OIL-BASED DRILLING FLUIDS DUE TO DISSOLVED GAS

In this chapter, a method is presented for estimating the swelling

of oil-based drilling fluids due to dissolved gas. Ths method can be

applied both (1) when the gas is fully miscible with the drilling fluid,

and downhole mixing is limited and (2) when gas initially contacts the

drilling fluid in volumes above the solution gas-drilling fluid ratio,

and mixing is enhanced by the initial development of gas bubbles.

Experimental PVT data were used to verify the calculation method

presented for a range of compositions and pressures at 100°F. The

method was also verified by experiments in a 6000-foot test well.

Examples are presented showing typical computed values for swelling

volumes at various depths, drilling fluid densities, and gas

concentrations. Pit gain comparisons are made with water-base drilling

fluids for a wide range of conditions. These examples illustrate

situations in which it is difficult to detect a gas kick in an oil-based

drilling fluid.

In addition to determining the amount of the dissolved gas present

in a given field situation, the method can also be used to determine the

sensitivity requirements of kick-detection equipment for any specified

hole geometry. The method applies to both surface and subsurface

kick-detection equipment.

7.1 Oil Swelling Calculations

The Peng-Robinson equation of state model described in Chapter III

was used to calculate the swelling of base oil due to dissolved gas.

65


66

The equations used are presented in Appendix A. Critical pressures,

critical temperatures, and acentric factors, needed for the equation of

state model, are shown in Table 7.1 for carbon numbers typically found

in base oils commonly used in oil-based drilling fluid preparation.

In order to calibrate the equation of state model, the use of an

adjusted molecular weight for the gas-free oil phase was found to be

necessary. The value, G that must be added to the gas-free oil phase

molecular weight is determined as,

G = 26.41 - 1.607E -02 R + I.641E - 07 R ^___ (7.1)so sowhere R^^ is the solution gas-base oil ratio in SCF/STB. Equation 7.1

was obtained empirically based on experimental data. Use of an adjusted

average molecular weight for the base oil was found to decrease the

error in the calculation of subsurface oil-phase swelling from about 10%

to less than 1%. Shown in Table 1-2 is a comparison of equation of

state calculations to experimentally obtained PVT data for methane and

No. 2 Diesel oil mixtures.

7.2 Pit Gain Calculations

The pit gain associated with a given standard volume of gas is

typically less in an oil-based drilling fluid than in a water-based

drilling fluid because the gas occupies less volume in solution than in

a free-gas phase. A closer average molecular spacing is permitted

because of high forces of attraction between the molecules of the gas

phase and the oil phase. The pit gain in an oil-based drilling fluid

also depends on the volume of drilling fluid in which the gas is mixed.

The volume of drilling fluid displaced from the well by a given standard


67

Table 7.1 - Base Oil Critical Properties

Carbon AcentricNo. Tc, °R Pc, psia Factor

8 1007.5 381.8 .3329 1049.9 350.4 .37310 1090.8 326.4 .41111 1125.4 304.7 .44812 1156.7 285.4 .48413 1185.7 268.1 .51814 1212.4 253.4 .55115 1237.7 244.4 .58216 1261.6 227.1 .61217 1283.2 216.4 .64118 1303.9 207.1 . 66819 1323.5 197.7 .69420 1342.2 190.7 .71921 1360.7 182.4 .74422 1378.7 175.4 .76723 1395.3 169.0 .78924 1410.6 163.0 .81125 1426.5 157.0 .832


68

Table 7.2 - Comparison of Experimentally Measured and Computed Values of Volume Factor, Bo, for Methane in No. 2 Diesel Oil at 100°F

Gas-OilRatio

(SCF/STB)Pressure(psia)

Molecular Weight Correction

(G)_______

ExperimentalBo

(bbl/STB)

PredictedBo

(bbl/STB)

3320377547054940

26.2 .993.991.987.986

.993

.991

.987

.986

234 12251585220

23.0 1.0701.0601.053

1.0641.0601.054

259 1475212526903365

22.5 1.0691.0541.0491.045

1.0701.0631.0581.052

467 254526253710

18.5 1.1371.1271.117

1.1311.1301.119

695 3825412046605305

15.2 1.1971.1911.1861.182

1.1991,1951.1891.182

821 4075426544905070

13.5 1.2541.2431.2331.225

1.2461.2431.2401.230


69

volume of gas tends to decrease as the volume of drilling fluid in which

it is dissolved increases.

When a kick is taken, the volume of drilling fluid that the gas

contacts is controlled to a great extent by the rate at which drilling

fluid is being circulated past the bit (Figure 7.1). The initial

gas-drilling fluid ratio, in SCF/STB, when the kick is being taken

can be computed using,

V i " % .......................................

where is the gas flow rate from the formation in SCF per minute

(SCF/min) and is the circulation rate of the pump in STB per minute

(STB/min). If this initial gas-drilling fluid ratio is less than the

solution gas-drilling fluid ratio for existing bottomhole conditions,

then little additional mixing will take place as the gas goes into

solution. However, if the initial gas-drilling fluid ratio is greater

than the solution gas-drilling fluid ratio, then free-gas bubbles will

tend to rise into the previously uncontacted drilling fluid above and go

into solution (Figure 7.1). Natural mixing due to bubble rise will

cause new drilling fluid to be contacted until the gas-drilling fluid

ratio is approximately equal to the solution gas-drilling fluid ratio.

The pit gain volume in barrels per 1000 SCF of gas kick, V^, can be

estimated using,

' ' g ’ 5 ^ ' V V V > ............................................................(7 -3 )

where f is the volume fraction of the oil in the drilling fluid, B and o oB are the volume factors of the oil-phase without and saturated with oggas in volume per surface volume, and R^^ is the gas-drilling fluid

ratio in SCF/STB.


70

MUDCIRCULATION

PITGAIN

FREE GAS BUBBLES WILL RISE AND CAUSE NATURAL MIXING

FORCED MIXING DUE TO MUD CIRCULATION

GAS FLOW

Figure 7.1 - Gas/Oil-Based Drilling Fluid Downhole Mixing.


71

The volume factors can be determined for any gas mixture and base oil

using the Peng-Robinson equation of state model as outlined in Appendix

A. Equation 7.3 neglects the solubility of the gas in the water phase

due to the small effect the swelling of water saturated with gas has on

the overall pit gain.

The pit gain calculation procedure was tested by conducting two gas

kick experiments in a 6000 foot well. Appendix B summarizes the

experimental procedures, facilities used, and the conditions of each

experiment. A comparison of the observed and predicted pit gains for

each experiment is shown in Table 7.3. Note that good agreement between

the predicted and observed pit gains for both experiments was attained.

7.3 Field Application

As stated in previous chapters, most natural gas kicks are

predominantly methane in composition. In order to develop a method that

will allow field personnel to estimate the pit gain to be expected for a

given gas kick volume, the equation of state model outlined in Appendix

A and the gas solubility correlation presented in Chapter V were used to

generate Figures 7.2-7.5 which show No. 2 Diesel oil swelling as a

function of pressure, temperature, and methane solubility in the base

oil. Using these curves along with Equation 7.3, the pit gain to be

expected for a given kick volume can be estimated. Although the curves

were generated for No. 2 Diesel oil, they also provide a close

approximation for other base-oils when used in conjunction with equation

7.3 since this equation is sensitive only to the change in volume

factors caused by the dissolved gas.


72

Table 7.3 - Comparison of Experimentally Measured and Predicted Pit Gains in 6000 ft. Experimental Well

Gas-Mud Mud Flow Measured Pit Predicted Pit Kick Size Ratio Rate Gain Gain

Experiment (SCF) (SCF/STB) (Gal/min) (bbl) (bbl)

1 4978 185 81.9 1.20 1.13

2 8132 178 119.7 2.20 1.96


CD■DI8Û.

■DCD

C/)(go"3

CD

8■DC5-

3CD

C3.

CD"OSÛ.CaO3T33

(DQ .

OC

"OCD

mI— if)

CDCD

Om

oo

<ü

Eo>

1.400 deg F No. 2 Diesel

MethaneOilGas

1.3

1.2

800

600.1

400

200G

Miscibility Pressure

0.9 18 2 014 164 6 8Pressure, (1000's psia)

121020

Figure 7.2 - No. 2 Diesel Oil Swelling Due to Dissolved Methane (T = 100°F). •vjw

74

a > ( N £

l - O O

815/188 O p D Ja i u n i o A


CD■DOQ.CgQ.

■DCD

C/)C/)

8■D

CD

3.3"CD

CD■DOQ.CaO3"OO

CDQ.

■DCD

C / )C / )

1.4 rm

(/)T = 3 0 0 deg F Oil = No. 2 Diesel Cas = Methane

—I 1.3 -æCD

m 1.2 -

0)

E 1.0o>

0.9


J I I I I I L j I4 6 8 10 12 14 16Pressure, (1000's psia)

18 20

Figure 7.4 - No. 2 Diesel Oil Swelling Due to Dissolved Methane (T = 300®F).Ln

■oâgÛ.

" OCD

C/)C/)

5'3

CD

85(5'

i3CD

C§CD

CD-OOQ .

O3

O3"

8.

OC■oCD

(/)o"3

T = 4 0 0 deg F Oil = No. 2 Diesel Cas = Methane


Figure 7.5

4 6 8 10 12 14 16P r e s s u r e , (1000‘s p s ia )

No, 2 Diesel Oil Swelling Due to Dissolved Methane (T = 400°F) o>

77

7.4 Example Calculations

The use of Figures 7.2-7.5 for simplified pit gain estimations is

best illustrated using examples. Three examples will be discussed. The

first example illustrates a situation in which gas initially contacts

the drilling fluid in concentrations below the allowable gas solubility.

The second example illustrates a situation in which gas initially

contacts the drilling fluid in concentrations above the allowable gas

solubility, and natural mixing will occur due to the rise of gas

bubbles. The third example illustrates a situation in which the gas and

drilling fluid are miscible in all proportions, and natural mixing due

to rise of gas bubbles cannot occur.

Example #1:

A 17.5-in. hole is being drilled at a depth of 4000 ft when gas

begins to enter the well on bottom at a rate of 2000 SCF/min. The 9.0

Ibm/gal drilling fluid has an oil volume fraction of 0.76, a water

fraction of 0.19, and a solids fraction of 0.05 and is being circulated

at 20 STB/min. At the bottomhole pressure of 1900 psia and the

bottomhole temperature of 100*F, the gas deviation factor is 0.85.

Estimate the pit gain expected per 1000 SCF of gas which enters the

borehole.

Solution - Using Eqn. (7.2), the initial gas-drilling fluid mixture is

2000/20 = 100 SCF/STB.

Since the volume fraction of oil is 0.76, the initial gas-oil ratio is

(100/0.76) = 132 SCF/STB.


78

Entering Figure 7.2 at 1900 psia, it can be seen that the solubility of

the gas in the base oil is 300 SCF/STB (value of solution gas at bubble

point curve), which is more than the gas-drilling fluid ratio. Thus,

all of the gas can go into solution in the oil. Also from Figure 7.2,

the volume factor of the gas-free oil is 1.005, and the volume factor of

the 132 SCF/STB gas-oil solution is 1.037. Using these values in

Equation 7.3 yields

1000/100 [0.76 (1.037-1.005)] = 0.24 STB/1000 SCF or4.11 MSCF/STB

The volume of the gas in a free-gas phase prior to going into solution

can be determined using the gas law as

1000 (14.7/1900) (560/520) (0.85/5.615) = 1.26 STB/1000 SCFor 0.79 MSCF/STB

Thus, for these conditions, the amount of gas in the well when a kick is

detected would be about 400% more in an oil-base drilling fluid than in a

water-base drilling fluid.

Example #2:

A 12.5-in. hole is being drilled at a depth of 8000 ft when gas



fraction of 0.16, and a solids fraction of 0.20, and is being criculated

at 10 STB/min. The bottomhole pressure is 5000 psia, the bottomhole

temperature of 200°F, and the gas deviation factor is 1.03. Estimate

the pit gain expected per 1000 SCF of gas which enters the borehole.

Also, repeat the calcultions assuming the gas enters the well on bottom

at a rate of 600 SCF/min.


79

Solution - Using Equation 7.2, the initial gas-drilling fluid mixture is

6000/10 = 600 SCF/STB.

Since the volume fraction of oil is 0.64, the initial gas-oil ratio is

(600/0.64) = 938 SCF/STB.

Entering Figure 7.3 at 5000 psia, it can be seen that the solubility of

the gas in the base oil is 670 SCF/STB (value of solution gas at bubble

point curve), which is less than the gas-oil ratio. This means that gas

bubbles can form and invade the previously uncomtaminated drilling fluid

region above until the gas-oil ratio is lowered to the solution gas-oil

ratio of 670 SCF/STB. This would yield a gas-drilling fluid ratio of

0.64 (670) = 429 SCF/STB.

Also from Figure 7.3, the volume factor of the gas-free oil is 1.012,

and the volume factor of the 670 SCF/STB gas-oil solution is 1.239.

Using these values in Equation 7.3 yields

1000/429 [0.64 (1.239-1.012)] = 0.34 STB/1000 SCF or2.95 MSCF/STB

The volume of the gas in a free-gas phase prior to going into solution

can be determined using the gas law as

1000 (14.7/5000) (660/520) (1.03/5.615) = 0.68 STB/1000 SCFor 1.46 MSCF/STB

Thus, for these conditions, the amount of gas in the well when a kick is

detected would be about 100% more in an oil-base drilling fluid than in

a water-base drilling fluid.

Repeating the calculations at a gas rate of 600 SCF/min gives a

gas-drilling fluid ratio of 60 SCF/STB and a gas-oil ratio of 94

SCF/STB. Use of Equation 7.3 yields

1000/60 [0.64 (1.034 - 1.012)] = 0.23 STB/1000 SCF or4.26 MSCF/STB

which is about 300% more than for a water base drilling fluid.


80

Example #3:

An 8.5-in. bit is withdrawn from a 15,000 ft. borehole when gas



fraction of 0.13, and a solids fraction of 0.35. At the bottom-hole

pressure of 11,700 psia and the bottom-hole temperature of 300°F, the

gas deviation factor is 1.20. Estimate the pit gain expected per 1000

SCF of gas which enters the borehole.

Solution - Since no drilling fluid was being circulated when the kick

was taken, forced gas-drilling fluid mixing was not significant.

Entering Figure 7.4 at 11,700 psia, it can be seen that the pressure is

above the value (6,500 psia) at which the gas is miscible with the oil

phase of the drilling fluid in all proportions. This implies that gas

bubbles will not form to create an efficient natural mixing process.

Thus, the gas region below the drilling fluid is thought to behave

essentially as a free-gas phase with a transition mixed zone separating

it from the drilling fluid above. The volume of the gas in a free-gas

phase can be determined using the gas law as

1000 (14.7/11,700) (760/520) (1.20/5.615) = 0.39 STB/1000 SCFor 2.55 MSCF/STB

Thus, for these conditions, the initial gain observed would be

approximately the same for oil-based and water-based drilling fluids.

However, this would not be true if forced mixing cccured. For example,

if the gas contacted sufficient mud to result in a gas-oil ratio of 500

SCF/STB and a gas drilling fluid ratio of 260 SCF/STB, then the pit gain

for the oil-based drilling fluid would be.


81

1000/260 [0.52 (1.130-1.001)] = 0.26 STB/1000 SCF

or 3.88 MSCF/STB

which Is about 50% more gas per STB gained than for a water-based

drilling fluid.

7.5 Drilling Fluid Density Calculations

The volume factors used to estimate subsurface drilling fluid

swelling can also be used to determine drilling fluid density. The

drilling fluid density in Ibm/bbl is equal to the mass in one surface

barrel of drilling fluid plus the mass of dissolved gas divided by the

volume factor of the drilling fluid. Thus, techniques presented in this

chapter can also be used to assist field personnel in estimating changes

in subsurface oil-based drilling fluid density due to changes in

temperature, pressure, and gas concentration.

One possible early kick detection scheme being currently

investigated is through the use of a measurements-while-drilling (MWD)

tool to detect changes in drilling fluid density just above the bit.

The required sensitivity of such a device was estimated for the well

conditions of Examples 1 and 2 presented previously, and the results are

shown in Figure 7.6. Note that the required sensitivity is greater in

the surface hole example.


82

to

eu

CO

o(0

5(X0 z> z1CO<C9

‘ 3NVH13W 03A10SSI0 01 300 A1ISN30 Onw-niO NI 39NVH3

gUS0)oco03

•HQ

Q)3Q030)00cCDJ=O

a»Q"3*r4b00c

wQ•33033POI«"H•HO

0s:s1Q

vO

3U3005:


CHAPTER VIII

HANDLING DRILLED-GAS IN OIL-BASED DRILLING FLUIDS

This chapter presents techniques for estimating the amount of

drilled-gas entering an oil-based drilling fluid and for predicting the

behavior of the gas-drilling fluid mixture in the annulus as it is

circulated to the surface. Using the methods presented, the depth at

which gas would begin evolving from the drilling fluid and the resulting

loss in hydrostatic pressure can be calculated. The volime of drilling

fluid that would be expelled from the well and the associated gas rate

can also be estimated. The calculation procedures presented were

verified by experiments conducted in a 6000 foot well. Also, methods

for handling drilled-gas in oil-based drilling fluids were investigated

by means of the calculation procedures developed.

8.1 Drilled-Gas Concentration

The concentration of drilled gas entering the drilling fluid at

bottomhole depends primarily on the penetration rate of the bit, the

diameter of the bit, the circulation rate of the drilling fluid, and the

formation pore pressure. The gas influx rate, in SCF/min can be

estimated using,

p.. dj ♦ S„ R-S - 310.97 z 4 « • «

where is the bottomhole pressure in psi, d^ is the bit diameter in

inches, <l> is the formation porosity expressed as a fraction, is the

formation gas saturation expressed as a fraction, R is the penetration

83


84

rate of the bit in ft/hr, z is the gas deviation factor, and T,, is theD£l

bottomhole circulating temperature in °R.

The resulting drilled-gas-drilling fluid ratio, in SCF/STB is

approximated using,

*3. - 42 ....................................

where is the drilling fluid flow rate in gal/min. In Equation 8.2,

it is assumed that the drilled-gas goes into solution at the bit and no

upward migration of gas bubbles occurs. This assumption is reasonable

since the value of R calculated from Equation 8.2 is small (i.e., <sm100 SCF/STB) as will be shown later in this chapter.

The total volume of drilled-gas entering the well, in SCF can be

calculated as.

V = 60 -#— ................................... (8.3)'g R

where h is the formation thickness in feet.

8.2 Circulating Time to Gas Evolution

The circulating time to gas evolution is an important parameter to

know because it allows drilling to continue for a time before the well

should be shut-in and the gas contaminated drilling fluid circulated out

of the well if it is not allowable to have free gas in the wellbore.

Current practice in the petroleum industry is to shut-in and circulate

bottoms-up (Figure 8.1) to remove possible gas contaminated oil-based

drilling fluid associated with a drilling break (the sudden increase or

decrease in penetration rate due to a change in lithology)

(Billingsley). However, significant costs can be incurred because of

the lost drilling time that is a consequence of this practice.


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CIRCULATING PUMPSSEPARATOR . MUD OUT

SEA LEVEL

CHOKE LINE

MUD LINEGAS CONTAMINATED MUD

Figure 8.1 - Circulating Gas Contaminated Drilling Fluid Out of Well.00Cn

86

To calculate the circulating time to gas evolution, the depth at

which the gas will begin to breakout of solution has to be determined.

For a given drilled-gas-drilling fluid ratio, an iterative procedure

having the following steps must be used:

1. Calculate the frictional and the hydrostatic pressure

gradients as outlined by Bourgoyne et. al. (Appendix C) for

gas free drilling fluid as this fluid will be above the gas

contaminated drilling fluid.

2. Move down-hole one length step. The distance moved is equal

to the length step size selected.

3. Calculate the pressure using the gradients from Step 1 and the

circulating temperature (Table 6.1) at this depth.

4. Using the gas solubility equations presented in Chapter V,

calculate the solution gas-drilling fluid ratio at the

pressure and temperature from Step 3.

5. If the solution gas-drilling fluid ratio calculated in Step 4

is equal to the given drilled-gas-drilling fluid ratio the

depth is the bubble point depth. If not, repeat Steps 2-4.

Once the bubble point depth has been determined, the bottoms-up

circulating time to this depth, t in minutes is,

t = (L-D, )/60 V ............................... (8.4)op awhere is the bubble point depth in feet, L is the vertical length of

the well in feet, and is the average annular velocity in ft/sec for a

concentric hole.

In most drilling applications, laminar flow in the annulus is

required to provide efficient drilled cuttings transport. Also most

wells drilled are not concentric but rather eccentric. The combination


87

of laminar flow and hole eccentricity results in the development of

velocity profiles in the annulus (Figure 8.2) and will cause Equation

8.4 to over-estimate the circulating time to gas evolution. To account

for the velocity profiles in the annulus. Equation 8.4 should be divided

by 1.5 for a concentric wellbore where the annular velocity will be the

smallest and by 2.5 for a fully eccentric wellbore where the annular

velocity will be the greatest as recommended by lyoho and Azar. These

two extreme cases are conveniently assumed since the eccentricity of a

wellbore is seldom known in actual practice and will allow the upper and

lower limits of the circulation time to gas evolution to be available.

8.3 Calculation of the Decrease in Bottomhole Pressure Due to Gas

Evolution

Knowledge of the decrease in bottomhole pressure due to drilled-gas

evolution will allow field personnel to determine whether or not

wellbore conditions will be such that gas may flow into the well from an

exposed gas sand. In addition, the volume of drilling fluid that will

be expelled from the well when the drilled gas breaks out of solution

can be estimated so that surface equipment can be designed to accomodate

the excess drilling fluid flow from the well.

To calculate the circulating bottomhole pressures with and without

gas, a computer model was developed. The program was written in FORTRAN

and was executed on an IBM Time Sharing Option Mainframe Computer. The

wellbore geometry modelled is shown in Figure 8.3.

The circulating bottomhole pressure, in psi is calculated as,

P,, = P, + AP- + P ............................. (8.4)bh hs f s


88

ISO VELOCITY

/5’/\VZ

DEPTH

Figure 8.2 - Annular Velocity Profiles Due to Laminar Flow and Hole Eccentricity.


89

A Drill Pipe OD

Casing Shoe ^ -----

Diameter

Casing ID

Figure 8.3 - Computer Model Wellbore Geometry.


90

where is the hydrostatic pressure due to the annular fluids in psi,

AP^ is the annular frictional pressure losses in psi, and P^ is the

surface pressure in psi.

For the case where no drilled gas has contaminated the well, the

hydrostatic pressure is due to the drilling fluid and drilled cuttings

in the annulus. For the purposes of this study, the effects of drilled

cuttings on the hydrostatic pressure is neglected. The annular

frictional pressure losses are calculated using the power law model to

approximate the apparent Newtonian viscosity of the oil-based drilling

fluid (Appendix C).

To calculate the circulating bottomhole pressure when the top of

gas contaminated drilling fluid reaches the surface which corresponds to

the maximum decrease in bottomhole, an iterative method was used. The

steps used are:

1. Start at the surface where the pressure and temperature is

known.



3. Assume a pressure and calculate the circulating temperature

(Table 6.1) at this depth.

4. Using an average pressure and temperature, calculate the free

gas rate and density, and the density of the oil-based

drilling fluid containing dissolved gas.

5. Calculate the hydrostatic and frictional pressure gradients

and sum these values to get the total pressure gradient over

the length step.


91

6. Using the calculated pressure gradient, calculate the pressure

and compare with the assumed pressure. If the two pressures

compare favorably continue to the next step. If not, use the

new pressure and repeat Steps 4-6.

7. Calculate the volume of free and dissolved gas contained in

the annular section associated with the selected length step.

8. Repeat Steps 2-7 until the sum of the volume of free and

dissolved gas contained in the annular sections equals the

volume of gas that entered the well as calculated using

equation 8.3

9. Use the frictional pressure gradient and hydrostatic gradient

calculated for gas free drilling fluid to calculate the

pressure due to a column of gas free drilling fluid that may

exist below the region of gas contaminated drilling fluid.

10. The sum of the last pressure calculated in Step 6 and the

pressure calculated in Step 9 will be the circulating

bottomhole pressure.

The solution gas-drilling fluid ratios are calculated as outlined

in Chapter V and the oil-based drilling fluid densities are calculated

as outlined in Chapter VII and Appendix A. The frictional and

hydrostatic pressure gradients of the gas-drilling fluid mixture were

determined as recommended by Langlinais, et. al. and is outlined in

Appendix D.

Once the circulating bottomhole pressures have been calculated for

gas free and contaminated drilling fluid, the decrease in bottomhole

pressure due to gas evolution is simply the difference between the two

pressures.


92

8.4 Drilling Fluid Expelled Due to Gas Evolution and Surface Gas Rate

The maximum volume of drilling fluid that will be expelled from the

well due to gas evolution, in surface barrels can be estimated as,

\ - aPg/.052 ..................... (8.5)where AP^ is the decrease in bottomhole pressure due to gas evolution in

psi, is the oil-based drilling fluid density in Ibm/gal, and is

the annular capacity in bbl/ft.

The surface gas rate, in SCF/Day can be estimated as,

Qg - 34-3 4m*sm.................................. (*'*)where is the drilling fluid rate in gal/min and is the

drilled-gas-drilling fluid ratio in SCF/STB.

8.5 Experimental Verification of Calculation Procedure

The experimental well and procedures as described in Appendix B

were used to veryify the calculation procedure. The loss in bottomhole

pressure due to gas evolution and the circulation time before gas

evolution occurred were noted for each experiment and compared to the

theoretical calculations. The first evolution of gas could be detected

by observing a sharp change in the bottomhole pressure, pump pressure,

pump speed, and pit gain. A comparison between the experimental results

and the theoretical calculations are shown in Table 8.1. Note that

there was good agreement between the observed and calculated results for

both the loss in bottomhole pressure and in the circulation time to gas

evolution.


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Table 8.1 - Comparison of Experimental Observations and Theoretical Predictions

Theoretical Predictions Observed ResultsCirculating Circulating

Time TimeGas-mud Pump Change To Cas Change To CasRatio, Rate, In BHP*, Evolution, In BHP, Evolution,SCF/STB STB/MIN psla mln psla mln

185 1.95 170 54 177 53

178 2.85 112 40 114 36

235 1.05 376 51 385 48

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94

8.6 Evaluation of Field Procedures

Sensitivity analyses were made to determine the effects of a number

of drilling variables on the severity of the problems caused by

drilled-gas dissolving in an oil base drilling fluid. The effect of the

most important parameters affecting the initial gas concentration

dissolving in the drilling fluid are shown in Figures 8.4 and 8.5.

Shown in Figure 8.4 are the effects of penetration rate and formation

pore pressure for a well drilling at 8000 ft with a 12.25-in. bit. It

is assumed that the drilling fluid density used is near the formation

pore pressure. Note that for the well conditions assumed, the initial

drilled-gas concentration could sometimes be as high as 40 SCF/STB.

The effect of increasing well depth on initial drilled-gas

concentration can be seen by comparing Figures 8.4 and 8.5. Note that

for a typical well plan of decreasing hole size with increasing well

depth, the maximum anticipated drilled-gas concentration would tend to

decrease with depth.

Figure 8.6 shows the calculated circulating time to gas evolution

as a function of the drilled-gas-drilling fluid ratio for a concentric

hole (eccentricity = 0) and for a fully eccentric hole (eccentricity =

1) for the conditions shown. Note that as the gas-drilling fluid ratio

increases the circulating time to gas evolution decreases. This is to

be expected since the bubble point pressure increases as the

gas-drilling fluid ratio increases resulting in the bubble point depth

occuring deeper in the well. Also note that the circulating time to gas

evolution is much less for the eccentric hole than for the concentric

hole. This is due to the higher annular velocities associated with the

fully eccentric hole.


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4 0

O 30

to20

5004 0 0300200PENETRATION RATE, FT/HR

100

Figure 8.4 - Effect of Penetration Rate and Drilling Fluid Density on Drilled-Gas Concentration (D = 8000 Feet). VOU1

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Figure 8.5 - Effect of Penetration Rate And Drilling Fluid Density on Drilled-Gas Concentration (D » 15000 Feet). VO

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10 15 2 0 25 3 0 35G A S -M U D RATIO, SCF/STB

4 0 45 50

Figure 8,6 - Effect of Drilled-Gas Concentration on Circulation Time To Gas Evolution. VO

98

Figure 8.7 shows the effect of penetration rate on the decrease In

bottomhole pressure due to gas evolution for a range of sand thicknesses

and the conditions shown. Notice that for a given sand thickness, at

low penetration rates the sand will appear Infinite and a worst case of

gas contaminated drilling fluid throughout the entire annular section

will exist (Point A). However, as the penetration Is Increased this

apparent Infinite sand thickness will not exist rather the actual sand

thickness will be realized (Point B). For both Point A and B, the

decrease In bottomhole pressure Increases with an Increase In

penetration rate. A further increase In penetration rate will cause a

decline In the rate with which the bottomhole pressure decreases (Point

C). This Is because the higher gas-drllllng fluid ratios associated

with the higher penetration rates Increases the free gas rate causing

the majority of the drilled gas to slip past the drilling fluid and to

exist in the upper portion of the well.

Table 8.2 shows the calculated volumes of drilling fluid that can

be expelled from the hole for the conditions shown In Figure 8.7. Note

that as the sand thickness increases the volume of drilling fluid that

can be expelled from the well increases which is to be expected since

the decrease In bottomhole pressure increases with increasing sand

thickness as shown In Figure 8.7. This happens because the volume of

gas In the well Is Increasing as the sand thickness Increases as uhown

in Figure 8.8.

Shown in Figure 8.9 are the effects of drilled-gas concentration

and pump rate on the required surface gas handling rate. This figure

shows that gas flow rates from the well in the range of .5 to 1.5

MMSCF/Day can occur for typical drilled-gas concentrations. This


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3 0 0

Flgurfi 8.7 “ Effect of Penetration Rate and Gas Sand Thickness on Bottomhole Pressure Reduction. VO

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100

Table 8.2 - Volume of Drilling Fluid Expelled Due to Gas Evolution

V , bbls inR, ft/hr

50

100

150

200 250

300

h, ft = 25

2 21

49

56

59

61

50

3

22

50

77

84

89

150

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81

109

138

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127

166


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Pbh • 5 0 0 0 psi Tbh » 200*F Z « 1.03Hole Diameter « 12.25 In

4

2

0 200 2 5 0 3 0 0100 ISO50GAS SAND THICKNESS, Ft.

Figure 8.8 - Effect of Gas Sand Thickness on Gas Volume In Well.

102

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103

suggests the need for a flowllne degasser or separator capable of

handling these rates that is placed upstream of the shale-shaker. It

also indicates the need for a rotating head to prevent gas from being

vented at the rig floor reducing an explosion hazard to the rig

personnel. This design was suggested by O ’Brien and Matthews as pointed

out previously.

As pointed out in Chapter III, the solubility of gas in an

oil-based drilling fluid is a function of the volume fraction of oil in

the drilling fluid. For a constant gas-drilling fluid ratio and

temperature, the bubble point pressure for the mixture will increase

with a decrease in the volume fraction of oil in the drilling fluid.

If it is desired to prevent any gas from breaking out of solution

in the wellbore, a rotating head can be used to exert a backpressure on

the well equal to the bubble point pressure of the gas-drilling fluid

mixture (Figure 8.10). Figure 8.11 shows a plot of rotating head

pressure needed to keep gas in solution versus gas-drilling fluid ratio

for various volume fractions of oil in the drilling fluid. Note that a

considerable backpressure is needed to keep typical values of drilled

gas in solution for low volume fractions of oil in the drilling fluid.

The high backpressures needed to keep drilled gas in solution make

this approach unattractive since it requires rig personnel to work with

a well under pressure and requires rotating heads with working pressure

ratings in excess of those commonly available. The most safe design

appears to be a rotating head operated at a low pressure to prevent gas

from being expelled on the rig floor and a flowline degasser or

separator downstream of the rotating head but before the shale-shaker as

shown in Figure 8.12. The separator, gas vent line, and drilling fluid


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- MUD OUTDISSOLVEDGAS

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5

105

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FLOWLINE DEGASSERGAS BREAKING-----OUT OF SOLUTION

DISSOLVED GAS

Figure 8.12 - Rotating Head - Separator Flow Arrangement With Free Gas in Wellbore.

oa\

107

flow Unes should be sized such that excessive backpressures are not

placed on the well when the gas and drilling fluid are expelled from the

well. This will prevent the risk of fracturing exposed subsurface

formations.

Note that in the design of Figure 8.12, some free gas will exist in

the wellbore. Use of the calculation methods presented will allow the

effects of the free gas in the well to be determined and the proper

rotating head pressure rating and drilling fluid density to be selected

to minimize the effects of the free gas in the well.


CHAPTER IX

CONCLUSIONS

1. A method for estimating the solubility of gas in an oil-based

drilling fluid has been developed.

2. Curves for estimating the upper limit depth of gas miscibility in

the wellbore has been presented.

3. The Peng-Robinson equation of state model has been calibrated using

PVT data, and curves for predicting the swelling of base oils used

in drilling fluid preparation due to dissolved gas have been

generated.

4. A method for predicting the pit gain to be expected for given field

conditions has been developed.

5. The standard volume of gas in the borehole when a given pit gain is

observed at the surface:

a) tends to be greater in an oil-based drilling fluid than in a

water-based drilling fluid.

b) tends to increase as the gas is mixed in increasingly larger

volumes of oil-based drilling fluid.

c) can be as much as 400% more than for a water-based drilling

fluid.

6. A technique has been presented for calculating the annular behavior

of drilled-gas in an oil-based drilling fluid.

7. Drilled-gas concentration in oil-based drilling fluids is

controlled primarily by bit size- penetration rate, drilling fluid

flow rate and formation pore pressure and usually varies from 5-40

SCF/STB.

108


109

I-

8. Drllled-gas concentrations decrease with increasing depth for

typical wells where hole size decreases with depth.

9. The decrease in hottomhole pressure due to drilled-gas evolution

increases with increasing penetration rate and gas sand thickness.

10. Design criteria for determining the proper rotating head pressure

rating and separator size to be used when handling drilled-gas in

oil-based drilling fluids have been presented.


CHAPTER X

RECOMMENDATIONS

1. Data should be generated for the solubility of hydrogen sulfide in

base oils over a range of temperatures (i.e., 100, 200, and 300°F)

and pressures.

2. Using the data from 1., a correlation should be developed for

predicting the solubility of hydrogen sulfide in base oils.

3. Experimental data for gas/oil-based drilling fluid miscibility is

needed to further define this complex phase behavior as it relates

to the wellbore.

4. Experimental data for the time rate of gas solubility will be

useful in determining how gas bubbles migrate up the well when the

initial gas-drilling fluid ratio is in excess of the allowable

bottomhole gas-drilling fluid ratio.

5. Experimental data on how gas dissolved in an oil-based drilling

fluids affects the drilling fluid properties would be of interest.

Particularly of interest would be the effects of gas solubility on

barite settling in the wellbore when the well is shut in for a

considerable period of time after a gas kick has been detected.

110


CHAPTER XI

REFERENCES

Billingsley, J.L., Tenneco Oil Exploration and Production, personal communication.

Bourgoyne, A.I., Jr., Millheim, K.K., Chenevert, M.E., and Young, F.S., Jr., Applied Drilling Engineering, Society of Petroleum Engineering, 1986, pp. 152-155.

Brill, J.P. and Beggs, H.D., Two-Phase Flow In Pipes, University of Tulsa, 1982, pp. 3-11-3-18.

Craft, B.C. and Hawkins, M.F., Applied Petroleum Reservoir Engineering, Prentice Hall, 1959, p. 131.

Crawford, H.R., Neill, G.H., Lucy, B.J., and Crawford, P.D., "Carbon Dioxide - A Multipurpose Additive for Effective Well Stimulation," JPT, March 1963.

Ekrann, S. and Rommetveit, R., "A Simulator for Gas Kicks In Oil-Based Drilling Muds," SPE 14182, Presented at the 60th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Las Vegas, NV, September 22-25, 1985.

Hagedom, A.R. and Brown, K.E., "Experimental Study of Pressure Gradients Occurring During Continuous Two-Phase Flow in Small Diameter Vertical Conduits," JPT, April 1965, pp. 475-483.

lyoho, A.W. and Azar, J.J., "An Accurate Slot Flow Model for Non- Newtonian Fluid Flow Through Eccentric Annuli," SPEJ, October 1981, pp. 565-572.

Katz, D.L. and Firoozabadi, A., "Predicting Phase Behavior of Condensate/Crude-Oil Systems Using Methane Interaction Coefficients," JPT, November 1978, pp. 1649-1655.

Langlinais, J.P., Bourgoyne, A.T., and Holden, W.R.,: "FrictionalPressure Losses for Annular Flow of Drilling Mud and Mud Gas Mixtures", Transactions of the ASME, Vol. 107, March 1985, pp. 142-151.

Lee, A.L., Gonzalez, M.H., and Eakin, B.E., "The Viscosity of Natural Gases," JPT, August 1966, pp. 997-1000.

McCain, William D., The Properties of Petroleum Fluids, Penn Well, Tulsa, OK (1973), pp. 284-285.

Matthews, W.R., "How to Handle Acid Gas H^S and CO^ Kicks," Petroleum Engineer International, 15 November 1984, pp. 22-29.

Ill


112

O’Brien, T.B., "Handling Gas in an Oil Mud Takes Special Precautions," World Oil, January 1981, pp. 83-86.

Peng, D.Y. and Robinson, D.B.: "A New Two Constant Equation ofState", Ind. Eng. Chem. Fund., Vol. 15, No. 1, 1976, pp. 59-64.

Salisbury, D.P., Milchem Incorporated, personal communication.

Stalkup, F.I., Miscible Displacement, Society of Petroleum Engineers, Dallas, TX, 1983, pp. 3, 4, 99, 100, 140.

Standing, M.B., Volumetric and Phase Behavior of Oil Field Hydrocarbon Systems, Society of Petroleum Engineers, Dallas, TX, 1977, pp. 40-42.

Thomas, D.C., Lea, J.F. Jr., and Turek, E.A., "Gas Solubility in Oil- Base Drilling Fluids: Effects on Kick Detection," JPT, June 1984, pp.959-974.

Thomas, D.C. and Lea, J.F., Jr., "Blowouts - A Computer Simulation Study," lADC/SPE 11375, Presented at the 1983 I ADC/SPE Drilling Conference, New Orleans, LA, February 20-23.

The Western Company of North America, Engineers Handbook, Fort Worth, TX, p. 7-19.

Whitson, C.H., "Characterizing Hydrocarbon Plus Fractions," SPEJ, August, 1983, pp. 683-694.


APPENDIX A

PENG-ROBINSON EQUATION OF STATE

In its general form, the Peng-Robinson equation of state is given

as,

p = H _________a(T)v-b v(v+b) + b(v—b)

where P is the pressure in psia, T is the temperature in °R, v is the

molar volume in ft^/lb-mole, R is the universal gas constant, 10.73

psia • ft^/lb-mole • °R, a(T) is the Peng-Robinson molecular

attraction parameter which is a function of temperature, and b is the

Peng-Robinson molecular repulsion parameter.

Rewritten, Equation A.1 becomes.

where.

- (l-B)z^ + (A-3B^-2B)z - (AB-B^-B^) = 0 (A.2)

A = (A.3)R T

B - g (A.4)

Pv ^ RT (A. 5)

with z being the deviation factor. Equation A.2 yields one or three

real roots, and for liquids, the smallest positive root is desired.

Equation A.5 is then used to calculate the molar volume, v, in barrels

per pound-mole. Knowing the molar volume and n, the pound-moles of

liquid, the volume of liquid in barrels at a given pressure and

temperature can be determined as,

V = V • n (A. 6)

113


114

To determine the molecular attraction parameter, a(T) and the

molecular repulsion parameter b for use in Equations A.3 and A.4,

parameters a(T) and b are evaluated at the critical pressure, and

temperature, for the component of interest as,

R^T 2a(T^) = 0.45724 (A. 7)

c

RTb(T^) = 0.0778 (A.8)

c

Parameter a(T^) is corrected to the temperature of interest by

aCT) = a(T ) • a(T^,w) (A.9)c rwhere.

a = [1 + (.37464 + 1.54226w - .269920)^) (1-T^^) (A. 10)

with being the reduced temperature defined as the temperature of

interest divided by the component critical temperature, both being in

absolute temperature units and w being the component acentric factor.

To calculate parameters a(T) and b for a mixture, mixing rules

given as,

a = Z Z X . X . a(T).. (A.11)i j ^

b = Z X. b . (A.12)i ^

where x^ and x^ are the i- and j-component mole-fractions respectively

and b^ is the i-component repulsion parameter defined by Equation A. 8.

The parameter a(T)^^ is calculated as,

a(T) = (1-C ) aCT) a(T)^ (A. 13)-J 1 3

where a(T)^ and a(T)j are the i- and j-component attraction parameters

calculated by Equations A.7 and A.9 and is the binary interaction


115

parameter for the 1- and j-component binary. Commonly used binary

interaction coefficients are listed in Table A.I.

Once the volume of a mixture at a given pressure and temperature is

determined by Equation A.6, the volume factor, can be calculated as,

B = V/V (A. 14)o scwith the units of B^ being volume at pressure and temperature per volume

at standard conditions (i.e., pressure = 15.025 psia and temperature =

60°F).

rReproduced with permission of the copyright owner. Further reproduction prohibited without permission.

116

Table A.1: Peng-Robinson Equation of State Binary InteractionCoefficients

CarbonNo.

Methane Binary* Interaction Coefficient

23

n4n5n6n789

1011121314151617181920 21 22232425

00

.0200

.0200

.0250

.0250

.0381

.0407

.0427

.0442

.0458

.0473

.0488

.0502

.0512

.0523

.0500

.0537

.0544

.0551

.0558

.0565

.0571

.0575

Binary MixtureInteractionCoefficient*

Nitrogen + Hydrocarbon .1200Carbon Dioxide + Hydrocarbon .1500Hydrogen Sulfide + Hydrocarbon .1200Ethane + Hydrocarbon .0100Propane + Hydrocarbon .0100

*-Carbon numbers 8 - 2 5 methane binary interaction coefficients from Whitson. All other interaction coefficients from Katz and Firoozabadi.


APPENDIX B

FULL SCALE EXPERIMENTS

Experiments were conducted in a 6000 foot test well in which gas

was injected into an oil-based drilling fluid and the well monitored for

pit gain, circulation time to gas evolution, and decrease in bottomhole

pressure due to gas evolution. Figure B.l shows the flow arrangement

used.

The experimental test well is designed to simulate drilling 3000

feet below the seafloor in 3000 feet of water. The drillstring is

modelled using 2.875 inch tubing set at 6000 feet. Gas can be injected

into the bottom of the well through 1.315 inch tubing run concentrically

inside the drillstring. Gas storage and compression wells permit 0.62

specific gravity natural gas (Table B.l) to be injected at any desired

bottomhole pressure, up to a maximum of 5500 psi, and at any desired

bottomhole feed rate, up to a maximum of about 3 STB/min. The choke and

kill lines to the simulated subsea blowout preventer stack are modelled

using 2.375 inch tubing.

To conduct each experiment, the well was circulated at a given rate

while gas was injected down the 1.315 inch gas injection line.

Bottomhole pressure, pit gain, pump pressure, and pump speed were

monitored during the course of each experiment.

The conditions and results of the experiments are summarized in

Tables B.2 and B.3. Figures B.2 - B.4 are plots of the measured data

versus time for each experiment. Pit gain was not recorded for

Experiment No. 3 (Figure B.4) due to difficulty with the pit gain

monitoring equipment during the experiment.

117


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119

TABLE B.l: Full Scale Experimental Gas Composition

Component Mole Percent

Nitrogen 0.28

Carbon Dioxide 0.89

Methane 90.18

Ethane 4.84

Propane 2.05

i-Butane 0.49

n-Butane 0.53

i-Pentane 0.23

n-Pentane 0.15

Hexanes 0.14

Heptanes+ 0.22


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Exp. No. Pm* PP8 o m up, cp Y.P., lb/100 ft^ Rate, bpm Injected, SCF SCF/STB

1 8.2 64:36 22 16 1.95 4,978 185

2 8.1 64:36 21 12 2.85 8,132 178

3 7.85 64:36 21 12 1.08 10,274 235

Surface Temperature: 80®FSurface Pressure: 15.025 psia Geothermal Gradient: 1.3°F/100 ft

Measured kill line and drill pipe pressure losses:

Pump Speed, SPM

0 50

60

70

Kill Line AP, pslg

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215

300

Drill Pipe AP, pslg

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o-o Bottom Hole Minimum

Circulating Bottom Hole Circulating

Exp. No..Pressure

(No Gas), pslgPressure Due

To Gas Evolution, pslgCirculating Time

To Gas Evolution, mlnPitGas

Gain Before Evolution, bbl

1 2,695 2,518 53 1.2

2 2,824 2,710 36 2.2

3 2,487 2,102 48 -

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Figure B.2 - Experiment No. 1 Measured Data.N>

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APPENDIX C

GAS FREE DRILLING FLUID PRESSURE CALCULATIONS

To calculate the frictional pressure losses in an annulus, the

average annular velocity, V in ft/sec, is calculated as,

’ * 2.448 ............................where is the drilling fluid rate in gal/min, d^ is the hole diameter

in inches, and d^^ is the drill-pipe diameter in inches.

The apparent Newtonian viscosity of the drilling fluid, in

centipoise (cp) is calculated as,

Kf^h-^dp)^ , 2 + 1/n f 2)

where,

and.

'"a 144 ÿ(l-n) ' 0.0208

n = 3.32 log ©6oo/®300.......................... (^.3)

K = 510 Qgog/Sll^............................... (C.4)

K is known as the consistency index of the drilling fluid having units

of equivalent centipoise and n is the flow behavior index which is

dimensionless. ©goQ ®3QG the 600 and 300 rpm readings from a

Fann Viscometer.

The Reynolds number, N^^ is used as the flow regime, either laminar

or turbulent, criteria. It is given as,

. , , . 3,

Re

If N^^ is less than the critical Reynolds number for the given n value,

flow is laminar. If it is greater then the critical Reynolds number for

125


126

the given n value, flow is turbulent. The critical Reynolds number for

values of n can be determined from Figure C. 1 as well as the friction

factor, f for turbulent flow calculations.

If flow is laminar, the frictional pressure loss, AP^ in psi is

calculated as,

u V LA P , ...... (C.6)

1000 (d^-djp)"

If flow is turbulent, the frictional pressure is calculated as,

f v \•f - 21— (d^-d^p)AP, = ™ — 3— r ............................ (C.7)

To calculate the hydrostatic pressure due to a column of gas free

oil-based drilling fluid, an iterative calculation technique is used to

account for the compressibility and expansion of the drilling fluid

caused by pressure and temperature. The steps are:

1. Start at the surface where the pressure and temperature is

known.



3. Assume a pressure and calculate the circulating temperature

(Table 6.1) at this depth.

4. Calculate the drilling fluid density using the PREOS model

described in Appendix A.

5. Using an average density over the length step and the

frictional gradient as determined above, calculate the

pressure due to a column of drilling fluid associated with the

length step size selected and compare with the assumed


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128

pressure. If the two pressures compare favorably continue to

the next step. If not, use the new pressure and repeat Steps

4 and 5.

6. Repeat Steps 2-5 until bottomhole is reached with the last

pressure calculated being the bottomhole pressure for a column

of gas free drilling fluid.


APPENDIX D

TWO-PHASE PRESSURE GRADIENT CALCULATIONS

The procedure outlined by Langlinais, et. al. for calculating

flowing pressure gradients for two-phase annular flow uses the Hagedom

and Brown correlation with an equivalent diameter defined by the

hydraulic diameter concept and the power law model to define the

apparent Newtonian viscosity of the drilling fluid. The hydraulic

diameter, in inches is given as,

*e = 'Hi ■ 'dp.................. (D'l)where d, is the hole diameter and d, is the drill pipe diameter both in h dpinches.

The Hagedom and Brown correlation for calculating the two-phase

pressure gradient, CdP/dz)^^^ in psi is given as,

CdP/dz)^^^ = (dP/dz)j + (dP/dz)g^.............. (D.2)

where.

and.

(dP/dz) - = g/g [p H + p (1-H )]........... (D.3)61 c in m g m

. 2(dP/dz). = -------------------------- (D.4)

2.9652 X lOr p^ dg

(dP/dz)^^ and (dP/dz)^ are the pressure gradients due to elevation and

friction respectively.

Equation D.4 was rewritten by Brill and Beggs as,

f p.(dP/dz) = f (D.5)

f 2 8c dgwhere,

V , = V + V ............................... fD.6)mix sm sg

129


130

and,

%s = = Vg ...........................3

In Equations D.3-7, is the drilling fluid density in Ibm/ft

calculated using the Peng-Robinson equation of state as outlined in3

Appendix A, is the gas density in Ibm/ft , is the H a g e d o m and

Brown liquid holdup expressed as a fraction, f is the friction factor,

d^ is the hydraulic diameter in inches defined b y Equation D.l, w is the

mass flow rate in Ibm/day, is the two-phase mixture superficial

velocity in ft/s, is the superficial drilling fluid velocity in

ft/s, is the superficial gas velocity in ft/s, is the two-phase

mixture viscosity in cp, is the power law apparent Newtonian

viscosity for the drilling fluid in cp as calculated in Appendix C, y^

is the gas viscosity in cp as determined using the Lee, et. al.

correlation.3

In Equation D.5, p^ in Ibm/ft is defined as,

Pg = Pjj /Pg................................... (D.8)where.

and.». - ...................

p = p H + p ( 1 — H ) ........................................................... (D. IO)s in m ^ Ts

Note that in Equation D.l, the pressure gradient due to

acceleration are neglected. This is commonly done in practice due to

the small contribution in the total pressure gradient made by

acceleration of the fluid.


VITA

Patrick Leon O'Bryan is the son of Mr. and Mrs. L. K. O’Bryan of

Brandon, MS. He was b o m in Hattiesburg, MS on August 17, 1961. He is

married to the former Pamela Elizabeth Bramlett, also from Brandon, and

they have a son, Taylor Patrick. Patrick graduated from Brandon High

School in 1979 and then attended Mississippi State University where he

received a Bachelor of Science degree in Petroleum Engineering in May,

1983. He then began graduate studies at Louisiana State University

where he received a Master of Science degree, also in Petroleum

Engineering in December, 1985. He began work towards the Doctor of

Philosophy degree in Petroleum Engineering at Louisiana State

University in January, 1986.

131


w

DOCTORAL EXAJVnNATION AND DISSERTATION REPORT

Candidate; Patrick Léon O’Bryan

Major Field: Petroleum Engineering

Title of Dissertation: Well Control Problems Associated With Gas Solubility InOil-Based Drilling Fluids

Date of Examination:

April 26, 1988

Approved:

Major Professor a6l c64irmtm

Dean of the Graduate/School

EXAMINING COMMITTEE:


well control problems associated with gas solubility in

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