spe 102488 (cox) errors intro multiphase flow cor production anal

7/25/2019 SPE 102488 (Cox) Errors Intro Multiphase Flow Cor Production Anal

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Copyright 2006, Society of Petroleum Engineers

This paper was prepared for presentation at the 2006 SPE Annual Technical Conference andExhibition held in San Antonio, Texas, U.S.A., 2427 September 2006.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than300 words; illustrations may not be copied. The abstract must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

Abstract

First and foremost, production analysis techniques requireaccurate rate and bottomhole pressure histories. In most cases

the pressure history of the well is not measured directly at the

bottomhole condition, but is calculated from surface

measurements by the use of single or multiphase flowcorrelations. In some cases significant error is introduced

through the use of these correlations.

This paper evaluates the magnitude of such errors for oil and

gas producers with regard to the estimation of flow capacity,completion efficiency, and effective drainage area. Synthetic

cases are used as control sets in order to evaluate the

sensitivity of the results to the various multiphase flowcorrelations and flowing conditions. In addition to synthetic

(simulated) performance behavior, field cases are presented

and the variance in estimated reservoir and completion

properties is evaluated.

The technical contributions of this paper are:

a. Systematic evaluation of the effect of errors in flow

rates and bottomhole flowing pressures on productiondata analysis using both synthetic and field derived

well performance data.

b. Qualitative guidelines as the effect of errors in rate and

pressure on estimated reservoir properties.

In most cases the flowing bottomhole pressure is not measured

directly, but is calculated based on the measured (surface)tubing pressure profile and flow rate data. Pressure drop

correlations for multiphase flow are used to "convert" thesurface pressure profile into a bottomhole pressure profile

suitable for analysis and interpretation. Depending on the

(multiphase flow) pressure calculation method that is selected,

as well as the producing conditions, significant errors in thecalculated flowing bottomhole pressure can (and will) result

which affects the estimation of reservoir/well parameters.

Three synthetic (simulation) cases were constructed for thepurpose of serving as control data sets for this study. Eachcase represents a single well reservoir producing from the

center of a radial flow geometry system. These simple

scenarios are used to avoid any multiwell (interference)effects, as well as partial or irregular boundaries, etc.

Specifically, the cases considered for this study include:

Fracture stimulated well, low permeability gas reservoir,

Unfractured well, low permeability oil reservoir, andUnfractured well, high permeability oil reservoir.

An appropriate multiphase correlation for each case was

selected to control the simulator. The actual rates and

bottomhole pressures were used to validate the productionanalysis techniques. New bottomhole pressures were then

calculated utilizing different multiphase flow correlations, and

the evaluation process was repeated. The results of eachanalysis were compared to the parameters used in the

simulator in order to establish the conclusions in this paper.As a comprehensive statement, the results of this workhighlight the need for to acquire flowing gradients periodically

to calibrate the multiphase flow correlation.

Background Theory

The use of well production data to characterize reservoirperformance has been utilized by the oil industry for many

SPE 102488

Errors Introduced by Multiphase Flow Correlations on Production AnalysisS.A. Cox and R.P. Sutton, Marathon Oil Co., and T.A. Blasingame, Texas A&M U.


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2 SPE 102488

change continuously however, the analytical solutions

typically employed in production analysis require either

constant rate or constant pressure production behavior. In

order to overcome this issue, an equivalent time function mustbe incorporated into the analysis to account for the continuous

changes in rates and pressures. Palacio and Blasingame2

showed that the "equivalent time" function for oil is given bythe following equation:

q

Nt

pe= .........................................................................(1)

For gas wells the "equivalent time" function is defined as:

[ ])(2)(

)()()(

)()()(

0

pmpGz

tqct

pcptdtq

tqct

i

iiig

g

iga = =

........(2)

For the gas well case, the average reservoir pressure profile

must be known (or estimated) in order to calculate the correctequivalent time function. However the drainage area must be

known in order to calculate the average reservoir pressure

from material balance. Therefore, gas production analysis is

inherently iterative in nature.

Various plots are available to determine the effective drainagearea (or volume) of the well. For oil wells, a plot ofdimensionless rate (qDd) versus dimensionless cumulative

production (QDd) will form a straight line with an intercept of

1. For this plot qDdand QDdare defined as:

owa

e

wfi

ooDd q

r

r

ppkh

Bq

4

3ln

)(

1

10x08.7

1

3

=

.........................................................................................(3)

pwfit

oDd N

pphAc

BQ)(

1615.5

=

..............................(4)

For gas wells, a plot of reciprocal dimensionless pressure

(1/pwD) versus dimensionless cumulative production based ondrainage area (QDA) will result in a straight line with an

intercept of 1/2during boundary dominated flow.3 pwDandQDAare defined as:

])()([)(

1

1422

1

wfiwD pmpmtqT

kh

p =

........................(5)

=

)()([

)()([5.4

wfi

i

i

iiDA

pmpm

pmpm

hAp

GzTQ

..........................(6)

During the transient flow period the drawdown history can beused to estimate reservoir flow capacity and completion

this study follows below.

The accuracy of any bottomhole pressure calculation is

dependent on the quality of the input data. The largest

component of pressure drop in a well is normally thehydrostatic pressure constituent, which is dependent on oil,

gas, and water specific gravities, as well as the ratios of eachfluid phase relative to the other phases (GOR, WOR, GLR,

etc).

For multiphase flow, the pressure drop correlations develop

their character from the manner in which the fluid densitygradient is determined. The typical results from a number of

standard correlations for oil and gas producers are shown in

Figs. 1 and 2. These graphs depict the results of 16 flowcorrelations (refs. 4-22) which have been published in theliterature. For reference, Brill23provides further discussion of

these methods, their accuracy and applicability.

For the purpose of this paper, the Hagedorn and Brown16

correlation was used as the basis for simulation of the oil

cases. This method was chosen because the Hagedorn and

Brown method typically predicts pressure gradients that fall

near the midrange value of the solutions offered by all of the

pressure correlations. In other words, the Hagedorn andBrown method provides a consistent response of better than

average accuracy. Using the Hagedorn and Brown methodallows the effect of predicted pressures greater and less than

the actual pressure to be evaluated with production analysis.

For the gas case, the method proposed by Reinicke, et al.21

was used. This method was developed for gas wellsproducing free water.

Simulation Cases (Synthetic Performance)

Three simulation cases were constructed and used as control

sets to test the sensitivity of the production analysis results dueto the errors introduced in the bottomhole pressure estimates

from different multiphase flow correlations. In all cases the

well is in the center of the simulation grid. The gas case uses

a square simulation grid this case includes a hydraulicfracture. The oil cases (unfractured wells) are modeled using

a radial grid. Table 1 presents the reservoir parameters

common to all cases and Table 2 presents the specific

parameters for each case.

Simulation Case 1

Simulation case 1 is the case of a hydraulically-fracturedwell

in a low permeability gas reservoir. The simulation modelwas initialized with a flow capacity of 2 md-ft and an in-place

gas volume of 1,868 MMscf. For this case, the gas production

rate was controlled by setting a maximum rate of 5 000


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SPE 102488 3

Table 1 Model Parameters

Parameter Value Unit

Formation top, 10,000 ft

Initial reservoir pressure 5,000 psiaAverage porosity 25 percent

Net pay 40 ftAverage water saturation 30 percent

Reservoir temperature 225 FWater compressibility 3x10-6 1/psiRock compressibility 4.6 x10-6 1/psiWater specific gravity 1.05 g/cc

Oil case PVT properties:Oil gravity 32.7 API

Solution GOR 350 Scf/BblGas specific gravity 0.65 (air = 1)Bubblepoint pressure 2296 psia

Gas case PVT properties:

Gas specific gravity 0.65 (air = 1)

Table 2 Case-Specific Parameters

Case Value Unit

Case 1 - Effective Permeability 0.05 mdCase 1 - Fracture Half Length 200 ft

Case 1 - Fracture Conductivity 500 md-ftCase 2 - Effective Permeability 0.05 mdCase 3 - Effective Permeability 5 md

The "rate-cumulative production" plotting technique was usedto estimate the effective drainage volume for a given well.

This technique was found to be very accurate as the resulting

calculated volume was within 1 percent of the actual volume.

The reservoir flow capacity was estimated to be 1.83 md-ft(using type-curve matching), where this result is within 10

percent of the actual value. Figures 3 and 4present the "typecurve" matches for this case.

The flow rates and tubing pressures obtained from the

simulation model were used to calculate the flowing

bottomhole pressure responses for the well based on industry

accepted multiphase flow correlations. Sixteen different

correlations were used to estimate the flowing bottomholepressure for the well. The new (bottomhole) pressure

estimates were then used to estimate the flow capacity and

effective drainage volume for the well.

The production analysis results for each correlation are

summarized in Table 3. Most of the correlations yielded

acceptable errors in the estimate of flow capacity and in-place

volumes. For the purposes of this work, an unacceptable erroris considered to be an error in excess of 10 percent.

C l ti lti i t th 10 t i i

In general, if the multiphase flow correlation overestimates the

bottomhole pressure, then the estimated flow capacity will

also be high. The slope of the flowing bottomhole pressure

with time during boundary dominated flow controls the in-place volume estimate. An example of this would be the

Kaya17correlation in Fig. 6. This correlation under predicts

flowing pressures, which results in a large negative error inflow capacity, but this approach accurately predicts effective

drainage volume.

Table 3 Case 1: Tight Gas, Low Water Yield

Correlation

kh

(md-ft)

Error

(percent)

OGIP

(Bscf)

Error

(percent)

Simulation 1.83 -8.5 1.86 -0.4Ansari 1.89 -5.5 1.86 -0.4Aziz 1.89 -5.5 1.86 -0.4Baxendell 2.61 30.5 5.66 203.0

Beggs 1.87 -6.5 1.85 -1.0Chierici 2.17 8.5 2.09 11.9Cornish 1.88 -6.0 1.86 -0.4Duns 1.67 -16.5 1.86 -0.4

Fancher 1.94 -3.0 1.89 1.2Gray 1.89 -5.5 1.86 -0.4Griffith 2.20 10.0 2.04 9.2Hagedorn 1.67 -16.5 1.86 -0.4

Kaya 1.45 -27.5 1.86 -0.4Mukherjee 1.89 -5.5 1.86 -0.4Orkiszewski 2.04 2.0 1.96 4.9Poettmann 2.50 25.0 5.66 203.0

Reinicke 1.89 -5.5 1.86 -0.4

In Case 1 the impact of water yield was also explored to

test sensitivity we increased the water yield to 50 Bbl/MMscf.

Despite the increase in water, the calculated bottomhole

pressures were similar to the previous evaluation as illustratedby Fig. 7.

Simulation Case 2

Simulation case 2 is the case of an unfracturedwell in a low

permeability oil case. The model was initialized with a flow

capacity of 200 md-ft and for this case the oil production was

controlled by setting a maximum oil rate of 500 Bopd and aminimum flowing tubing pressure of 50 psia. As noted

earlier, the Hagedorn and Brown16multiphase flow correlation

was used to construct the tubing performance curves for thissimulation run.

The drainage area was estimated from a plot of dimensionless

rate versus dimensionless cumulative production as described

earlier. Figure 8illustrates the typical shape of the qDdversusQDdplot and we note that the effective drainage area for the

well can only be determined using production analysis after


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4 SPE 102488

time data should not be used to estimate the drainage area for

this well. We also note that, for this analysis, we assumed

that the total system compressibility was a constant based on

the initial pressure condition. This simplifying assumptionintroduced a slight error in the estimated drainage volume of

the well the effective drainage volume based on the

simulated bottomhole pressure was found to be 6.96 MMblsversus an actual value of 7.4 MMbls (i.e., the input volume)

The flow capacity of the well was estimated from type curve

matching the data in the transient flow period, again using acommercially available production analysis program. The

reservoir flow capacity was found to be 208 md-ft or

approximately 4 percent higher than the input value.The flow rates and tubing pressures from the simulation modelwere used to calculate flowing bottomhole pressure for this

well, utilizing industry accepted multiphase flow correlations.

As in Case 1, sixteen different multiphase correlations wereconsidered in this work. The production analysis results for

each correlation are summarized in Table 4.

Table 4 Case 2: Low Permeability Oil Reservoir

Correlationkh

(md-ft)

Error

(percent)

OOIP

(MMstb)

Error

(percent)

Simulation 208 4.0 6.96 -6.3

Ansari 207 3.5 7.89 6.2Aziz 226 13.0 10.45 40.6Baxendell 225 12.5 7.66 3.1

Beggs 232 16.0 8.12 9.3Chierici 262 31.0 9.75 31.2Cornish 158 -21.0 5.11 -31.3Duns 232 16.0 9.05 21.8Fancher 204 2.0 6.27 -15.6

Gray 166 -17.0 6.04 -18.8Griffith 284 42.0 9.05 21.8

Hagedorn 208 4.0 6.73 -9.4Kaya 220 10.0 8.36 12.5Mukherjee 249 24.5 9.05 21.8Orkiszewski 179 -10.5 7.89 6.2

Poettmann 225 12.5 7.89 6.2Reinicke 208 -17.0 6.96 -18.8

Most of the correlations resulted in unacceptable errors (> 10

percent) in the estimate of flow capacity and in-place volumes.

Only the algorithms of Ansari and Fancher provided estimatesof flow capacity that were within 10 percent error. Five

correlations resulted in in-place fluid volume estimates which

were within 10 percent of the input value.

A performance review of the multiphase flow correlationsprovides some insight into these conclusions. The correlations

higher estimated in-place volume. Conversely, the Cornish10

correlation exhibits a steeper slope, which results in a lower

estimate for in-place volume. Figure 10 also illustrates the

previous conclusion for flow capacity the Chierici, et al.correlation over predicts bottomhole pressure and also over

predicts flow capacity, while the opposite is observed for the

Cornish correlation.

Simulation Case 3

Simulation case 3 represents the higher permeability oil case.

The model was initialized with a flow capacity of 2,000 md-ft.For this case the oil production was controlled by setting a

maximum oil rate of 1,500 Bopd and a minimum flowing

tubing pressure of 50 psia. The Hagedorn and Brown16

multiphase flow correlation was again used to construct the

tubing performance curves for the simulation run.

The drainage area was estimated from a plot of dimensionless

rate versus dimensionless cumulative production (i.e., qDdversus QDd). The effective drainage area for the well can be

determined from production analysis after the well has

achieved boundary dominated flow. Boundary dominated

flow was reached in this case after approximately 5 days of

production (a product of the higher formation permeability)Since boundary dominated flow was reached in such a short

time period, the pressures in the model remained relatively

high and well above the bubblepoint pressure. Fig. 11showsthe bottomhole pressure versus rate performance for the16

multiphase flow correlations evaluated. In this case the

results were in better agreement than the results observed inCase 2 because the primary flow regime in the tubing was

single phase liquid.

It should be noted that the flowing bottomhole pressuredropped below the bubblepoint pressure near the end of the

simulation run, which as with the previous case, caused a gasaccumulation in the near well region. This accumulation

causes a change in the late time slope of the dimensionless rate

versus dimensionless cumulative production plot whichcomplicates the analysis of these data, as illustrated in Fig. 12.

For this analysis we assumed that the total system

compressibility was constant, evaluated at the initial pressure

condition. As with Case 2, this assumption caused a slighterror in the estimated drainage volume of the well. The

effective drainage volume based on the simulated bottomhole

pressure was found to be 6.96 MMbls versus an input value of

7.4 MMbls.

The flow capacity of the well was estimated from type curve

matching the data in the transient flow period using a


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SPE 102488 5

Half of the correlations resulted in unacceptable error in the

estimate of in-place volume.

Table 5 Case 3: High Permeability Oil Reservoir

Correlationkh

(md-ft)

Error

(percent)

OOIP

(MMstb)

Error

(percent)

Simulation 1990 -0.5 6.96 -6.3

Ansari 2140 7.0 6.73 -9.4Aziz 2460 23.0 6.96 -6.3Baxendell 1610 -19.5 6.04 -18.8Beggs 2060 3.0 7.20 -3.2

Chierici 2090 4.5 7.66 3.1Cornish 1800 -10.0 5.57 -25.0Duns 1790 -10.5 6.96 -6.3

Fancher 1870 -6.5 6.27 -15.6Gray 1650 -17.5 5.57 -25.0Griffith 2370 18.5 8.36 12.5Hagedorn 1880 -6.0 6.96 -6.3Kaya 1790 -10.5 6.73 -9.4

Mukherjee 1780 -11.0 6.96 -6.3Orkiszewski 2040 2.0 5.80 -21.9Poettmann 1910 -4.5 5.80 -21.9Reinicke 1780 -11.0 5.57 -25.0

Field Example 1

This well is producing from a sandstone reservoir at a depth of15,000 ft with an average porosity of 9 percent, water

saturation of 35 percent, and net pay of 100 ft. The initial

reservoir pressure was 5000 psia. The well was fracture

stimulated upon initial completion, and had an initialproduction rate of approximately 3.0 MMscf/D of wet gas and

120 Bw/D. Typical permeability values for this reservoir

range from 0.01 md to 0.1 md.

No measured bottomhole pressures exist for this well. Two-phase flow correlations were used to estimate the flowing

bottomhole pressure profile for this case and, due to the

condensate and water production from the well, the pressure

correlations resulted in a large variations in the estimatedbottomhole pressures. These results are shown in Fig. 13.

The effective gas permeability obtained using productionanalysis for this case ranged from a low of 0.03 md to 0.2 md

where these values lie with the generally expected range of

permeabilities for this reservoir. The effective fracture halflength ranged from a low of 18 ft for the high permeability

interpretation to a high of 289 ft for the low permeabilityinterpretation. The effective drainage volume obtained from

the normalized pressure plot averaged 1.5 Bscf over all of the

correlations. The results for each correlation are summarizedin Table 6.

Table 6 Field Example 1: Tight Gas

Correlation

kh

(md-ft)

OGIP

(Bscf)

Aziz 4.66 0.64Baxendell 5.16 2.26Beggs 2.70 0.88Chierici 3.97 2.2

Cornish 3.86 1.27Duns 8.16 2.47Fancher 3.00 1.07Gray 5.12 0.94

Griffith 9.15 2.73Hagedorn 4.52 0.89

Mukherjee 5.30 1.26Orkiszewski 18.90 1.49Poettmann 4.38 1.7Reinicke 4.13 1.33

Multiphase flow correlations were used to estimate the

flowing bottomhole pressure profile for the well. Figure 14

illustrates the range of flowing bottomhole pressures

calculated for the well. The effective gas permeability

obtained from production analysis for this well ranged from a

low of 4.5 md to 7.1 md, with and average of 5.6 md. Theeffective drainage volume obtained from the normalized

pressure plot ranged from 1.34 MMbo to 2.91 MMbo and

averaged 1.5 Bscf considering all correlations. The results foreach correlation are summarized in Table 7.

Table 7 Field Example 2: Low Permeability Oil

Correlation

kh

(md-ft)

OOIP

(MMstb)

Aziz 194 2.91

Baxendell 186 2.50Beggs 186 2.91Chierici 222 2.77

Cornish 156 1.38Duns 203 2.29Fancher 203 1.59Gray 163 1.47

Griffith 243 2.68Hagedorn 156 1.57Mukherjee 243 2.77Orkiszewski 163 1.63

Poettmann 186 2.51Reinicke 163 1.58

Observations and Conclusions

1. Multiphase flow correlations that over predict flowingbottomhole pressure also over predict flow capacity. The

converse is true for methods that under predictb h l


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6 SPE 102488

relationship remains important for the correct

determination of in-place volume.

4. The limitations of multiphase flow correlations need to be

recognized so that these correlations can be used properly.Accurate production rates and pressures must be

recorded, as errors in the rates and pressures affect the

material balance of the system, as well as estimates ofbottomhole pressure obtained from correlations. Periodic

flowing pressure surveys are recommended to ensure that

the pressure correlations are properly calibrated. In theabsence of (measured) pressure surveys, the authors offer

the following recommendations for computing/estimating

flowing bottomhole pressures using multiphase flow

correlations:

Gas Wells

Reinicke, Remer, HueniGrayHagedorn and BrownCornish

Oil Wells

Hagedorn and Brown

Duns and RosBeggs and BrillOrkiszewskiKaya

These recommendations are offered only as a guide we

believe that it is helpful to examine the results using

several methods in order to determine a range ofuncertainty.

Acknowledgments

We thank the management of Marathon Oil Company for

permission to print this article. Acknowledgment is due tovarious colleagues for providing production data for the field

cases.

Nomenclature

A = drainage area, ftBo = oil formation volume factor, RB/STB

ct = total compressibility, psi-1

G = original gas in place, Mscfh = reservoir thickness, ft

k = effective permeability to gas, md

m p( ) = real gas pseudo pressure, psi2/cp

m p( ) = m p m pi( ) ( ) , psi2/cp

Np = cumulative oil production, bbl

pwf = bottomhole producing pressure, psia

te = equivalent time oil, days

zi = gas compressibility factor atpi

= porosity, fraction

= viscosity, cp = 3.14159Subscripts

i = initial

g = gas

References

1. Arps, J.J. : "Analysis of Decline Curves", Trans., AIME(1945) 160, 228-47.

2. Palacio, J.C. and Blasingame, T.A.: "Decline-CurveAnalysis Using Type Curves Analysis of Gas Well

Performance Data," paper SPE 25909 presented at the

1993 Rocky Mountain Regional Meeting/LowPermeability Reservoirs Symposium and Exhibition,

Denver, 26-28 April.

3. Agarwal, R.G., Gardner, D.C., Kleinsteiber, S.W. andFussell, D.D.: "Analyzing Well Production Data Using

Combined-Type-Curve and Decline-Curve AnalysisConcepts," SPEREE(October 1999) 478.

4. Ansari, A.M., Sylvester, N.D., Shoham, O., and Brill, J.P.:"A Comprehensive Mechanistic Model for Upward Two-

Phase Flow in Wellbores," paper SPE 20630 presented atthe 65thAnnual Technical Conference and Exhibition, New

Orleans, LA (Sept. 23-26, 1990).

5. Aziz, K.: Ways to Calculate Gas Flow and Static Head,Handbook Reprint from Pet. Eng., Dallas, TX (1963).

6. Aziz, K., Govier, G.W., and Fogarasi, M.: "Pressure Dropin Wells Producing Oil and Gas," J. Cdn. Pet. Tech.

(July-Sept., 1972) 38-48.7. Baxendell, P.B. and Thomas, R.: "The Calculation ofPressure Gradients in High-Rate Flowing Wells," J. Pet.

Tech.(Oct., 1961) 1023-1028.

8. Brill, J.P. and Mukherjee, H.: Multiphase Flow in Wells,Monograph 17, SPE, Richardson, TX (1999).

9. Chierici, G.L., Ciucci, G.M. and Sclocchi, M.:"Two-Phase Vertical Flow in Oil Wells - Prediction ofPressure Drop,"J. Pet. Tech.(Aug., 1974) 927-938.

10.Cornish, R.E.: "The Vertical Multiphase Flow of Oil andGas at High Rates,"J. Pet. Tech. (July, 1976) 825-831.

11.Cullender, M.H. and Smith, R.V.: "Practical Solution ofGas-Flow Equations for Wells and Pipelines with Large

Temperature Gradients," Trans. AIME (1956) Vol. 207,281-287.

12.Duns, H., Jr. and Ros, N.C.J.: "Vertical Flow of Gas andLiquid Mixtures in Wells " Proc 6th World Petroleum


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SPE 102488 7

Two-Phase Flow in Small-Diameter Vertical Conduits," J.

Pet. Tech.(April, 1965) 475-484.

17.Kaya, A.S., Sarica, C., and Brill, J.P.: "Mechanistic

Modeling of Two-Phase Flow in Deviated Wells," SPEProduction and Facilities, (Aug., 2001) 156-165.

18.Mukherjee, H. and Brill, J.P.: "Liquid Holdup Correlationsfor Inclined Two-Phase Flow," J. Pet. Tech. (May, 1983)1003-1008.

19.Orkiszewski, J.: "Predicting Two-Phase Pressure Drops inVertical Pipe,"J. Pet. Tech.(June, 1967) 829-838.

20.Poettmann, F.H. and Carpenter, P.G.: "The MultiphaseFlow of Gas, Oil, and Water Through Vertical Flow

Strings with Application to the Design of Gas Lift

Installations,"Drill. and Prod. Prac.,API (1952) 257-317.21.Reinicke, K.M., Remer, R.J., and Hueni, G.: "Comparison

of Measured and Predicted Pressure Drops in Tubing for

High-Water-Cut Gas Wells," paper SPE 13279 presented at

the 59th Annual Technical Conference and Exhibition,

Houston, TX (Sept. 16-19, 1984).22.Ros, N.C.J.: "Simultaneous Flow of Gas and Liquid as

Encountered in Well Tubing," J. Pet. Tech. (Oct., 1961)1037-1049.

23.Beggs, H.D. and Brill, J.P.: "A Study of Two-Phase Flowin Inclined Pipes,"J. Pet. Tech.(May, 1973) 607-617.


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8 SPE 102488

Fig. 1 Multiphase Flow Correlations Oil

Fig. 4 Sim. Case 1 Rate Cumulative Decline Curve

Effective Drainage Area 40 Acres

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

QDA

1/PwD

Actual

Analytical

Fig. 3 Sim. Case 1 - Type-curve match

0.1

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100

tDA

PwD

orPwD'

Actual PwD

Actual PwD'

Analytical PwD

Analytical PwD'

Infinite Conductivity Fracture in 1 to 1 Rectangular Boundary at 1 year

Match Simulation

Kh = 1.83 md-ft, 2.0 md-ft

Xf = 209 ft, 200 ft

Area= 40 Acres, 40 Acres

Fig. 2 Multiphase flow correlations gas


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SPE 102488 9

Fig. 7 Sim. Case 1 - Water rate sensitivity comparison

Fig. 6 Sim. Case 1 - Multiphase flow Correlation Comparison

0

1000

2000

3000

4000

0 50 100 150 200 250 300 350 400

Time, Days

BottomholePressure,

Psia

Simulation

KAYA

Fig. 8 Sim. Case 2 - Normalized rate/cumulative production

0

0.5

1

1.5

2

0 0.25 0.5 0.75 1

QDd

qDd

Time to BDF Match Simulation

Volume 6.96, 7.4 MMbo

0

1000

2000

3000

4000

0 50 100 150 200 250 300 350 400

Time, Days

BottomholePressure,

Psia

Simulation

Baxendell & Poettman

Chierici

Fig. 5 Sim. Case 1 Multiphase Flow Correlation Comparison


10/11

10 SPE 102488

Fig. 10 Sim. Case 2 - Correlation comparison late time

Fig. 11 Sim. Case 3 Correlation comparison Fig. 12 Sim. Case 3 - Normalized rate vs. comumulative

production

0

0.5

1

1.5

2

0 0.25 0.5 0.75 1

QDd

qDd

Time to BDF Match Simulation

Volume 6.96, 7.4 MMbo

Fig. 9 Sim. Case 2 - Correlation comparison early time


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SPE 102488 11

Fig. 14 Field Case 2 Calculated Bottomhole Pressures

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

0 10 20 30 40 50 60 70

Time, Days

BottomholePressure,

Psia

CHIERICI

CORNISH

FANCHER

Fig. 13 Field Case 1 -- Calculated Bottomhole Pressures

0.0

1000.0

2000.0

3000.0

4000.0

5000.0

6000.0

7000.0

0 20 40 60 80 100 120 140

Time, Days

B

ottomholePressure,

Psia

AZIZ

ORKISZEWSKI

REINICKE

spe 102488 (cox) errors intro multiphase flow cor production anal

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