THE DETERMINATION OF HYDROCARBON RESERVOIR

RECOVERY FACTORS BY USING MODERN MULTIPLE

LINEAR REGRESSION TECHNIQUES

by

RICK L. GULSTAD, B.S.I.E., B.S.

A THESIS

IN

PETROLEUM ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

PETROLEUM ENGINEERING

Anoroved .-O

May, 1995

T 3 ^ ACKNOWLEDGMENTS

Of ^ The author is appreciative of the time that he spent at Texas Tech University working

on the requirements of a Master of Science in Petroleum Engineering.

An acknowledgment of gratitude is owed to Dr. Marion D. Arnold, chairperson of the

thesis committee, for his patience, guidance, and support in allowing for the completion of

this thesis project.

A special thanks is due to Dr. Robert E. Carlile for his interest in establishing a topic

for this thesis, for his willingness to allow the use of the proprietary data required for the

thesis, and for his recommendation of financial support as a graduate student in the

Petroleum Engineering Department.

The author would like to acknowledge Dr. John J. Day for serving on the thesis

committee. Dr. Carlon S. Land and Professor Duane A. Crawford for their wisdom and

professionalism in the Petroleum Engineering field, and to Dr. Thomas A. Langford,

Associate Dean of the Graduate School, for offering his support for the fiilfillment of the

thesis requirements.

TABLE OF CONTENTS

ACKNOWLEDGEMENTS ii

LIST OF TABLES v

LIST OF FIGURES vi

NOMENCLATURE vii

CHAPTER

I. INTRODUCTION 1

II. BACKGROUND: THE STATISTICAL MODEL 3

Least Squares Formulation . ." 4

Criteria for Choice of Best Model 9

Prediction Criteria 9

Analysis of Residuals II

III. A REVIEW OF LITERATURE 14

Craze and Buckley 14

Guthrie and Greenberger 15

Vietti 15

Arps 16

Barlow, Muskat 17

A.H. van Everdingen 17

API Bulletin D14: A Statistical Study of Recovery Efficiency, First Edition 18

111

API Bulletin D14: A Statistical Study of Recovery Efficiency,

2nd Edition 20

IV. ANALYSIS 27

Analyzing the Data Required to Develop Equations for Recovery Factors 27 Selecting the Statistical Analysis Software

to be Used for Analysis 29

The Developed Equations 32

V. CONCLUSIONS 43

BIBLIOGRAPHY 46

APPENDIX

A. API DATA AND CASEWISE PLOTS OF RESIDUALS 48

B. API SUBCOMMITTEE QUESTIONNAIRE 66

LIST OF TABLES

4-1. Results of Regression Analysis for Sandstone Reservoirs -Water Drive 35

4-2. Results of Regression Analysis for Carbonate Reservoirs -Water Drive 37

4-3. Results of Regression Analysis for Sandstone Reservoirs -Solution Gas Drive 39

4-4. Results of Regression Analysis for Carbonate Reservoirs -

Solution Gas Drive 41

A-1. API Data for Sandstone - Water Drive Reservoirs 49

A-2. API Data for Carbonate - Water Drive Reservoirs 51

A-3. API Data for Sandstone - Solution Gas Drive Reservoirs 52

A-4. API Data for Carbonate - Solution Gas Drive Reservoirs 54

A-5. Casewise Plot of Residuals for Sandstone - Water Drive Reservoirs 55

A-6. Casewise Plot ofResiduals for Carbonate-Water Drive Reservoirs 59

A-7. Casewise Plot ofResiduals for Sandstone-Solution Gas Drive Reservoirs . 60

A-8. Casewise Plot ofResiduals for Carbonate - Solution Gas Drive Reservoirs . . 64

LIST OF FIGURES

2-1. An Example of Least Squares Residuals 6

2-2. Classic appearance: Indicates a random pattern around zero with no detectable trend 12

2-3. Model underspecification: Indicates model should involve curvature - a higher degree term 12

2-4. Funnel effect: Indicates that as the response variable gets large, the

deviations of the residuals from zero become greater 13

4-1. Scatterplot for Sandstone - Water Drive Recoveries 36

4-2. Histogram for Sandstone - Water Drive Recoveries 36

4-3. Scatterplot for Carbonate - Water Drive Recoveries 38

4-4. Histogram for Carbonate - Water Drive Recoveries 38

4-5. Scatterplot for Sandstone - Solution Gas Drive Recoveries 40

4-6. Histogram for Sandstone - Solution Gas Drive Recoveries 40

4-7. Scatterplot for Carbonate - Solution Gas Drive Recoveries 42

4-8. Histogram for Carbonate - Solution Gas Drive Recoveries 42

VI

NOMENCLATURE

Engineering Symbols and Definitions

°API Oil Gravity, °API

B AF Recovery Factor, calculated ultimate recovery in barrels of stock tank oil

per acre foot of net pay, STB/NAF

Bo Oil Formation Volume factor, reservoir barrels per stock tank barrels,

RB/STB

Boa Bo at abandonment pressure, RB/STB

Bob Bo at bubble point pressure, RB/ STB

Boi Bo at initial pressure, RB/STB

D Average subsurface depth, ft

h Net pay thickness, ft

k Rock permeability to air, darcies

ko Rock permeability to oil, darcies

M Ratio of primary gas cap volume to oil column volume, dimensionless

NAF Reservoir pore volume, acre-ft

OOIP Original oil-in-place at initial pressure as reported by operator, STB/NAF

VII

Engineering Symbols and Definitions

OOEP^^^ Calculated value of original oil-in-place at initial pressure, STB/NAF

" 77580(1-^j" OOIP,,,, =

B, (for water drive reservoirs)

Calculated value of original oil-in-place at the bubble point pressure,

STB/NAF

OOIP,^, = 7 7 5 8 0 ( 1 - ^ J

B., (for solution gas drive reservoirs)

Pa Abandonment pressure, psig

Pb Bubble point pressure, psig

Pep Pressure at the end of primary recovery, psig

Pi Initial pressure, psig

Pb/Pa Pressure Ratio, dimensionless

PCT Operator estimate of solution gas drive or water drive contribution to total drive

mechanism, percent

ppm Water salinity, ppm total solids

Rs Solution gas-oil ratio, standard cubic feet per stock tank barrel, SCF/STB

Rsa Rs at abandonment pressure (differential liberation), SCF/STB

via

Engineering Svmbols and Definitions

Rsb Rs at bubble point pressure (differential liberation), SCF/STB

Rsbf Rsat bubble point pressure (flash liberation), SCF/STB

Rsi Rs at initial pressure (differential liberation), SCF/STB

R B Reservoir barrel of oil

R E C Recovery Factor, STB/NAF

RECb Recovery reported by operator at and below Pb, STB/NAF

RECi Recovery reported by operator starting Pi, STB/NAF

R O Recovery calculated from a statistical correlation, STB/NAF

Sw Connate water saturation, fraction

Swi Connate water saturation at kw/ko = 0 .1 , fraction

Sw2 Connate water saturation at kw/ko= 1.0, fraction

T Reservoir temperature, °F

V Dykstra-Parsons coefficient of permeability variance, dimensionless

"^^0 Hydraulic radius, darcies"^

p„ Density of reservoir oil, Ib/ft"

p„ Density of reservoir water, lb/ft"

ix

Engineering Symbols and Definitions

Ap Water-oil density difference at reservoir conditions, Ib/ft (Ap =p„- p,)

X ^ Oil mobility, rock permeability to air / oil viscosity at Pb, darcies/cp,

Oil-water mobility ratio, darcies A ^ = [kji^ I /i_,.]

0

0

l^bp

M.

r^oa

li-oi

M.

r^wi

Porosity, fraction

Oil viscosity at Pb, cei

Oil viscosity, cp

Oil viscosity at Pa, cp

Oil viscosity at Pi, cp

Water viscosity, cp

Water viscosity at Pi,

Probability and Statistical Symbols and Definitions

b^ Linear, unbiased regression estimate for Bo, b^ =y-b^x

b^ Linear regression estimate for Bi, Z), -S^ IS^

BQ Intercept of a regression model

B^ Slope of the regression line

Cp Mallow's Cp,

SSE Cp^—^-{n-2p)

e, Residual or vertical distance from a data point (xi,yi) to a regression line

E(x) Expected value of x

F Test statistic,

SSR/k SSR/k MSR

SSE I {n-k-\) s MSE

Ho The reduced linear regression model is appropriate, Bi=0

Hi The linear regression model is not appropriate, Bi ^O, an expanded model is needed

N (0, (7^) Normal distribution with mean = 0 and variance = a^

n Sample size or total number of data points

k Number of regressor variable

p Number of parameter estimates including Bo, p = k+1

XI

Probability and Statistical Symbols and Definitions

PRESS Prediction Sum of Squares,

PRESS =S(;;,-j),._,)^ =I(^,-,) i=l /=1

Correlation coefficient,

[Z:,(^,-W1"1E:,(.,--)

B^ Coefficient of determination or muhiple correlation coefficient.

1/2

—\2

R' = ^ ^ = -n , R" =SSR/S^.

^^"""' l(y^-yr 1=1

5 Mean squared error, MSE, an unbiased estimate of G ,

r. \2 , Uy.-y>) n-2

SSR Sum of Squares Regression, SS^^^, depicts y - variation produced by

changes in the regressor x, SSR = ^"^, (j), -y)^

SSE Sum of Squares Error or Sum of Squares Residual, SS^^^, chance variation

or variation due to the e, in the model, SSE = 2 " ^ (y. -y^Y

^xx — 2ui=\ \^i ^) r:\2

^^totai "^yy

Xll

Probability and Statistical Symbols and Definitions

S^ S^ = Eili (Xi - x){yi -y)

Sy Standard error of estimate, i.e., the range within which the probability of a

correct estimate is 68%, Sy = v^^

s^ , = X;=,(.y.-y)'=ssR + ssE

X. Symbol used for independent variables

y. Symbol used for dependent variables

y Estimated or predicted value of the dependent variable

y Average value of the dependent variable

Z Summation over a range of data points

a^ True variance, variability of each random variable yi about a true regression line

Xlll

CHAPTER I

INTRODUCTION

The determination of recovery factors for hydrocarbon reservoirs has been a subject of

interest for oil companies since the beginning of the oil industry. When a new oil/gas field

has been created with a discovery well, one of the first concerns of management is an

estimate of fiature earnings from the production of oil and/or gas from a reservoir.' The

fiature earnings are based upon the barrels of recoverable oil/gas as a fraction of the size of

the reservoir referred to as the recovery factor. Proven reserves of crude oil, natural gas,

or natural gas liquids are estimated quantities that geologists and engineers have

demonstrated with reasonable certainty to be recoverable in the fiature from known

reservoirs under existing economic conditions. However, there is a degree of uncertainty

with regard to the extent, recoverability, and economic viability of the proven reserves. A

company's financial position may depend upon the amount of reserves located, the rate at

which the reserves are recovered, and the economic and engineering principles and

strategies incorporated by the company to best facilitate the efficient management of the

oil/gas reservoir.

A knowledge of the extent of the reserves and rates of recovery are beneficial in the

sale or exchange of oil properties. The calculation of recoverable oil also serves as a

guide for reservoir engineers to develop programs to improve primary recovery factors.

Past attempts to develop reasonably accurate recovery factors for hydrocarbon reservoirs

have depended upon the particular reservoir under consideration. A reservoir study that

includes accurately reported values for reservoir parameters of a homogeneous nature can

result in more accurate estimates for recovery factors. However, many factors have

contributed to the calculation of recovery factors that have been erroneous. Data

collection procedures for reservoir parameters, the accuracy of the data being measured,

and the way the data is interpreted will all affect the accuracy of the recovery factors

calculated. Another critical reservoir property to consider is the heterogeneity of the

reservoir. Heterogeneous reservoirs can lead to the preferential depletion of certain

intervals of the reservoir and to significant re-routing of reservoir fluids. Other

considerations to take into account are the techniques used to deplete reservoirs, the

overall size of the reservoir, and the number of parameters used in the calculation of

recovery factors.

The purpose or goal of this study is to re-examine past attempts to develop meaningfiil

equations for recovery factors and to use the previous analysis as a guide to develop

improved equations for recovery factors by utilizing modem statistical, multiple linear

regression models.

CHAPTER II

BACKGROUND: THE STATISTICAL MODEL

Regression analysis has been described as a collection of statistical techniques that are

used as a basis for drawing inferences about relationships among quantities in a scientific

system. Regression has also been interpreted as seeking to discover mathematical

relationships between variables which may be linear or nonlinear.'^ The uses of regression

analysis can include:

1. Prediction,

2. Variable screening,

3. Model specification (system explanation),

4. Parameter estimation.

The results of a regression analysis are only as good as the data that produced them.

This implies that accurate data may resuh in a more meaningfiil regression analysis. The

model should also reflect a tradeoff of simplicity versus "goodness of fit." However, if a

sample size is too small, the analyst cannot compute adequate measures of error in the

regression results.

A simple linear regression model implies a single regressor variable, x, where:

y, = B,+B,x,+e^. (2-1)

The measured response variable y. is also referred to as the dependent variable, BQ is the

intercept, and 5, is the slope of the regression line. The residual, e, , represents the model

error and is composed of measurement errors and other independent variables. The

residual, e,. , also denotes the vertical distance from a point (x., y.) to the true regression

line. Simple linear regression assumptions include: ^

1. The X, are nonrandom, observed with negligible error. Any random variation in x is

negligible compared to the range in which it is measured.

2. The e, are random variables with mean zero and constant variance, O"

(homogeneous variance assumption).

3. A population mean is assumed which implies E(e,) = 0 and E(e,") = a^ (residual

terms are independent and follow a normal distribution ~ N (0, a^)).

4. The e, are uncorrelated from observation to observation.

5. For each x, there is a population of y's.

6. X and y are linearly related.

Least Squares Formulation"

The least squares procedure is designed to provide estimators b^ and b^ for B^ and 5,,

respectively, and the fitted value

y = bo+b,x, (2-2)

so that the residual sum of squares X"=,Cy. ->',)" is minimized. Consequently, b^ and b^

must satisfy

^ E U - ^ o - ^ ^ , ) ' =0 (2-3)

4-l(y.-K-b,x,r =0 (2-4) db, L ,=1 J

to obtain.

n n

«*o+^Z^,=Z.y, (2-5) 1=1 1=1

b, X , + *i E^,' = S.y, , (2-6) 1=1 1=1 1=1

hence,

^=S^IS„ (2-7)

b,=y-b,'x (2-8)

where 5^ = Xil, (^, " ^)(;^, -y) and i^^ = Xil, (^, - ^ ) ' -

An estimate of the error variance, G^, is required.'^ The estimate is used in the calculation

of estimated standard errors for hypothesis testing and plays a major role in determining

the quality of fit and prediction capabilities of the regression model j) = 6g +Z>,x:. An

unbiased estimator of cr , unbiased under the important assumption that the model is

correct, can be formulated:

hy.-y.f s'=^ r— (2-9)

n-2

where s^ is the mean squared error and (n-2) is the error or residual degrees of freedom

(residual degrees of freedom are the number of data points, n, or pieces of information

reduced by the number of parameters estimated [slope and intercept]).

The total observed variability in the dependent variable can be subdivided into two

components:

1. that which is attributable to the regression, and

2. that which is not (residual).

For a particular point, as shown on Figure 2-1, the distance from y. to y (the mean of the

y's) can be subdivided into two parts:

y^-y = iyi-y^) + (y^-y)- (2-10)

The distance from y. (the observed value) to j), (the value predicted by the regression

line), or y. -y., is called the residual from the regression. It is zero if the regression line

passes through the point.

The second component (y. -y) is the distance from the regression line to the mean of

the y's. This distance is "explained" by the regression in that it represents the improvement

in the estimate of the dependent variable achieved by the regression. Without the

regression, the mean of the dependent variable, y, is used as the estimate.

y^b,+b,x

Figure 2-1: An Example of Least Squares Residuals

The total sum of squares can be partitioned into two components as follows:"

S u -yf = S(j>-y)'+Zu -hf (2-11) 1=1 1=1 1=1

I.e.

^^ total — ^^reg + ^^res

where SS^^^ depicts y - variation produced by changes in the regressor x and SS^^^ is

viewed as chance variation or variation due to the e, in the model." Another way to view

the variation is,

Syy= SSR + SSE

Total Variability in Response = Variability Explained by Model + Variability Unexplained

About the Regression Line.

SSR is the variability in y attributed to the linear association between the predictor

variables, and the mean of y. If the regression is significant, then SSR should be large

relative to SSE.

Hypothesis testing often plays a role in determining if a regressor variable, x, really

influences the response variable, y. The hypothesis test under consideration is given by

H,:B,=B,=B,=Q.

H{.B.^O for at least one i, i=l,2,..., k. (2-12)

The null hypothesis, H^, is tested to determine if the regression equation does not

explain a sizable proportion of the variability in the response variable versus the alternative

that i/j does explain a significant proportion of this variability in the regression model.

If HQ is true, the model is reduced to E(y)= B^. Rejection of H^ in favor of //, alleges

that X significantly influences the response in a linear manner.

The F statistics is given by:

SSRIk SSR/k MSR

~ SSEI{n-k-\)~ S^ ~ MSE ^^'^^^

for Ff^ ,n-k-\.

It can be shown that if //Q is true, then this statistic follows an F distribution with k and n-

k-1 degrees of freedom. The test is always to reject H^ for large values of F, normally

when F >4. The correlation is usually terminated when the value of F falls below 4.0.

This procedure is equivalent to a 5% chance that the particular variable to be added is

significant.

When many significance tests are performed, each at a level of, say 5%, the overall

probability of rejecting at least one true null hypothesis is much larger than 5%. To guard

against including any variables that do not contribute to the predictive power of the model

in the population, a small significance level should be specified. In most applications many

variables considered have some predictive power, however small. In order to choose the

model that provides the best prediction using the sample estimates, one must guard against

estimating more parameters than can be reliably estimated with the given sample size.

Consequently, a moderate significance level, perhaps in the range of 10% to 25%, may be

appropriate.

Criteria for Choice of Best Model

Selecting the best regression model from a candidate pool of developed models can be

complicated due to the uncertainty of choosing the terms to be included in the model.

The model builder should consider prior views and prejudices regarding the importance of

individual variables. In addition, the model builder should learn something about the

system from which the data is taken. This may involve nothing more than the knowledge

of a "sign" of a coefficient and can be accounted for by conducting a variable selection or

variable screening exercise.

Prediction Criteria

The goal is to combine "selection of best model" with model validation.

1. Coefficient of determination (i?^)

n

ss SCv, -yf ^'=-^ = t (2-14)

1=1

• Proportion of variation in the response data that is explained by the model

• An increase in R^ does not imply that the additional model term is needed, R^ can

be made artificially high by overfitting (by including too many model terms).

2. Mean squared error : s^ (MSE)

MSE = SSE/(n-k-1) (2-15)

MSE plays an important role in hypothesis testing and confidence bounds. To get

narrow confidence intervals and accurate estimates s^ must be as small as possible

The value R^ can be increased by adding more terms to the model. However, the

addition of unneeded variables may result in an increase in MSE. Thus, the real task

is to balance R^ and MSE

3. PRESS Statistic (Prediction sum of squares)

PRESS ^ ^ ( J . - A - , ) ' J=l

n

= E(ei.-,)' (2-16)

1=1

The PRESS statistic is used with a set of data in which we withhold or set aside the

first observation from the sample and use the remaining n-1 observations to

estimate the coefficients for a particular candidate model. PRESS residuals are true

prediction errors with j5. _. being independent ofy.. The observation y^ was not

simultaneously used for fit and model assessment. The PRESS residuals give

separate measures of the stability of the regression and they can help the analyst to

isolate which data points have a sizable influence on the outcome of the regression. 4. Mallow's Cp

Cp is a measure of total squared error defined as

SSE Cp = —r- - (" - 2/?) where p= k+1 (2-17)

5

where 5" is the MSE for the fiill model and SSE is the sum-of-squares error for a

model with p variables plus the intercept. If Cp is graphed with p. Mallows

recommends the model where Cp first approaches p.

10

Four Criterion (in order of importance with 1 most important):

1. PRESS (want small),

2. Cp (near k+1) (small),

3. MSE, 5* (small-ifamodelisunderspecified, 5" is overestimated),

4. R" (large).

Analysis ofResiduals

As described eariier, residuals describe the error in the fit of the model of each data

point around the regression model. Another way to describe residuals is as what is left

over after the regression model is developed. Information retrieved from residuals can

help detect violations of assumptions in the regression model. Among the phenomena that

can be detected are model underspecification, departure from the homogeneous variance

assumption, existence of suspect data points, departure from normality in the model

errors, and isolated high influence data points.

If the assumptions of linearity and homogeneity of variance are met, there should be no

relationship between the predicted and residual values. The scatterplots depicted in

Figures 2-2, 2-3 and 2-4 describe patterns of residuals versus predicted values. If the

assumptions are met, the residuals are randomly distributed in bans clustered around the

horizontal line through 0, as shown on Figure 2-2. The scatterplot shown in Figure 2-3

indicates that the model is inadequate and that a linear or quadratic term should be

included in the model. In Figure 2-4, the fiinnel effect is an indication that the variance is

11

not constant and that possibly a weighted least squares model should be used with weights

assigned to each variable.

yi

Figure 2-2: Classic appearance: Indicates a random pattern around zero with no detectable trend

yi

Figure 2-3: Model underspecification: Indicates model should involve curvature - a higher degree term

12

e.

yi

Figure 2-4: Funnel effect: Indicates that as the response variable gets large, the deviations of the residuals from zero become greater.

The relative magnitude of residuals are easier to judge when they are divided by

estimates of the standard deviation. The resulting standardized residuals are expressed in

standard deviation units above or below the mean. The standardized residual for case i is

the residual divided by the sample standard deviation of the residuals. Standardized

residuals have a mean of 0 and a standard deviation of 1.

13

CHAPTER III

A REVIEW OF LITERATURE

In 1945, The American Petroleum Institute (API) initiated a data collection process for

the purpose of correlating hydrocarbon reservoir rock parameters and produced fluid

properties with oil recovery factors. An investigation was then conducted by a Special

Study Committee on Well Spacing. Data from 103 oil reservoirs, including 26 solution-

gas drive reservoirs and 74 water-drive reservoirs, were examined from sandstone,

limestone, and dolomite formations. The goal of the Special Study Committee was to

analyze the relationships between oil recovery and well spacing.

Craze and Buckley,* in connection with the special API study, determined that among

those factors which may exert an influence on the recovery of oil, the most important

factors were:

1. The characteristics of the producing formation such as the porosity, permeability,

interstitial or connate water content; and the uniformity, continuity, and structural

configuration.

2. The properties of the reservoir oil, including its viscosity, shrinkage, and quantity of

gas in solution.

3. The operating controls, including control of the available expulsive forces, the rate

of oil production, gas and water production, and the pressure behavior.

4. The well conditions, structural location, and spacing.

14

Those fields which produced primarily under the influence of a water drive mechanism

were expected to yield greater recoveries whereas the remaining fields, which produced

under dissolved-gas or gas-cap drive, were expected to have lower yields.

The analysis of the data concluded that the distance between wells is not one of the

primary physical factors upon which ultimate oil recovery is dependent. However, the

geometry of the reservoirs and the location of the wells with respect to such geometry are

important. Furthermore, the effects of well location and production rate on gas and water

production may also affect the ultimate oil recovery.

An observation proposed by Craze and Buckley* was that for any reservoir a sufficient

number of wells must be drilled adequately to drain the reservoir under the available

conditions and type of drive operative and to supply the desired total rate of production

without excessive individual well rates. This minimum number of wells required is subject

to determination on a sound engineering basis for each reservoir, based upon the reservoir

characteristics and the type of operation. Beyond this minimum number of wells, fijrther

increase of well density will not increase the ultimate oil recovery through shortening the

drainage distance. It is in this sense, and this sense only, that oil recovery has been shown

to be independent of the well spacing.

In a more recent statistical study of Craze and Buckley's water-drive recovery data,

Guthrie and Greenberger,^'* using multiple correlation analysis methods, found the

following correlation between water-drive recovery and five variables which affect

recovery in sandstone reservoirs:

15

/?O = 0.114 + 0.2721ogA: + 0.2565^-0.1361ogiU„ (3-1)

-1.5380-0.00035/;.

For k=1000md, ^,=0.25, ^^ = 2.0cp, 0 = 0.20, and h=10 feet:

i?O = 0.114 + 0.272xlogl000 + 0.256x0.25-0.1361og2

-1.538x0.20-0.00035x10

= 0.642 or 64.2% (of initial stock tank oil).

A test of the equation showed that 50% of the fields had recoveries within ±6.2 recovery

percent of that predicted by Eq. (3-1), 75% were within ±9.0 recovery per cent and 100

per cent were within +19.0 recovery per cent. For instance, it is 75% probable that the

recovery from the example above is 64.2 ± 9.0%.

In a study performed by Vietti'^ it was concluded that the unit recovery figures

calculated for the Mexia-Powell fault-line fields were not based on accurate subsurface or

reservoir information. When corrections were made in the net sand volumes, it was

determined that recovery of oil was practically independent of spacing. Also, Vietti

concluded that data for recoveries from areas within a reservoir (intrafield) should not be

used to substantiate a formula proposed to relate total recovery from a reservoir to the

spacing used to develop it.

Arps^ concluded that the ultimate recovery is found to increase with the oil gravity,

except for the higher solution gas-oil ratios. The type of reservoir rock, as identified by its

relative permeability relationship, appears to have a very pronounced effect on the ultimate

recovery. Sands and sandstones show higher recoveries than limestones and dolomites,

although certain intergranular limestones seem to show a higher theoretical recovery than

16

unconsolidated sand. The recovery from sands and sandstones generally decreases with

increasing cementation and consolidation, while the recoveries from limestones and

dolomites are highest for the intergranular type and lowest for the fracture type porosity.

Bariow"* determined that optimum well spacing for any pool is defined as the calculated

number of acres per well that would give the maximum economic return from the

development of the reservoir as a whole, under the known and assumed conditions used in

the calculations. Neither a general statistical nor theoretical solution applicable to all

pools appears feasible. For these reasons, Barlow recommended that well spacing be

considered an individual pool problem, the solution of which should be based primarily

upon reservoir engineering studies for the pool, and the economic and other factors

applicable to the pool.

Muskat"' found that the ultimate recoveries decrease with increasing oil viscosity.

Because of the predominant effect of the oil shrinkage associated with the liberation of the

gas in solution, the ultimate recovery will decrease with increasing gas solubility.

Increasing gas-cap volumes lead to higher recoveries, although the contribution made by

the gas-cap is small as compared with the oil expulsion by the equivalent amount of

solution gas.

A.F. van Everdingen''* determined that relationships between recovery efficiency,

reservoir characteristics, and fluid characteristics were established for depletion-drive as

well as water-drive reservoirs; however, a spacing/uhimate-recovery relationship could

not be determined, possibly because heterogeneity was not considered.

17

For a depletion drive type there is little or no water present along the flanks of the

structure to expand and help keep up the pressure. For heterogeneous reservoirs, material

balance computations invariably give oil-in-place volumes that are too low because this

method fails to include all portions of the reservoir.

A.F. van Everdingen concluded that for limestone/ dolomite reservoirs, the recovery

efficiency estimated for wide spacing (waterflooding) is barely above the efficiency for

depletion-type reservoirs where secondary recovery is not used. Flooding on 40-acre

spacing is highly inefficient.

API Bulletin D14: A Statistical Study of Recovery Efficiency (1st ed.)' presented

conclusions and equations which evolved from a study undertaken by the API

Subcommittee on Recovery Efficiency in 1956. The subcommittee's assignment was to

study reservoir recovery processes based on actual performance data from producing

fields rather than on theoretical or laboratory data and to develop an empirical correlation

for the prediction of the recovery efficiency.

The study was based on data received after 312 questiormaires were submitted to oil

companies requesting reservoir information. Seventy reservoirs had acceptable accuracy

for the water drive correlation from sandstone reservoirs, where oil reserves were under a

water drive mechanism and invading bottom or edge water was the dominant displacing

medium. Eighty reservoirs were used for solution gas drive correlations, of which 67

were sandstone and 13 were carbonate. The primary drive mechanism was the liberation

of gas from solution.

18

The selected reservoirs were weighted 1, 2, or 3 according to the subcommittee

members' estimates of the quality of the data. A "3" was considered good data, a "2" was

considered adequate data, and a "1" was considered poor data.

For water drive reservoirs:

R0 = 4259 5„.

1.0422

L Mo,

m.0770

[s.] -0.1903

1-0.2159

(3-2)

The multiple correlation coefficient, r = 0.9575, and the standard error of estimate, Sy, i.e.,

the range within which the probability of a correct estimate is 68% and only applies to the

mean of the distribution, was 17.6%.

For solution gas drive reservoirs:

R0 = 3244 0(1-^J

HI.1611

B Ob

10.0979

M, 06 [' J

0.3722 0.1741

^Pa (3-3)

The multiple correlation coefficient, r = 0.9317, and the standard error of estimate, Sy,

was 22.9%.

The correlations show an extremely strong dependence of recoverable oil on the

original oil-in-place. However, other reservoir and fluid parameters, were included in the

correlation since calculations showed a statistically significant increase in the correlation

coefficient when using the "F" test for multiple factor regressions.

API Bulletin D14, 1967' concluded that correlations predict the average value for

recoverable oil for large groups of reservoirs that have similar values of independent

parameters. However, it was observed that the occurrence of a large group of reservoirs

having similar values for oil-in-place does not widely occur.

19

API Bulletin D14: A Statistical Study of Recovery Efficiency (2nd ed.)^ attempted to

improve on the study of oil recoveries by gathering a larger sample of crude oil reservoir

data than what was available in the 1967 API Bulletin D14 Study.' Like the 1967 Study,

the Subcommittee's assignment in the 1984 study (roughly sk times as large) was to study

oil recovery based on actual field performance of producing fields rather than on theory or

laboratory data, and to develop an empirical correlation for the prediction of recovery

efficiency.

The goals of the updating subcommittee work:

1. Test the API Bulletin D14 (1967) correlations on a new, larger data set than that

which was available in the 1967 study.

2. Improve, if possible, the reliability of the Bulletin D14 (1967) correlations by

calculating new coefficients for the independent parameters.

3. Investigate the feasibility of alternative and possibly more usefiil correlations.

A total of 675 questionnaires were submitted to oil companies, where 620 reservoirs

in the U.S. and Canada could be verified to have a dominant drive mechanism of solution

gas or natural water drive and also had a well-defined lithological character, sandstone or

carbonate. The remaining 55 samples were dropped because the data on primary recovery

were lacking, or the primary drive was by gravity drainage or the lithology was ill-defined.

Of the 620 reservoirs for which data was available, 376 reservoirs produced by

solution gas drive and 244 reservoirs produced by natural water drive. The principal drive

mechanism was said to account for at least 75% of the reservoir energy.

20

As a first try to test the Bulletin D14, (1967) correlations, a set of sandstone reservoirs

having a rating of 2 or 3 (adequate or good, respectively) was chosen from the new data

as a pilot sample. A total of 116 solution gas drive sandstone reservoirs (about 40% of

the total) fell into this select sample. The predicted regression equation for recoverable oil

(RO) was:

i?6> = 6533 m-sj B Ob

1.312

M, 06

0.0816

[s.] 0.463 Pb-P.

o a

0.249

(3-4)

Where the coefficient of correlation, r = 0.74, and the standard error, Sy,^ = 0.27. Despite

a fairiy good fit, this correlation was thought to be of little value for reliably predicting

recoverable oil from a crude oil reservoir.^

The work already described suggested that original oil-in-place is the only parameter

that has a statistically significant relationship to recoverable oil. The Subcommittee chose

to continue to search for a regression relationship which might show that other parameters

in addition to the original oil-in-place had a significant effect on recoverable oil and

recovery efficiency.

A multi-variable, stepwise, linear regression program was employed that successively

sought to add independent variables, which represent reservoir data in a stepwise manner,

so as to progressively increase the quality of the fit of the regression equation to the data.

This program was used to develop correlations on a selected group of 112 solution gas

drive reservoirs consisting of 26 variables.

21

Solution Gas Type A - Unrestricted Linear Equation:

BAF = 557.5+.0373I 77580(1-5'J

B ob -242.S\n(PCr)-l01.4

M ob

+253.7(k) + U5.6\n(° API)+ 0.2\52(OOIP)

r = 0.8586, r '= 0.7372, 5,., - 66.13 STB/NAF.

(3-5)

Solution Gas Type B - Restricted Linear Equation:

5^F = 900.9-83.0 IW 77580(1-5J

B ob

+ 5.83W LM, ob

+ 24.53 ln(5J

+6.86 Inl + 0.11851 77580(1-5J

B ob -107.031

M ob

+ 2\9.6{k,)

-200.l9\n(PCT) + \2.570ln(°API)+.2405iOOIP)

r = 0.8635, r^= 0.7456, Sy,^ = 66.35 STB/NAF.

Solution Gas Type C - Unrestricted Logarithmic Equation:

ln(5.4/^) =-5.32058+1.4877 ln((90/P) + 0.4562 ln(5,) + 0.2251n

+0.0198(°ylP/) +0.4562(F)

r = 0.7820, r = 0.6115, Sy,^ = 0.4982 = 64.6%.

(3-6)

(3-7)

Solution Gas Type D - Restricted Logarithmic Equation:

ln(5^F) =-0.9057-0.267 In 77580(1-^J

B ob

f Ir \ f, N-.08881n

vMo6y f.0371n

v^.

+1.6251n(OOIP)+0.510441n(V)-4.274(5,)

r = 0.785L r^= 0.6163, 5„. =0.5001 = 64.9%.

(3-8)

22

Bulletin D14 (1967) Type Four-Term Logarithmic Correlation Equation:

'77580(l-5j" ln(5/4F) =-3.48538+1.35461n

B ob + 0.09166 In

\.^ob J

(n\ +0.41211n(5^)+0.069961n

BAF = 569\ m-sj B ob

1.3546

M, ob

yBo,

0.09166 / \ 0 0®56

/ r t \0.4121 £b_ K-^w) p

(3-9)

(3-10)

r = 0.7491, r^= 0.5612, Sy,^ = 0.5257 = 69.4%.

All the correlations that were developed showed the overwhelming influence of the

original oil-in-place, either calculated at the bubble point or as cited by the operator at

initial conditions. In many trials, the program chose a reservoir parameter more than once

(in different groupings), and in some cases specified the inclusion of a parameter in a sense

opposite to intuition, empirical observations, or fluid flow theory.

A similar attempt was made to develop an improved correlation for a subset of the

water drive reservoirs. This sample was of a very high quality in that all the data

necessary for the correlations were explicitly available in all the completed questionnaires.

Of the available 117 water drive samples, 58 had to be rejected because at least one of the

29 data variables to be considered was missing from the sample.

Water Drive Type A - Unrestricted Linear Equation:

5^F = -3957.3 + 0.756(OO/P) + 55.611n(PJ + 749.81n(PCr) + 39.561n(\J (3-11)

r = 0.9042, r ' = 0.8176, 5 _ = 134.8 STB/NAF.

23

Water Drive Type B - Restricted Linear Equation:

A4F = - 3 726.8+ 21.979 In 77580(1-^J

B ob + 49.188 ln( A„_ J +19.077 ln(5 J

-73.244 In + 0.7083(OO/P) + 786.43 ln(PCT) - 71.4594 ln(k) (3-12)

r = 0.909, r ' = 0.8263, Sy,^ = 135.4 STB/NAF.

Water Drive Type C - Unrestricted Logarithmic Equation:

In 5^F =-6.21253+0.00066(OO/P) + 0.11221n(PJ +1.25351n( p e r )

+0.08084 ln ( \^ ) + 0.77501n(OO/P)

r = 0.8855, r ' = 0.7841, Sy.^ = 0.2912 = 33.8%

Water Drive Type D - Restricted Logarithmic Equation:

ln(5.4F) =-90.3765-1.2537 In B„.

+ 0.10381n(\J + 0.16691n(^^)

fp^ .15011n -7

(3-13)

-25.9011n(PC7)+1.93861n(a9/P)-0.2772(PC7)+0.0008(OO/P) v^.y

r = 0.8976, r = 0.8057, S^., = 0.2844 = 32.9% (3-14)

Bulletin D14 ( 1967) Type Four-Term Logarithmic Correlation

'77580(1-5 j " ln(BAF) = -1.98288 +1.24009 In B„

+ 0.09321n(\J

-0.2450 In fp\

yP^j + 0.06143 ln(5^) (3-15)

24

BAF = 9\72\ 5„

1.24009

0 .0932/r . V 0.06143 (\J°°' '(^J°-/ p YO-2450

P„ (3-16)

r = 0.8348, r^ = 0.6969, Sy.^ = 0.3418 = 40.7%.

The overall quality of the 59 samples turned out to be excellent, and it was concluded that

the quality of the water drive correlation is better than that of the solution gas drive

correlation.^ The original oil-in-place in the reservoir was the dominant term, although not

at the same level of significance as in the case of the solution gas drive subset.

The results confirmed that an adequate predictive correlation for the recovery of crude

oil could not be achieved. The dominant independent parameter is the original oil-in-

place. The foregoing investigation suggests that consideration should be given to a much

simpler form of correlation that would be based only on original oil-in-place.

The four correlations did a better job of removing variance from the data than did the

Bulletin D14 (1967) type. Simpler correlation forms were chosen that would be based

solely upon calculated values of original oil-in-place. In this study no statistically valid

correlation could be found between oil recovery and definable reservoir parameters

(revalues < 0.1). By breaking the total data sample into subsets based on geographical

area (state), lithology (sandstone or carbonate), and producing mechanism (solution gas

drive or water drive), the quality of the correlations was improved. However, the

improvement was still inadequate for the resulting correlations to be of value as tools for

predicting the recoverable oil from any one reservoir.

25

The impact of older, less accurate measurement techniques on such a study as this can

be appreciated when it is recognized that about 75% of anticipated ultimate oil production

from presently known U.S. fields will be derived from fields discovered prior to 1951.

The calculated average recoveries in a single geological trend are significant.

Comparison of these calculated averages shows substantial recovery efficiency differences

between reservoirs with different indigenous drive mechanisms, with the application of

different secondary recovery techniques, and in different producing areas.

The subcommittee, with completion of this study, concluded that a reliable statistical

correlation cannot be achieved for the prediction of recovery and/or efficiency for

individual reservoirs based on the readily definable and available reservoir parameters. An

important factor, reservoir heterogeneity, could not be readily defined. The accuracy of

definable parameters such as porosity and initial water saturation is limited by the quality

•y

of measurement techniques available at the time of discovery and development.

26

CHAPTER IV

ANALYSIS

Analyzing the Data Required to Develop Equations for Recovery Factors

The data used for this study came from the American Petroleum Institute on a

proprietary and confidential basis. The same database had been used for the development

of API Bulletin D14, Statistical Analysis of Recovery Efficiency (2nd ed.).^ The data was

accumulated as a result of 675 oil field questionnaires being submitted to the API

Subcommittee. Of the original 675 hydrocarbon reservoirs, 620 reservoirs were known to

have a dominant drive mechanism, solution gas or natural water drive. The 620 reservoirs

under consideration also had a well-defined lithological character, including sandstone and

carbonates. Solution gas drive was the primary drive mechanism for 376 reservoirs and

244 reservoirs produced by natural water drive. The principal drive mechanism accounted

for at least 75% of the reservoir energy in API Bulletin D14, Statistical Analysis of

Recovery Efficiency (2nd ed.).^ The original parameters included in the questionnaires are

listed in Appendix B.

For the purposes of this analysis, the data selected for analysis varies from the 1984

study. Four discernible categories of data were grouped for analysis. Tables A-1 thru A-4,

with the principal drive mechanism, either water drive or solution gas drive accounting for

at least 70%) of the reservoir energy:

27

1. Water drive for sandstone reservoirs -128 samples

2. Water drive for carbonate reservoirs - 30 samples

3. Solution gas drive (at the bubble point) for sandstone reservoirs -139 samples

4. Solution gas drive (at the bubble point) for carbonate reservoirs - 70 samples

Ultimately, 367 samples from the original 675 samples were grouped for analysis. The

rest of the samples were dropped for many reasons including lack of a fijll set of data. Of

the original 34 parameters, as listed in the Appendix B, twenty-one parameters were

chosen to be included as part of a statistical analysis. In addition, grouped parameters

such as the calculated original oil-in-place, OOIP,^,, the hydraulic radius, -Jk /0, the oil

mobility, A„, the oil-water mobility ratio, A ^ , Pi/Pa, and Pt/Pa were included for analysis.

The parameters cited in this section are defined in the Nomenclature section. The sample

data is listed in Tables A-1 thru A-4 of Appendix A for the 4 categories listed above. The

selected parameters for Solution Gas Drive reservoirs and for Water Drive reservoirs are

as follows:

Solution Gas Drive parameters: h net,0, k,A , Sw, T, °API, Pi, Pb, Pep, Pb/Pa, /x ,,

^bp. ^oa, M . , Rsi, Rsb, Rsa, Boi, Bob, Boa, O O I P , R E C , OOIP,^,

Water Drive parameters: h net, 0 , k, v A / 0 , Aj, , Sw, T, °API, Pi, Pb, Pep, Pi/Pa,

M., M6. , M.. M., Rsi, Rsb, R«, Boi, Bob, Boa, OOIP, REC, OOIP,,,

28

The dependent variable in each case, was the Recovery Factor, REC, expressed in

STB/NAF. The remainder of the variables represent the independent variables. In

addition, the natural logarithm. In, of each independent variable was included for analysis.

Selecting the Statistical Analysis Software to Be Used For Analvsis

The primary statistical analysis software package employed was SAS for DOS'^ with

SPSS for Windows Release 6.0'^ serving as a secondary statistical analysis software

package. Multiple linear regression analysis, part of both software packages, was used to

generate equations. The Stepwise procedure, included in both SAS and SPSS, and the

REG regression procedure, included in SAS, were used to choose the parameters to be

used in the developed models.

The Stepwise procedure is usefial when there are many independent variables to choose

from in developing a regression model. The Stepwise procedure is most helpfiil for

exploratory analysis because it can give insight into the relationships between the

independent variables and the dependent or response variable. However, the Stepwise

procedure is not guaranteed to give the "best" model for your data, or even the model

with the largest R^ And no model developed by these means can be guaranteed to

represent real-world processes accurately.

In the Stepwise procedure variables are added one by one to the model. The F statistic

for variable screening must be significant at the SLENTRY = 0.10 for variables to enter

the model. After a new variable is added, the Stepwise method looks at all the variables

29

already included in the model and removes any variable that does not produce an F

Statistic significant at the SLSTAY = 0.15. Only after this check is made and the

necessary deletions accomplished can another variable be added to the model. The

Stepwise process ends when none of the variables outside the model has an F Statistic

significant at the SLENTRY = 0.10 and every variable already included in the model is

significant at the SLSTAY = 0.15, or the Stepwise procedure ends when the variable to be

added to the model is the variable just deleted from the model.' To prevent the same

variable from being repeatedly entered and removed, the value for SLENTRY must be

less than the SLSTAY value.

The REG procedure fits least-squares estimates to linear regession models. The REG

procedure uses the principle of least squares to produce estimates that are the best linear

unbiased estimates under classical statistical assumptions. The REG procedure:

a. handles multiple MODEL statements,

b. can use either correlations or crossproducts for input,

c. prints predicted values, residuals, studentized residuals, and confidence limits, and

can output these items to an output SAS data set,

d. prints special influence statistics,

e. produces partial regession leverage plots,

f estimates parameters subject to linear restrictions,

g. tests linear hypotheses,

h. tests multivariate hypotheses,

i. writes estimates to an output data set,

30

j . writes the crossproducts matrix to an output SAS data set,

k. computes special collinearity diagnostics.

The Stepwise procedure will generate Cp, MSE, R^ and the F statistic as output data.

Unlike the Stepwise procedure which continues until the F criteria for parameter entry and

removal are satisfied, the REG procedure relies on a MODEL statement to completely

specify the dependent variable, in this case the Recovery Factor, and the selected input

independent variables. The REG procedure will generate the PRESS value in addition to

the MSE, R' , and the F statistic. Recall from Chapter II, that the goal of this analysis is to

select the generated equations that attempt to optimize the four criterion:

1. Small PRESS value,

2. Small Cp value,

3. Small s^

4. Large R^

The relative size of the PRESS statistic, Cp, MSE, and R can be used to develop a

more statistically correct model. In addition, a more complete analysis of residuals is

necessary for the detection of violation of assumptions. For example, residuals must be

independent of the independent variables. Most importantly, the parameters included in

the regression models developed should make sense from a petroleum engineering

perspective.

31

The Developed Equations

Tables 4-1 through 4-4 show the values for the PRESS, s^ Cp, and R statistics for

variable lists for each of the 4 categories of reservoir type/drive mechanism under

consideration. The original variable lists for solution gas drive and water drive samples

were reduced to the variables shown in Tables 4-1 through 4-4 by using the Stepwise

procedure and arriving at those variables that would most influence the equations for the

Recovery Factor. At that point, the goal was to arrive at the selected equation for the

Recovery factor by optimizing the values for the PRESS, s , Cp, and R statistics.

For Sandstone Reservoirs with a water drive mechanism. Table 4-1 shows that the

selected equation for Recovery Factor includes the lowest values for the PRESS and s

statistics and a R value that is very close to the highest value for R at 0.675. Note that

the selected equation does not include a value for Cp The reason for this is that values for

Cp are only generated for the Stepwise procedure in the SAS package and the values of

the F statistic had halted the Stepwise procedure once the variable, Uoi had been entered.

However, as shown in Table 4-1, the values for the PRESS and s statistics continued to

decrease until the variable, T, had been entered into the equation as part of the REG

procedure, which was run independently of the Stepwise procedure. Intuitively, the

selected equation appears to optimize the PRESS, s , and R statistics.

Figure 4-1 represents a scatterplot of standardized predicted values for Recovery

Factors versus Standardized Residuals. A scatterplot may suggest what type of

mathematical ftmctions would be appropriate for summarizing the data. Many fiinctions

including parabolas, hyperbolas, polynomials, and trignometric fiinctions, are usefiil in

32

fitting models to data. The resulting standardized predicted values and standardized

residuals are expressed in standard deviation units above or below the mean after dividing

each estimate by its standard deviation. In Figure 4-1, the residuals appear to be randomly

distributed around the horizontal line through 0, which is an indication that the assumption

of linearity has not been violated. Figure 4-2, a histogram of standardized residuals, gives

an indication of the normality of the model. For the Sandstone Reservoirs with a water

drive mechanism, the appearance of the histogram in Figure 4-2, gives an indication of

not quite having a true normal distribution based upon two exaggerated peaks and the

straggling negative values indicated.

For the Carbonate Reservoirs with a water drive mechanism. Tables 4-2 indicates the

selected equation from a group of representative variables that will best influence the

Recovery Factor. Note that the chosen equation does not include the lowest values for

the PRESS and s statistics, however the improvement in the model by adding the In API,

term does not appear to be significant in terms of the PRESS, and s , and R statistics.

Plus the value for Cp is not available for this step when adding In API. Figure 4-3 appears

to indicate a somewhat random pattern for residuals which is an indication of linearity in

the model. However, Figure 4-4 indicates a pattern that is not quite representative of a

normal distribution.

For Sandstone Reservoirs with a solution gas drive mechanism. Tables 4-3 indicates

the selected equation which was primarily arrived at by choosing the model with the

lowest value for the PRESS statistic. Figure 4-5 hints at the appearance of a fiinnel shape

which is an indication of heterogeneous variance. Possibly another linear term or a

33

quadratic term should have been included in the model specification. The histogram in

Figure 4-6 does not seem to represent a true normal distribution. There is an exaggerated

clustering of residuals toward the center and a straggling tail toward large positive values.

For Carbonate Reservoirs with a solution gas drive mechanism. Table 4-4 displays the

selected equation from a group of candidate models. As shown in Table 4-4, the selected

equation best represents a compromise of the PRESS, s , Cp, and R statistics. The fiinnel

shape in Figure 4-7 hints at a heterogeneous variance and the histogram displayed in

Figure 4-8 shows a somewhat exaggerated shape which does not quite represent a normal

distribution.

Figures A-1 through A-4, located in Appendix A, show casewise plots of residual

outliers for each of the reservoir/drive type categories. The casewise plots include the

actual value, predicted value, and residual values for the Recovery Factors. In addition,

plots displaying the standardized residual values in absolute value form, can give an

indication of outliers that have a more pronounced negative or positive value away from

the true value of the Recovery Factor.

34

TABLE 4-1

Results of Regression Analysis for Sandstone Reservoirs - Water Drive

VARIABLES PRESS C. R'

OOIP OOIP, In «,, OOIP, In M„ , In Sw

OOIP, lnw„„lnSw,Pep

OOIP,lnw„„lnSw,Pep,Mo,

OOIP,lnw„„lnSw,Pep,Mc/."o. O O I P , In W„,, In Sw, Pep, Mo,. Ka^ OOIPcalc

OOIP, In M,,, In Sw, Pep, Mo,. u,,. OOIPcaic, T OOIP, In u^,. In Sw, Pep,Mo,' ^'oa^ OOIPcaic,T, lnM„ OOIP, In M„„ In Sw, Pep, Mo,» "o., OOIPcaieJ, InjU,., K.

612415 516999 488808 480756 592984 631796 511343 468687 469107 530460

47834 39794 37322 36374 35547 35573 35324 35156 35426 35639

44.46 0.531 17.30 0.613 9.76 0.640 7.49 0.652 5.69 0.663 * 0.665 * 0.670 * 0.675 * 0.675 * 0.676

* No Cp available for this step

** The selected equation

Equation for Sandstone Reservoir - Water Drive:

REC = -274.94 + 0.44{OOIP) - 56.70 ln( Mo J -119.451n(5J + 0.04(P,^)

-4.73(Mo,) + 4.38(Mo J + 0.24(OO/P,^,) - 0.88(r) (4-1)

35

3-

_ 2-

I

§ -21

I.

_B • D A

- 3 - 2 - 1 0 1 2 3

Regression Standardized Predicted Value

Figure 4-1: Scatterplot for Sandstone - Water Drive Recoveries

Std. Dev=.98 Mean = 0.00 N = 127.00

^ ^ / ^ /> ^ j ^ >. '^^. ^^. <e. '^^. <?. ^^ ^^ ' ^ '^^ - ^ ^^ 0 \ r -3- '''^ ^^ ^^ ''^ "^

Regression Standardized Residual

Figure 4-2: Histogram for Sandstone - Water Drive Recoveries

36

TABLE 4-2

Results of Regression Analysis for Carbonate Reservoirs - Water Drive

VARIABLES PRESS C„ R'

M,,,lnPOR M,,,OOIP,lnPOR

M,,, OOIP, Mo, M,,, OOIP, Mo„h

M,,, OOIP, Mo„h, In Pi M,^,OOIP,Mo„h,lnPi,lnBoa Mfc , OOIP, Mo,, h. In Pi, In Boa, InM^ Mfcp, OOIP, ,„ h. In Pi, In Boa, In M^ , In T M, , OOIP, ^i,^, h. In Pi, In Boa, InM^ ,, In T, In API M, , OOIP, 11^^, h. In Pi, In Boa, InM* , In T, In API, InM M,,, OOIP, ii„,, h. In Pi, In Boa, InM*,, In T, In API, InMO„ T

129857 3489

167065 2639

67091 2059

79911 1804

75616 1576

84787 1431

57523 1251

** 41179 938

40762 862

:,. 54226 885

:„,,T 85884 888

82.66

55.52

25.37

30.67

24.42

20.85

16.69

9.73 *

*

*

0.709

0.788

0.835

0.861

0.883

0.898

0.915

0.939

0.946

0.947

0.950

* No Cp available for this step

** The selected equation

Equation for Carbonate Reservoir - Water Drive:

PEC =-177.26-57.11(M^ ) + 0.34(OO/P) + 33.90(M^.) + 0.17(A)-86.831n(P.)

+283.27 ln(P^^) + 75.19ln(M^ ) +175.89 \n(T)

(4-2)

37

1 2 3

Regression Standardized Predicted Value

Figure 4-3: Scatterplot for Carbonate - Water Drive Recoveries

Std. Dev = .86 Mean = 0.00 N = 31.00

-1.75 -1.25 -.75 . - .25 .75 1.25 1.75 -1.50 -1.00 -.50 0.00 .50 1.00 1.50 2.00

Regression Standardized Residual

Figure 4-4: Histogram for Carbonate - Water Drive Recoveries

38

TABLE 4-3

Results of Regression Analysis for Sandstone Reservoirs - Solution Gas Drive

VARIABLES PRESS 5' C. R'

OOIP OOIP, In Rsi OOIP, In Rsi, A„ OOIP,lnRsi, A„,lnA„ OOIP, In Rsi, A„, InA,, In h OOIP, In Rsi, \ , lnA„, In h. Pep OOIP, In R,i, A„, lnA„, In h. Pep, In Sw OOIP, In Rsi, A„ lnA„, In h. Pep, In Sw, M, OOIP, In Rsi, A„, lnA„, In h. Pep, In Sw, M,, h

839061

810117

931935

878871

860577

880048

876873

900825

928625

6643

6383

6210

6006

5905

5894

5839

5859

5860

17.64

13.35

10.85

7.83

6.85 *

*

*

*

0.649

0.666

0.678

0.691

0.699

0.702

0.708

0.709

0.712

* No Cp available for this step

** The selected equation

Equation for Sandstone Reservoir - Solution Gas Drive:

REC = -264.59 + 0.34(OO/P) + 29.371n(P„.) - 0.06(AJ + 10.701n(AJ -12.64 ln(A)

(4-3)

39

s (A

TO

I J fej)

2 -2

-4i -2

Regression Standardized Predicted Value

Figure 4-5: Scatterplot for Sandstone - Solution Gas Drive Recoveries

Std. Dev = .98 Mean = 0.00 N = 139.00

-3.00 -2.00 I I 2.00 3.00 4.00 5.00 -2.50 -1.50 -.50 .50 1.50 2.50 3.50 4.50 5.50

Regression Standardized Residual

Figure 4-6: Histogram for Sandstone - Solution Gas Drive Recoveries

40

TABLE 4-4

Results of Regression Analysis for Carbonate Reservoirs - Solution Gas Drive

VARIABLES PRESS C„ R'

k. In OOIP k. In OOIP, M„

k. In OOIP, M., Pi k. In OOIP, M„, Pi, API

k. In OOIP, M., Pi, API, InM„ k, In OOIP,M., Pi, API, InM^, Sw k. In OOIP, M., Pi, API, InM., Sw, lnM6;, k. In OOIP, M., Pi, API, InM., Sw, InM ,, k. In OOIP, M., Pi, API, InM., Sw, InM,,, k, In OOIP, M., Pi, API, InM., Sw, InM.,, In Pi, In API, A„

**

In Pi

In Pi, In API

In Pi, In API, A.

126140

99878

95371

84296

78966

78787

75165

75257

81212

83746

89666

1560

1094

1027

912 849 816 778 766 775 788 792

67.98

28.56

23.62

14.89

10.65

8.91

6.95 *

*

*

*

0.491

0.648

0.675

0.715

0.739

0.753

0.768

0.776

0.777

0.777

0.780

* No Cp available for this step

** The selected equation

Equation for Carbonate Reservoir - Solution Gas Drive:

P£:C =-711.29 + 0.30(A:) + 46.64 ln(00/P) + 420.18( M.) +0.0 l(i^.) +2.19( v4P/)

-190.00ln(M.) +79.32(5,)

(4-4)

41

I -o

.i I

5

4

3i

2

1

Oi

-1 '

-2

-31

"• ._! o _ °a

- 2 - 1 0 1 2 3 4

Regression Standardized Predicted Value

Figure 4-7: Scatterplot for Carbonate - Solution Gas Drive Recoveries

std. Dev = .95 Mean = 0.00 N = 70.00

-1.50 -.50

Regression Standardized Residual

Figure 4-8: Histogram for Carbonate - Solution Gas Drive Recoveries

42

CHAPTER V

CONCLUSIONS

A statistical analysis of oil field data was conducted using modem, multiple linear

regression techniques to develop equations that best describe the recovery of oil from

hydrocarbon reservoirs in terms of applicable reservoir rock properties and reservoir fluid

properties. As a result of the analysis the following conclusions were made:

1. All four of the developed equations for carbonate/sandstone reservoirs with a water

drive/solution gas drive mechanism show a common dependence upon the original

oil-in-place. In addition, all four developed equations include a combination of

reservoir rock properties such as OOIP, h, Sw, k, T, Pep, and Pi, and reservoir fluid

properties such as API gravity, Uw, Uoa, Uoi, Ubp,Boa, Rsi, and A„. There appears to be

no bias towards either reservoir rock properties or reservoir fluid properties.

2. The equation for carbonate reservoirs with a water drive mechanism appears to

represent the best model if the values for R = 0.939 and Cp= 9.73 are considered

accurate measues of fit of the regession line. The value for R represents the

proportion of variance in the response data that is explained by the model. The

value for R^ can range from 0 to 1, and when an upper bound is achieved the fit of

the model is supposed to be perfect, i.e., all residuals are zero. However, the

correlation between a statistically valid relationship and empirical data is not an

absolute science. It is important to keep in mind that only realistic oil field

parameters should be used as independent variables for entry into a regression

43

model. In addition, only realistic oil field parameters with the appropriate +/- sign

should show up in the regression models for REC recovery factors.

3. The R^ values for carbonate reservoirs are higher than those for sandstone

reservoirs. This result may be due to the respective sample sizes of the carbonate

reservoirs versus the sandstone reservoirs. The sample sizes for the carbonate

reservoirs are smaller, 30 samples and 70 samples, versus sandstone reservoirs, 128

samples and 139 samples. One might conclude that smaller sample sizes may reduce

the variability in geologic trends and the variablity in indigneous drive mechanisms.

4. It has been ascertained in prior studies that the heterogeneity of a reservoir plays an

important role in characterizing a reservoir. The heterogeneous effects of a

reservoir can lead to preferential depletion of certain intervals of the reservoir and to

fluid by-passing or channeling of fluid.^ There is not a well defined parameter to

account for the heterogeneous nature of most reservoirs. Consequently, the

importance of heterogeneity is left unaccounted for in the developed equations.

5. It is important to keep in mind that in developing statistical relationships from

empirical data, that the validity of the developed equations relies heavily on the

accuracy of the reported input data. Much of the data requires planning to obtain

accurate data and much of the data must be obtained during the initial stages of

production. Well log data provides information concerning the net pay thickness,

the porosity, water and oil saturations, and the lithology of the reservoir. Core data

can indicate permeability, water-oil contacts, gas-oil contacts, and porosity

correlation with well logs. Drill stem tests can indicate the initial pressure of the

44

reservoir and can provide fluid samples for determination of oil viscosity and gas in

solution. However, it must be pointed out that 75% of anticipated ultimate oil

production from current oil fields in the United States has been derived from oil

fields produced prior to 1951 ^ It is questionable whether reservoir rock and

reservoir fluid properties resulting from less than modem techniques provide

accurate data for analysis.

6. It can be concluded from this analysis that reliable equations for recovery factors,

expressed in units of STB/NAF, cannot be derived due to: the inability of statistical

derived equations to account for the characteristics of oil field properties; the

heterogeneous nature of reservoirs; and the inaccuracies in reporting oil field data in

terms of reservoir rock properties and reservoir fluid properties.

45

BIBLIOGRAPHY

1. API Bulletin D14: A Statistical Study of Recovery Efficiency, American Petroleum Institute, Production Dept., Dallas, TX, October, 1967.

2. API Bulletin D14: Statistical Analysis ofCmde Oil Recovery and Recovery Efficiency, 2nd Ed., April 30, 1984.

3. Arps, J.J. and Roberts, T.G.: "The Effect of Relative Permeability Ratio, the Oil -Gravity, and the Solution Gas - Oil Ratio on the Primary Recovery from a Depletion Type Reservoir," Trans., AIME (Petroleum Development and Technology), 1955, 204,120.

4. Bariow, W.H. and Berwald, W.B.: "Optimum Oil - Well Spacing," Drilling and Production Practices, API, 1945, 129 .

5. Craft, B.C. and Hawkins, M.F., Jr.: Applied Petroleum Reservoir Engineering. Prentice-Hall, Inc., Englewood Cliffs, NJ, 1959.

6. Craze, R.C. and Buckley, S.E.: "A Factual Analysis of the Effect of Well Spacing on Oil Recovery," Drilling and Production Practices, API, 1945, 144 .

7. Draper, N.R. and Smith, H.: Applied Regression Analysis. 2nd ed., John Wiley & Sons, Inc., New York, 1981.

8. Guthrie, R.K. and Greenberger, M.H.: "The Use of Multiple Correlation Analysis for Interpreting Petroleum Engineering Data," Drilling and Production Practice, API, 1955, 130.

9. Mihon, J.S. and Arnold, J.C; Probability and Statistics in the Engineering and Computing Sciences. McGraw-Hill, Inc., New York, 1986.

10. Muskat, M. and Taylor, M.O.: "Effect of Reservoir Fluid and Rock Characteristics or Production Histories of Gas Drive Reservoirs," Trans., AIME (Petroleum Development and Technology), 1946, 165,78.

11. Myers, Raymond H.: Classical and Modem Regression with Applications, PWS Publishers, Boston, MA, 1986.

12. SAS Institute Inc. SAS User's Guide, Version 5 Edition. SAS Institute Inc., Cary, NC, 1985.

46

13. SPSS Inc. SPSS for Windows: Base System User's Guide, Release 6.0. SPSS Inc., Chicago, IL, 1993.

14. van Everdingen, A.F. and Kriss, H.S.: "A Proposal to Improve Recovery Efficiency," Journal of Petroleum Technology, July, 1980.

15. Vietti, W.V, MuUane, J.J., Thomton, O.F., and van Everdingen, A.F.: "The Relation Between Well Spacing and Recovery," Drilling and Production Practices, API, 1945, 160.

16. Walpole, R.E. and Myers, R.H.: Probability and Statistics for Engineers and Scientists. 3rd ed., MacMillan, Inc., New York, 1985.

47

APPENDIX A

API DATA AND CASEWISE PLOTS OF RESIDUALS

48

aX

•SS

SS

SS

?;

o n 5 9 **

ss

ts

I?

ss

fs

ss

ss

il

ss

sg ss

49

ss

" S i , ^ ^ <o

3283 q q * c

^?

SK

ss

o o _, in m

o rw '^ o O o

50

51

?sg! id

M S S 3 •> S 15 f^ B n S V

iSS iiu ?sss? Si^S

;^» =

3»SS sss;

3 S 3 3

sss;

ssss 8 S S ! 8SS S 3 S °

ss l^S'c iSSf

igSs «g 0 S S f

") S ^ P

3 S S S ; s i ! ssss ;sss

s.Iss SRSi ? 3 S r 3S§

:aa-; S s 8

3 8 8 ?|S jQSQ 8 S | SS

o[o o

ssii Isss s i i i § 1

is iiS^

' IS ! ?sss SS

3 O O T II jo p c

2SS RSf

J S S ! i S S 3 O O O C

ss CS » lA C - m m ct c 3 o 6 b c

: s s °

1 S S g

2SS » 0 9

•^i".'

i S S c • g s ;

i S S SS sss SSi BSSS-SP

S | | i i^S!:

n rt R p

52

3 = S 3 OS v ^

sss 3gS|

issi

^m 3S$; 0 « K t

;S

s«

rS

S$

SS

ss S3i

51? ss RS S9

^ R Z; '

si s = S8 S?St SB s

ss ss ss

ss ss S'S

S3

o o c

? S 5 sR

q 3 1 :SS a S c ss ss

SSRI SS SS

ss

isli iQS si

ss ss

3SS S3S ss ss ss 8 ss

S3

SS

= g 8SS SS

SS

2S§I SSS5 SS

ss

S3 SS SS

SS si ss

53

SSRIP ssqsi

m

§1

? S 3 f

n fy f^ r lo -- r -• - m e T-' "- N •

ils CN cp N C

n ^ M **

?SS5

Sf^Sjp

S S

ss

i s

ss

ss

?s

5 S

§3

SS

i i i

K t S I

s i

I o o <

sss '

sS

ss

ss

ss

38S

SS

ss

ss

ss

b rt S tf

SsiS

sg

3^iS N !0 5 P n « n p

S3

^Si

a m

§ss

o o o

steg O D

S S i

3|0 O

31

3jq o

88

s?s

3 3 8

SS

SS

SS 3 3 S

88 33 S S S SJS s; S 3 ss S3 S S

ss ss ss

ss §s§ S3

s ^ ^ ss ss 'M^

s ss SIS n ss

ss ss sss sss 3 S

Is g | S

5 3 V o o d d

sg Ss 8si S|3 SS cc » n

SS

?«¥ 3 S SS

54

TABLE A-5

Casewise Plot of Standardized Residuals for Recovery for Sandstone - Water Drive Reservoirs

*: Selected M: Missing

-3.0 Case 0-

1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . 11 . 12 . 13 * 14 . 15 . 16 . 17 . 18 . 19 . 20 . 21 . 22 . 23 . 24 . 25 . 26 . 27 . 28 . 29 . 30 . 31 . 32 . 33 . 34 . 35 . 36 . 37 . 38 . 39 . 40 .

0.0 3.0 ....: :0 if

* 4:

* *

* *

* *

* *

*

* *

* * * * *

* * *

* * *

* * * *

* >l<

* *

* *

* *

* *

REC 272 277 214 508 550 1171 546 1050 1100 723 866 750 30 750 716 540 488 342 158 472 779 266 510 169 475 493 530 840 530 260 650 950 811 832 500 977 750 950 907 600

*PRED 445.3414 461.0330 224.2535 334.6689 562.9594 864.1768 627.6613 802.8022 730.8635 756.3516 722.9178 844.8293 772.4172 432.8843 536.0936 633.6479 627.2442 385.5628 132.7254 602.9663 585.8587 375.9276 520.2207 19.7492 664.1577 635.1686 422.1305 871.6572 559.6481 198.3540 797.0754 945.5267 674.1718 447.1120 633.3676 857.7368 944.5610 753.9877 698.4053 930.8678

*RESID -173.3414 -184.0330 -10.2535 173.3311 -12.9594 306.8232 -81.6613 247.1978 369.1365 -33.3516 143.0822 -94.8293 -742.4172 317.1157 179.9064 -93.6479

-139.2442 -43.5628 25.2746

-130.9663 193.1413 -109.9276 -10.2207 149.2508 -189.1577 -142.1686 107.8695 -31.6572 -29.6481 61.6460

-147.0754 4.4733

136.8282 384.8880 -133.3676 119.2632 -194.5610 196.0123 208.5947 -330.8678

55

TABLE A-5

Continued

*: Selected M: Missing

-3.0 Case 0;, 41 . 42 . 43 . 44 . 45 . 46 . 47 . 48 . 49 . 50 . 51 . 52 . 53 . 54 . 55 . 56 . 57 . 58 . 59 . 60 . 61 . 62 . 63 . 64 . 65 . 66 . 67 . 68 . 69 . 70 . 71 . 72 . 73 . 74 . 75 . 76 . 77 . 78 . 79 . 80 .

0.0 3.0 : :0 REC *

* * * * * *

* *

* *

* *

* *

* *

* * *

* * * *

if

if

* if

if

* * *

* * *

* * *

if

*

990 750 395 158 166 125 135 160 480 350 122 992 670 602 300 500 375 760 640 696 700 670 733 174 884 679 302 561 857 666 150 280 648 1052 1109 760 823 1370 803 902

*PRED 849.4677 778.0951 496.1569 375.4157 396.4246 185.7515 273.4408 12.6260

410.5751 382.9216 335.2825 877.4215 591.4684 700.1981 647.4726 580.5522 503.2535 575.6958 730.1478 857.5582 553.6892 597.9166 672.1609 138.8771 674.9075 718.6046 454.7302 626.9371 646.2236 699.6898

1.6586 277.3991 888.5483 1029.6628 889.2495 792.0440 736.0478 1151.0738 685.7419 883.2668

•RESID 140.5323 -28.0951

-101.1569 -217.4157 -230.4246 -60.7515

-138.4408 147.3740 69.4249 -32.9216

-213.2825 114.5785 78.5316 -98.1981

-347.4726 -80,5522

-128.2535 184.3042 -90.1478

-161.5582 146.3108 72.0834 60.8391 35.1229

209.0925 -39.6046

-152.7302 -65.9371 210.7764 -33.6898 148.3414 2.6009

-240.5483 22.3372

219.7505 -32.0440 86.9522

218.9262 117.2581 18.7332

56

TABLE A-5

Continued

*: Selected M: Missing

-3.0 Case O 81 . 82 . 83 . 84 . 85 . * 86 . 87 . 88 . 89 . 90 . 91 . 92 . 93 . 94 . 95 . 96 . 97 . 98 . 99 . 100 . 101 . 102 . 103 . 104 . 105 . 106 . 107 . 108 . 109 . 110 . Ill . 112 . 113 . 114 . 115 . 116 . 117 * 118 . 119 .

0.0 3.0 ....: :0 *

* *

*

*

.* * *

* *

* * * * *

* *

* * _

if

if

* if

* if

* *

*. * * * *

* *

*

* *

REC 723 1470 1085 445 144 259 822 173 187 125 1370 950 742 617 774 1094 1039 805 385 333 827 1367 584 461 335 115 497 300 296 401 400 904 696 596 219 334 314 783 224

*PRED 911.7763 1359.1200 1008.1640 443.3106 540.1430 372.9498 777.9776 406.9700 183.5665 226.3167 912.1947 870.9796 792.7705 511.3484 710.9853 822.9776 1019.2143 834.5402 589.0119 446.7865 796.8566 1149.2327 474.3977 576.8188 470.0958 105.1242 417.3544 349.7075 364.6350 316.6082 204.1817 837.1041 402.1700 525.3423 245.4374 568.5788 930.7691 901.8945 481.6981

*RESID -188.7763 110.8800 76.8360 1.6894

-396.1430 -113.9498 44.0224

-233.9700 3.4335

-101.3167 457.8053 79.0204 -50.7705 105.6516 63.0147

271.0224 19.7857 -29.5402

-204.0119 -113.7865 30.1434

217.7673 109.6023 -115.8188 -135.0958

9.8758 79.6456 -49.7075 -68.6350 84.3918 195.8183 66.8959

293.8300 70.6577 -26.4374

-234.5788 -616.7691 -118.8945 -257.6981

57

TABLE A-5

Continued

*: Selected M: Missing -3.0 0.0 3.0

Case O 120 121 122 123 124 125 126 127

* *

) REC 517 460 476 1081 862 762 271 446

*PRED 505.3086 366.3782 511.8608 785.4618 985.9161 650.5633 114.4618 366.4995

*RESID 11.6914 93.6218

-35.8608 295.5382 -123.9161 111.4367 156.5382 79.5005

58

TABLE A-6

Casewise Plot of Standardized Residuals for Recovery for Carbonate - Water Drive Reservoirs

*: Selected M: Missing

-3.0 Case 0'

1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . 11 . 12 . 13 . 14 . 15 . 16 . 17 . 18 . 19 . 20 . 21 . 22 . 23 . 24 . 25 . 26 . 27 . 28 . 29 . 30 . 31 .

0.0 3.0 : :(

*

* *

* * * *

*

* * *

* *

* +

* >i<

* * * * :tc

* *

if

* if

•

:): *

*

3 R E C 304 209 29 31 127 336 177 398 121 174 102 54 185 147 244 102 56 53 106 64 168 296 228 35 215 59 44 203 50 161 382

*PRED 311.2061 157.4821 34.5811 33.9789 129.5446 360.5542 166.8606 417.0464 122.8702 160.8255 103.3678 105.3025 124.9923 97.1633 245.3976 80.6533 56.4496 89.5838 110.1015 76.0955 181.4231 301.1304 225.2339 43.5104 199.2766 102.2810 41.3849 176.4889 62.3466 197.8542 345.0132

*RESID -7.2061 51.5179 -5.5811 -2.9789 -2.5446

-24.5542 10.1394 -19.0464 -1.8702 13.1745 -1.3678

-51.3025 60.0077 49.8367 -1.3976 21.3467 -0.4496

-36.5838 -4.1015 -12.0955 -13.4231 -5.1304 2.7661 -8.5104 15.7234 -43.2810 2.6151

26.5111 -12.3466 -36.8542 36.9868

59

TABLE A-7

Casewise Plot of Standardized Residual for Recovery for Sandstone - Solution Gas Drive Reservoir

*: Selected M: Missing

-3.0 Case 0- ,

1 . 2 . 3 . 4 . 5 . 6 . 7 . 8 . 9 . 10 . 11 . 12 . 13 . 14 . 15 . 16 . 17 . 18 .* 19 . 20 . 21 . 22 . 23 . 24 . 25 . 26 . 27 . 28 . 29 . 30 . 31 . 32 . 33 . 34 . 35 . 36 . 37 . 38 . 39 . 40 .

0.0 3.0 ....: :0 * *. * *

* * * * *

* *

* *

* * * *

* if

* *

* if

* * * * * * if

* *

if

* *

.* * * *

REC 150 147 78 330 138 211 58 144 190 174 452 644 55 563 274 120 98 287 297 314 224 102 107 100 84 137 229 209 226 69 90 80 208 277 289 226 231 254 168 361

*PRED 218.0545 168.2701 121.0637 310.1787 227.6713 258.5792 67.9097 190.1253 294.615 171.1811 549.3436 459.6378 54.2717

295.8889 292.8821 143.3883 82.0363

549.9019 397.9083 275.7174 310.1107 50.2156 151.4153 148.1242 76.5641 111.9415 205.7410 239.2588 224.7840 108.8012 108.4522 143.1604 225.1768 210.2846 169.3928 289.2064 187.8214 297.9253 202.6155 276.1981

*RESID -68.0545 -21.2701 -43.0637 19.8213 -89.6713 -47.5792 -9.9097

-46.1253 -104.6159

2.8189 -97.3436 184.3622 0.7283

267.1111 -18.8821 -23.3883 15.9637

-262.9019 -100.9083 38.2826 -86.1107 51.7844 -44.4153 -48.1242 7.4359

25.0585 23.2590 -30.2588 1.2160

-39.8012 -18.4522 -63.1604 -17.1768 66.7154 119.6072 -63.2064 43.1786 -43.9253 -34.6155 84.8019

60

TABLE A-7

Continued

*: Selected M: Missing

-3.0 Case 0

41 . 42 . 43 . 44 . 45 . 46 . 47 . 48 . 49 . 50 . 51 . 52 . 53 . 54 . 55 . 56 . 57 . 58 . 59 . 60 . 61 . 62 . 63 . 64 . 65 . 66 . 67 . 68 . 69 . 70 . 71 . 72 . 73 . 74 . 75 . 76 . 77 . 78 . 79 . 80 .

0.0 3.0 : :0 REC

* * * *. * * * * * * * * 4<

* * * * *

•

* * *

* *

* *

+

* *

* if

* :<I

* s|<

if

* * *

160 148 69 65 79 112 159 100 49 94 98 183 133 60 79 103 92 496 738 344 655 87 36 93 206 82 233 296 425 424 110 100 16 132 100 186 141 193 103 159

*PRED 180.9081 202.6804 161.1579 96.8056 167.7226 186.1938 208.7337 138.6859 104.3941 111.8978 45.3907 106.4240 51.5218 87.1523 1.8205

76.2111 109.7598 489.7952 439.7442 249.2042 488.3628 129.5868 -21.4619 129.3012 127.1003 173.2389 101.7527 368.7682 494.8224 436.7509 219.7799 152.8457 -39.8988 137.1015 107.5079 89.8405 177.4160 174.1740 84.8227 105.4778

*RESID -20.9081 -54.6804 -92.1579 -31.8056 -88.7226 -74.1938 -49.7337 -38.6859 -55.3941 -17.8978 52.6093 76.5760 81.4782 -27.1523 77.1795 26.7889 -17.7598 6.2048

298.2558 94.7958 166.6372 -42.5868 57.4619 -36.3012 78.8997 -91.2389 131.2473 -72.7682 -69.8224 -12.7509 -109.7799 -52.8457 55.8988 -5.1015 -7.5079 96.1595 -36.4160 18.8260 18.1773 53.5222

61

TABLE A-7

Continued

*: Selected M: Missing

-3.0 0.0 3.0 Case 0 81 . 82 . 83 . 84 . 85 . 86 . 87 . 88 . 89 . 90 . 91 . 92 . 93 . 94 . 95 . 96 . 97 . 98 . 99 . 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119

: : :0 REC * * * * *. * * .* * * * * *

if

if

* +

* +

* *

•

* if

if

if

if

*

*. if

* *

if

* *

* * *

*

78 28 23 153 80 148 245 140 129 141 165 613 908 214 250 460 437 68 420 190 77 98 137 230 127 96 100 82 100 410 250 115 113 91 33 94 212 120 200

*PRED 154.3066 -14.1867 -6.9713

142.9837 95.9747 135.5230 222.0590 120.8729 119.7561 98.3720

101.0303 446.2168 445.2585 144.5236 251.8798 386.5380 383.3416 85.2303

364.1063 313.6192 10.9605

106.1239 163.3449 171.2522 85.5171 43.9020 141.2861 55.2761 122.6354 307.4070 381.4460 111.5010 190.3780 160.3233 24.4947 197.3689 223.6524 117.3380 141.1261

*RESID -76.3066 42.1867 29.9713 10.0163 -15.9747 12.4770 22.9410 19.1271 9.2439

42.6280 63.9697 166.7832 462.7415 69.4764 -1.8798 73.4620 53.6584 -17.2303 55.8937

-123.6192 66.0395 -8.1239

-26.3449 58.7478 41.4829 52.0980 -41.2861 26.7239 -22.6354 102.5930 -131.4460

3.4990 -77.3780 -69.3233 8.5053

-103.3689 -11.6524 2.6620

58.8739

62

*: Selected

-3.0 Case 0

120 . 121 . 122 . 123 . 124 . 125 . 126 . 127 . 128 . 129 . 130 . 131 . 132 . 133 . 134 . 135 . 136 . 137 . 138 . 139 .

M: Missing

0.0

* *

*. *.

* *

* *

* 4:

* *

* *

* 4:

* +

* Hi

3.0 0 REC

180 100 133 133 40 69

321 184 86

125 270 334 189 137 36 49 83

138 87

256

*PRED 217.6512 187.9361 166.1547 162.1074 93.0909

114.0609 247.4450 116.2972 120.8734 122.9948 442.3120 263.6407 166.3037 275.3985 132.8537 135.8937 80.0447

116.6772 130.0138 301.1736

TABLE A-7

Continued

*RESID -37.6512 -87.9361 -33.1547 -29.1074 -53.0909 -45.0609 73.5550 67.7028 -34.8734

2.0052 -172.3120

70.3593 22.6963

-138.3985 -96.8537 -86.8937

2.9553 21.3228 -43.0138 -45.1736

63

TABLE A-8

Casewise Plot of Standardized Residuals for Recovery for Carbonate - Solution Gas Drive Reservoirs

*: Selected M: Missing

-3.0 0.0 3.0 Case 0: : :C

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

* *

* *

* *

* .*

* *

* *

* * *

* *

* *

* *

* *

* * *

* *

* *

* *

* *

* *

* *

* *

» REC 100 59 72 38 35

5 202

83 42

179 45 56 28 38 66

120 27 45 28 32 37 67

106 34 39 79 24 35 54 86 62 26 31 40

189 67 83

0 40

0

*PRED 96.8111 80.0479 61.1195 44.8266 53.7623 13.0041 85.8645 76.8859 88.9708

205.6039 53.9831 71.0653 26.5219 58.0922 85.0978

111.8471 67.3707 36.5761 37.1682 20.3582 37.4712 52.8948 81.2997 93.2102 33.6294 76.7430 36.4734 44.3826 72.9166 70.9060 51.5285

8.3695 36.1302 48.2212

214.1711 65.2241 99.8726 30.3159 33.2319 41.0538

*RESID 3.1889

-21.0479 10.8805 -6.8266

-18.7623 -8.0041

116.1355 6.1141

-46.9708 -26.6039

-8.9831 -15.0653

1.4781 -20.0922 -19.0978

8.1529 -40.3707

8.4239 -9.1682 11.6418 -0.4712 14.1052 24.7003 -59.2102

5.3706 2.2570

-12.4734 -9.3826

-18.9166 15.0940 10.4715 17.6305 -5.1302 -8.2212

-25.1711 1.7759

-16.8726 -30.3159

6.7681 -41.0538

64

TABLE A-8

Continued

*: Selected M: Missing

-3.0 Case 0-

41 . 42 . 43 . 44 . 45 . 46 . 47 . 48 . 49 . 50 . 51 . 52 . 53 . 54 . 55 . 56 . 57 . 58 . 59 . 60 . 61 . 62 . 63 . 64 . 65 . 66 . 67 . 68 . 69 . 70 .

0.0 3.0 : :(

*

* :«: *

* * * *

* *

* *

* *

* *

* * * * *

* *

* M<

* He

:<< *

*

0 REC 80

6 84 52

187 88 54 67 62 80 70 28 27 44 81

119 78 68 32 49 32 51 45 41 19 94

123 80

344 163

*PRED 81.0448 -2.5008 81.8383 39.5612

221.6547 73.7701 36.1657 61.3132

103.5174 81.7288 77.7412

9.4204 64.1250 27.5519 79.4032 99.2475 66.4225 60.4938 19.6151 39.2228 16.6411 68.0607 33.7403 51.3763 -1.6858 91.6445 90.5566 95.4159

257.9726 118.9183

*RES1D -1.0448 8.5008 2.1617

12.4388 -34.6547 14.2299 17.8343

-41.5174 -1.7288 -7.7412 18.5796

-37.1250 16.4481 1.5968

19.7525 11.5775 7.5062

12.3849 9.7772

15.3589 -17.0607 11.2597

-10.3763 20.6858 2.3555

32.4434 -15.4159 86.0274 44.0817

65

APPENDIX B

API SUBCOMMITTEE QUESTIONNAIRE

66

INFORMATION INCLUDED ON THE API SUBCOMMITTEE QUESTIONNAIRE

1. STATE

2. GEOLOGIC AGE

3. FORMATION TYPE:

A. SANDSTONE: consolidated, semiconsolidated, unconsolidated, clean, silty, calcareous

B. CARBONATE: granular, vuggy, oolitic, other

C. STRATIGRAPHY: massive, stratified, lenticular

D. FRACTURED: yes, no, unknown

4. h-GROSS: oil and gas, ft

5. h-NET: oil and gas, ft

6. WELL SPACING, acres

7. 0 , POROSITY, %

8. kair, md

9. Sw, %

10. Sg, Gas Saturation, %

11. Wettability: water, oil, unknown

67

12. Solution gas-oil ratio, SCF/BBL

13. Gas Gravity

14. T, Reservoir temperature, °F

15. API Gravity, °^P/

16. Salinity, ppm

17. Initial Pressure, psig

18. Bubble Point Pressure, psig

19. Reservoir Pressure at the End of Primary, psig

20. Initial Oil Viscosity, cp

21. Oil Viscosity at Bubble Point, cp

22. Oil Viscosity at Abandonment of Primary, cp

23. Water Viscosity, cp

24. Initial Gas-Oil Ratio, SCF/BBL

25. Gas-Oil Ratio at the Bubble Point, SCF/BBL

26. Gas-Oil Ratio at Abandonment of Primary, cp

68

27. Initial Oil Formation Volume Factor, BBL/STB

28. Bubble Point - Oil Formation Volume Factor, BBL/STB

29. Oil Formation Volume Factor at Abandonment of Primary, BBL/STB

30. TYPE DRIVE: (Totals 100%)

A. Solution Gas, %

B. Gas - Cap, %

C. Gravity, %

D. Water, %

31. Induced Recovery? yes, no

If yes. Type: Gas , Water

32. lOP, BBL/NAF

3 3. Estimated Primary Recovery, BBL/NAF

34. Year of Initial Production

69

PERMISSION TO COPY

In presenting this thesis in partial fulfillment of the requirements for a master's degree

at Texas Tech University, I agree that the Library and my major department shall make it

freely available for research purposes. Permission to copy this thesis for scholarly

purposes may be granted by the Director of the Library or my major professor. It is

understood that any copying or publication of this thesis for financial gain shall not be

allowed v^thout my fiirther written permission and that any user may be liable for

copyright infiingement.

Agree (Permission is granted.)

Student's Signature Date

Disagree (Permission is not granted.)

Student's Signature Date