# ESTIMATION OF COEFFICIENT OF ISOTHERMAL OIL COMPRESSIBILITY FOR UNDERSATURATED RESERVOIR BY CUBIC EQUATION OF STATE

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ESTIMATION OF COEFFICIENT OF ISOTHERMAL OIL COMPRESSIBILITY FOR UNDERSATURATED RESERVOIR BY CUBIC EQUATION OF STATE

ABSTRACT

Evaluation of reservoir performance for petroleum reservoirs require accurate knowledge of the volumetric behavior of hydrocarbon mixtures, both liquid and gaseous. Prior to the evaluation of reservoir performance, coefficient of Isothermal oil compressibility is required in transient fluid flow problems, extension of fluid properties from values at the bubble point pressure to lower pressures of interest and in material balance calculations. The coefficient of isothermal oil compressibility is a measure of the fractional change in volume as pressure is changed at constant temperature. It is usually obtained from reservoir fluid analysis. Reservoir fluid sampling and analysis is often expensive and time consuming operation that cannot be carried out whenever the volumetric properties of reservoir fluids are needed. Hence, engineers resort to correlations developed for estimating fluid properties including the coefficient of isothermal oil compressibility. In this project, a new mathematical model for estimating the coefficient of isothermal oil compressibility based on Soave Redlich Kwong equation of state (EOS) was developed and an Excel based program. Data from four fields were used as case study and the results obtained showed that the new coefficient of isothermal oil compressibility matches closely with the experimentally values. Also, the new correlation was validated with other models and gave the least average absolute relative error range of 2.45 -  5.19 while that of Soave Redlich Kwong EOS is between 21.2 – 27. 7 and Peng Robinson EOS is between 11.8 – 16.5.

Title Page

Certification                                                                                                                                                                    ii

Dedication                                                                                                                                                                 iii

Acknowledgement                                                                                                      iv

Abstract    v

Table of content    vi

List of Tables                                                                                             vii

List of Figures                                                                                            vii   Chapter One: Introduction1

1.1.    Background of study                                                                           1

1.2.    Problem statement                                                                             3

1.3.    Aim of Study                                                                                     3

1.4.    Objectives of Study                                                                         3

1.5.    Significance of work                                                                   3

1.6.    Scope and Limitation of Study                                                     4   Chapter Two: Literature Review                                                                                   5   Chapter three: Methodology                                                                  13

3.1 Derivation of Mathematical Model (New Model) for this Study                                       15

3.2 Simulation run to determine model parameters                             19

3.3 Mixing Rules                                                                                         19

3.4    Characterization of Heavy Petroleum Fractions                                                            20

3.5    Step by Step Calculation Process Using Excel Software                     20

3.6    Other oil isothermal compressibility correlations                                   23

3.7    Error Analysis                                                                                                                     24   Chapter Four: Result and Discussion                                                                              25

4.1    Discussion of Result                                                                                                             27

4.2    Error Analysis                                                                                      30   Chapter Five: Conclusion and Recommendation                                                           32

5.1    Conclusions                                                                                                               32

5.2    Recommendation                                                                                                       32

References                                                                                                          33

LIST OF TABLES

3.1 Model parameters                                                                                                                   24

4.1Compositional input data                                                                                         25

4.2Well ASHA #4678                                                                                                              26

4.3Well ALPHA #2356                                                                                                  26

4.4Well JEKATA #7655                                                                                                 27

4.5 Well REHITA #5556                                                                                                           27

4.6 Well ASHA #4678 error analysis                                                                         30

4.7 Well ALPHA #2356 error analysis                                                                        31

4.8Well JEKATA #7655 error analysis                                                                     31

4.9Well REHITA #5556 error analysis                                                                     31

LIST OF FIGURES

2.1Trube’s pseudo reduced compressibility of undersaturated crude Oils  5

2.2 Coefficients of isothermal compressibility of undersaturated black oils.6

2.3 Coefficient of isothermal compressibility of saturated black oil (mccain, 1988)7

3.1 Project work flow 14

3.2 Algorithms for isothermal oil compressibility estimation using cubic equation of state18

3.3Excel worksheet for oil isothermal compressibility to determine molar volume                    22

4.1 Well ASHA #4678 isothermal compressibility chart28

4.2Well ALPHA #2356 isothermal compressibility chart28

4.3Well JEKATA #7655 isothermal compressibility chart29

4.4Well REHITA #5556 isothermal compressibility chart30

CHAPTER ONE:

INTRODUCTION:

1.1    Background of Study -

Laboratory PVT analysis is used to acquire data that are used in the estimation ofthe isothermal compressibility. Pressure, volume and temperature(PVT) analysis is the determination of the characteristics and behavior of reservoir fluids under various conditions such as pressure, volume and temperature. For example, a constant composition expansion test is performed on gas condensates or crude oil to simulate the pressure-volume relations of these hydrocarbon systems.

The test is conducted for the purposes of determining:

• Saturation pressure (bubble-point or dew-point pressure)

• Isothermal compressibility coefficients of the single-phase fluid in excess of saturation pressure

• Compressibility factors of the gas phase

• Total hydrocarbon volume as a function of pressure

The experimental procedure, involves placing a hydrocarbon fluid sample (oil or gas) in a visual PVT cell at the reservoir temperature and a pressure greater than the bubble-point pressure of the crude oil. At these initial conditions, the reservoir fluid exists as a single-phase liquid. The volume of the oil is allowed to expand as its pressure declines. This volume is recorded and plotted as a function of pressure. If the experimental pressure/volume diagram for the oil is available, the instantaneous compressibility coefficient, co, at any pressure can be calculated by graphically determining the volume, V, and the corresponding slope reservoir temperature and at a pressure in excess of the initial reservoir pressure. The pressure is reduced in steps at constant temperature by removing mercury from the cell, and the change in the total hydrocarbon volume is measured for each pressure decrease.

Reservoir fluid behavior can also be described by an equation of state which can also be used in accomplishing the above objectives hence, an equation of state (EOS) is an analytical expression relating the pressure, P, to the temperature, T, and the volume, V, the term cubic equation of state implies an equation that, if expanded, would contain volume terms to the first, second, and third powers.while the isothermal compressibility coefficient is defined as the rate of change in volume with respect to pressure increase per unit volume, all variables other than pressure being constant, including temperature. Mathematically, the isothermal compressibility, c, of a substance at a point is defined by the following expression (equation 1.1):

Image

For a crude oil system, the isothermal compressibility coefficient of the oil phase, Co, is categorized into the following two types based on reservoir pressure.

1.    At reservoir pressures greater than or equal to the bubble-point pressure (P≥ Pb), the crude oil exists as a single phase with all its dissolved gas still in solution. The isothermal compressibility coefficient of the oil phase, Co, above the bubble point reflects the changes in the volume associated with oil expansion or compression of the single-phase oil with changing the reservoir pressure. The oil compressibility in this case is termed undersaturated isothermal compressibility coefficient.

2.    Below the bubble-point pressure, the solution gas is liberated with decreasing reservoir pressure or dissolved with increasing the pressure. The changes of the oil volume as the result of changing the gas solubility must be considered when determining the isothermal compressibility coefficient. The oil compressibility in this case is termed saturated isothermal compressibility coefficient.

Isothermal compressibility can also be determined from correlations involving API gravity, formation volume factor or compressibility factor or based on the compositional material balance equation.

Several correlations have been developed to estimate the oil compressibility at pressures above the bubble-point pressure, that is, an undersaturated crude oil system. Three of these correlations follow: Vasquez-Beggs’s correlation, Petrosky-Farshad’s correlation, and Standing’s correlation (see chapter two).

1.2 Problem Statement

The sampling of fluid to determine PVT properties such as the measurement of isothermal compressibility has its limitation due to the fact that experimental data from laboratory analysis are seldom available and cannot be taken at every pressure drop due to costs implication, therefore obtaining an accurate PVT behavior of each reservoir fluid encountered will be costly and time-consuming. Hence, in cases when the experimental data are not available, PVT properties such as the isothermal oil compressibility are determined from empirically derived correlations or equation of state. Each of the developed PVT correlations is only applicable to a good degree of reliability only in a well-defined range of reservoir fluid characteristics. This is due to the fact that each correlation is developed based on fluid samples from a restricted geological area with similar fluid composition and API gravity.

1.3 Aim of Study

To developed an excel spreadsheet for estimating undersaturated isothermal compressibility using a modification of Soave Redlich Kwong equation of state.

1.4 Objectives of Study

The objective of this proposed project is to develop a new correlation for undersaturated isothermal compressibility that should be able to minimize time and cost of regular fluid sampling whenever reservoir performance evaluation is carried out on the reservoir as it declines and as well can be used for any geographical area as long the reservoir fluid composition is known or can be evaluated from other sources.

1.5 Significance of Work

The significance of these study find its application in;

⦁    solutions of transient flow problems in the form of the total isothermal compressibility

⦁    well testing analysis applicable in problems of pressure buildup and drawdown

⦁    material balance equation for undersaturated oil reservoirs, to estimate the initial reserve and predict future production.

⦁    modeling well performance (inflow performance relationship) under transient flow conditions for both single phase and two phase reservoir.

1.6 Scope and Limitation of Study

The scope of this proposed project is to develop a mathematical model based on cubic equation of state (a modification of Soave Redlich Kwong, Soave Redlich Kwong and Peng-Robinson equation of state) to determine the isothermal compressibility of reservoirs above bubble point only (undersaturated reservoirs).

The expected limitation of this project is the acquisition of real life field data to validate the new correlation to be developed

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## ESTIMATION OF COEFFICIENT OF ISOTHERMAL OIL COMPRESSIBILITY FOR UNDERSATURATED RESERVOIR BY CUBIC EQUATION OF STATE

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