Theoretical Justifications for Rate Decline Trends in Solution-Gas Drive Reservoirs, and Reservoir Property Estimation Using Production Data

Theoretical Justifications for Rate Decline Trends in Solution-Gas Drive Reservoirs, and Reservoir Property Estimation Using Production Data.

ABSTRACT

Rate decline analysis is an essential tool in predicting reservoir performance and formation property estimation.

The use of historical production data to predict future performance is the focus of the empirical domain of decline analysis while the theoretical domain focuses on the use of such data to estimate formation properties.

A number of attempts have been made to establish the theories of rate decline in solution- gas drive reservoirs. Such attempts have established the theoretical decline exponent b as a function of formation properties.

However, none of the attempts have established a direct link between the empirical and theoretical domains of decline analysis. The purpose of this work is to establish the missing link and deploy such link in reservoir property estimation.

In  this  work,  a  functional  relationship  (equation)  between  the  empirical  (b_enp)  and  the theoretical (b_th) was derived; based on the definition of a new parameter known as time- weighted average of the theoretical exponent.

This new parameter was found  to be related to the empirical exponent, b_enp thus establishing the link. Theoretical justifications for the ranges of values of the theoretical exponent were also offered.

Consequent upon the establishment of the relationship, this work developed a new improved technique for estimating reservoir permeability. The technique was applied to a number of cases and was found to yield excellent estimates of permeability even for an heterogeneous reservoir.

Sensitivity analyses were performed on the results. The work also investigated non-Darcy flow effects on decline parameters. Lastly, this work provided mathematical justification for the existence of the hyperbolic family of curves in solution-gas drive reservoirs.

TABLE OF CONTENTS

List of Figures            vii

List of Tables        viii

Acknowledgements            ix

Abstract   x

1. Introduction 1
   • Overview of Rate Decline Analysis ………. 1

1.2 Statement of Problem ……         3

• Literature Review 5
  • Fundamentals of Empirical Decline Curves Analysis ………………… 5
  • Modern Decline Curve Analysis ………………………………………………. 6
  • Effects of Reservoir/Fluid Properties and Drive Mechanism on Production Rate Decline …………………………………………………………. 8
  • Performance Prediction of Two-Phase Flows in Saturated Reservoirs …        11

• Material Balance for Saturated Reservoirs ……………………… 12
• Inflow Performance Relationships for Solution-Gas Drive Reservoirs 13
• Diffusivity Equation for Solution-Gas Drive Reservoirs ….. 17

• Decline Curves Analysis for Multi-Phase Flows …… 20
• Theoretical Basis for Decline Curves Analysis in Solution-Gas

Drive Reservoirs ……        22

2.6.1 Fetkovich Type Curves ………  22

• Camacho and Raghavan Attempt ………………………………….. 25
• The Non-Darcy Considerations ……………………………………. 27

3. Theoretical Developments 29
   • Overview and Background Information …… 29
   • Relationship between Empirical and Theoretical Decline

Parameters ………     30

• Derivation of Relationship ……………………………….. 32
• Significance of Relationship: Permeability Estimation … 35

• Considerations for the Effects of Non-Darcy Flow on the Decline Parameter … 36

• Inner Boundary Condition and the Existence of Hyperbolic Family in Solution-Gas Drive Reservoirs …     46

4. Simulation and Computational Procedures 52

4.1 Reservoir and Fluid Data Set ………         53

• Simulation Data Deck and Run Specifications………………. 58

4.2.1 Simulation Data Deck ……    58

4.2.2 Simulation Specifications and Controls ……      59

4.2.3 Output Requests …………               60

4.2.4 Simulation Initial Solution …  62

• Computational Procedures ……………. 62

5. Verification of Theories and Reservoir Property Estimation 66
   • Theoretical Decline Parameter Trend through Time …… 67
   • Theoretical Justifications for the Decline Parameters Trend …. 68
   • Effects of Incorporating Non-Darcy Flow …………………………… 71
   • Verification of Derived Relationships ………………………………….. 73
   • Proposed Reservoir Property Estimation Techniques ………… 76
     • Reservoir Permeability Estimation: Procedures and

Application ………                76

• Reservoir Radius Estimation ……… 82

5.6 Sensitivity Analysis ……   83

• Case 1: Effects of Critical Gas Saturation …………………….. 84
• Case 2: Effects of Permeability Value …………………………. 87
• Case 3: Effects of Reservoir Drainage Radius …………….. 89
• Case 4: Effects of Critical Bottomhole Pressure…………… 92
• Case 5: Effects of Peak/Initial Rate ……………………………. 95
• Case 6: Effects of Reservoir Heterogeneity ………………. 99

6. Conclusions and Recommendations 103

Nomenclature         108

References            109

Appendix            113

INTRODUCTION

1.1 Overview of Rate Design Analysis

Production rate decline analysis is an essential tool for predicting reservoir/well performance and for estimating reservoir properties.

The production life of hydrocarbon reservoirs typically shows three phases: the build-up phase, the peak phase, and the rate decline phase1.

The build-up phase corresponds to the increasing field production rate as new wells are drilled. Thereafter, the field peak rate is attained and maintained for some time after which the rate decline phase sets in.

For a well, during the peak phase, the bottomhole flowing pressure P_wf declines until it reaches a critical value, P_wfc whereupon the production begins to decline as the critical bottomhole pressure P_wfc is maintained3.

REFERENCES

Hubbert, M.K.: “Nuclear Energy and Fossil Fuels,” paper presented at the 1956 Spring Meeting of the Southern District, American Petroleum Institute, Plaza Hotel, San Antonio, Texas, March 7-9.

Arps, J.J.: “Analysis of Decline Curves,” Trans., AIME (1945) 160, 228-247.

Guo, B., Lyons, W.C. and Ghalambor, A.: Petroleum Production Engineering, a Computer-Assisted Approach, Elsevier Science and Technology Books, (2007), pages 98-105.

Ahmed, T. and McKinney, P.D.: Advanced Reservoir Engineering, Gulf Professional Publishing, (2005), pages 237-264

Mian, M.A.: Project Economics and Decision Analysis, Volume 1: Deterministic Models,

Pennwell Corporation, (2002), pages 2-5.

Gentry, R.W. and McCray, A.W.: “The Effect of Reservoir and Fluid Properties on Production Decline Curves,” JPT (September, 1978) 1327-1341.

Muskat, M. and Taylor, M.O.: “Effects of Reservoir Fluid and Rock characteristics on Production Histories of Gas-Drive Reservoirs,” Trans., AIME (1946) 165, 78.