**MOTION
OF FLUIDS
in Oil & Gas Reservoirs **

The following introductory comments were made by some of the conspicuous reservoir engineers who helped the author with the final corrections of the original “manuscript”.

*You do not know
what you see, but you see
what you know.”*

Jean Piaget

Piaget’s quote summarizes my feelings when faced with the ideas presented in this book. For some time I had been feeling that something “was not working" when trying to describe fluid motion in the reservoir through relative permeability curves. However, I was not able to identify where the difficulty was.

When I went over
the differentiation made by Marcelo among **injection, conduction** and **
production,** I felt he had become aware of something that has always been in
front of our eyes but has remained unobserved. This re-evaluation of the
difference among the mentioned three concepts sheds light on a problem that has
been repeatedly glimpsed and evaded.

The most outstanding merit of this book lies in the identification of the problem; and, above all and for the first time, its straightforward proposal of a different solution where formerly “only patches were placed.”

**
Norberto Galacho.**

Really good! As the time this book reaches readers, we will be able to assert that “Reservoir Engineering is possible in Argentina”. It may be the end of pure empiricism exalted to exacerbation and the beginning of an “era” among us (Reservoir Engineers), of analysis, discussion and reflection. There is no doubt that Marcelo’s ideas will at least cause a conflict in the analyst or reader, who will have to discuss old paradigms and decide if a change is needed. From my point of view, the position does not imply “not to measure” but to know “what for”, “how to measure” and finally “how to use measurements”. That is the challenge.

**
Miguel Angel Laffitte**

In spite of the fact that the relative permeability concept is deeply rooted and seems natural, it is in fact a simple macroscopic approximation to a complex microscopic problem. Marcelo argues more about its use or application to explain the displacement phenomena than about the concept itself. However, it is the starting point on the road to search for different formulations, whose application requires only an appropriate description of the reservoir (including all the inherent complexities) and the fluids, and not the necessarily assumptions or simplifications, which, in general, are not applicable.

I hope and wish this is our opportunity to start introducing a great change, which would be feasible due to the full participation and cooperation of those people interested in the topic.

**
Antonio A Paradiso**

Dear readers:
Hold on! This is an amusing and clear book, however its reading is hard and not
suitable for dogmatic people. It is difficult to say how much you agree with
this book. Perhaps you discover things that you looked at years ago, but you
were unable to see~~;~~ or you may disagree with others. Many times you will
be unable to say whether you agree or not, and you may need to postpone the
judgment till knowledge is consolidated.

Marcelo suggested to “beat hard” the relative permeability curves, but he goes further. He questions deeply rooted issues, such as numeric simulation itself. I can not say how much I agree and I must postpone my judgment. Hold on!

**Juan Rosbaco**

- Book Contents
- Introduction
- Chapter I
- Chapter II
- Chapter III
- Chapter IV
- Chapter V
- Chapter VI (Upon Request)
- Chapter VII (Upon Request)
- Chapter VIII
- Appendixes (Upon Request)

(*)shipping cost not included.

Book Request: infolab@inlab.com.ar

Questions to the Author: mcrotti@inlab.com.ar

**Back to the Reservoir Enginnering Forum**

---- Reservoir Engineering ----

WHO IS THIS BOOK INTENDED FOR? 5

BOOK ORGANIZATION 6

ACKNOWLEDGMENTS 6

THE RELATIVE PERMEABILITY CONCEPT 8

PERMEABILITY OF POROUS MEDIA 8

SIMPLIFIED MODEL OF POROUS SYSTEM 8

RELATIVE PERMEABILITY 10

Biphasic Flow 10

Case I: Low rate displacement in water wet system 10

Case II: Oil wet displacement. 13

Case III: Displacement under gravity segregated flow conditions. 14

Case IV: Displacement under gravity segregated flow conditions with random distribution 14

A more General Case 15

REMARKS 15

MAIN CONSEQUENCES 16

SUMMARY OF CHAPTER I 16

THEORY AND APPLICATIONS 17

CHAPTER CONTENTS AND OBJECTIVES 17

PROCEDURES, NUMBERS AND CONCEPTS 17

Experimental Data 17

Plots 19

Fitting Experimental Data 20

A Direct Calculation 21

Observations: 21

Results 22

Numerical Simulation of the Displacement Test 26

FAQs 28

SUMMARY AND CONCLUSIONS 30

REFERENCES 30

APPENDIX 31

Measurements and Calculation of Relative Permeability Curves 31

Theory 31

The Quality of Measurements 31

What Happens During the Water Displacement Test? 32

Water and Oil Production Rates 33

Numerical Simulation Using a Spreadsheet 37

INJECTION, CONDUCTION AND PRODUCTION 39

MULTIPHASE FLOW 39

Relative Permeabilities 39

Injection, Conduction and Production 40

Validity of the Relative Permeability Concept 40

Undefined Variables 41

Historical “Solutions” 41

The Practical Problem 42

FAQs 43

SUMMARY AND CONCLUSIONS 43

REFERENCES 44

INCONSISTENCIES 45

FIRST EXAMPLE. THE FRACTIONAL FLOW CURVE AND THE RELATIVE PERMEABILITY PSEUDO FUNCTIONS 46

Properties of Fractional Flow Curves 47

Simplification of Complex Systems 47

Homogeneous Block under Predominant Gravity Forces 48

SECOND EXAMPLE THE SAME RELATIVE PERMEABILITY AND TWO DIFFERENT PRODUCTION HISTORIES 51

Case I: Non-communicated Layers (no cross-flow). 52

Case II: Interconnected Layers. Full Gravitational Segregation. 54

Further Explanations 55

Both models in the same reservoir 55

Minor differences 55

Why M=1? 55

Generalization 55

FAQs 55

SPECIAL COMMENTS 56

Gravity and Capillary Forces in Darcy’s Equation 56

The Fractional Flow Curve and Capillary Forces 57

Average and Point Saturations 57

Continuous and Discontinuous Values 57

Volumetric Properties 58

SUMMARY AND CONCLUSIONS 58

REFERENCES 58

HETEROGENEITIES AND AVERAGES 59

FLUIDS FLOW IN HETEROGENEOUS SYSTEMS 59

Case I. Unsteady-State Flow 61

Water Saturation (Sw) 62

Relative Permeabilities 62

Summary 64

Remarks 64

Case II. Steady-State Flow 64

Summary 66

Comments 67

ANALYSIS OF RESULTS 67

Mathematical Average 67

Physical Average 67

A Conceptual Answer 68

FAQs AND COMMENTS 68

SUMMARY AND CONCLUSIONS 69

REFERENCES 69

NUMERICAL SIMULATION 70

FIRST EXAMPLE – CELL SIZE 70

Displacement diagram 70

Fractional Production Curves 72

Analysis and First Conclusions 74

Observation 75

FAQs 77

SECOND EXAMPLE – CELL LOCATION 77

Additional Analysis and Conclusions 80

Observations: 80

FAQs 80

SUMMARY AND CONCLUSIONS 82

REFERENCES 82

SUPPLEMENTARY DISCUSSION 83

Tending to an infinite number of cells. 83

Vertical gridding and SPC 86

SPECIFIC PRODUCTIVITY 90

VISCOUS-DOMINATED DISPLACEMENT IN HOMOGENEOUS LINEAR SYSTEMS 90

VISCOUS-DOMINATED DISPLACEMENTS IN TWO-DIMENSIONAL HOMOGENEOUS SYSTEM 91

TWO-DIMENSIONAL HOMOGENEOUS GRAVITY-DOMINATED SYSTEM. 93

GENERAL SOLUTION 94

FAQs 94

SUMMARY AND CONCLUSIONS 95

REFERENCES 95

EPILOGUE 96

A BIT OF HISTORY 96

THE WAY TO GO 98

FINAL WORDS 99

SUPPLEMENTARY TOPICS 100

RESIDUAL OIL SATURATION 100

Wettability 100

The Displacement mechanism 101

Initial Water Saturation 101

Extrapolations 102

IRREDUCIBLE WATER SATURATION 102

Scarcely laminated Average Permeability Samples (between 20 and 200 mD). 102

High Permeability Samples (more than 500 mD), or Average Permeability, very Laminated Samples. 102

Scarcely Permeable Samples (less than 20 mD). 103

Conclusions 103

Scarcely laminated average permeability samples (between 20 and 200 mD). 103

High permeability samples (more than 500 mD) or average permeability and very laminated samples. 103

Scarcely permeable samples (less than 20 mD). 103

CORRELATIONS 103

VISCOSITY RATIO 104

THREE-PHASE RELATIVE PERMEABILITIES 104

IMPLICIT CALCULATION METHOD 105

WETTABILITY 106

The Essential Concepts 106

Lab Measurements 106

Consequences 107

Edge Effects. 107

Relative Permeabilities. 107

How to Introduce Wettability in Reservoir Models? 107

REFERENCES 108

CONTENTS 109