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Immiscible Displacement in Porous Media
The analysis and description of the immiscible displacement process by analytical methods are still of fundamental importance for the prediction of reservoir behaviour, despite the ready availability of numerical modelling methods.
Before any numerical simulation study an engineer should analyse, by non-numerical means, the displacement processes that are considered likely in the reservoir.
In Chapter 5 Waterdrive of Dake's "The Practice of Reservoir Engineering", he highlights the need to caution in applying core flooding experiments directly in numerical simulation studies and the dangers of conducting these simulation studies in isolation of parallel analytical calculations. An extract from chapter 5 is given below, in which he states :
"There are three levels on which the phenomenon of water-oil displacement can be viewed:
| • | the electron microscope scale (EMS) |
| • | the microscopic, one-dimensional scale of a core flooding experiment |
| • | flooding in hillsides......which is the reality of practical reservoir engineering |
.....The perennial difficulty in the description of waterdrive has always been how to relate the core flooding results, which are little affected by such complications as heterogeneity and gravity, to the hillside in which these same factors are usually dominant. The scaling-up of laboratory results for use in a meaningful fashion in field studies is one of the main topics in this and subsequent sections and particularly the sensitive matter of how the results of relative permeability experiments are input to numerical simulation models in such a way as to honour the basic laws of physics."
Reservoirs are, of course, three-dimensional.
However, reservoir thickness is almost always much smaller than the areal dimensions. Therefore, the study of displacement processes can be reduced to a two-dimensional heterogeneous (layered) problem, with the reservoir divided into vertical slices in the x-z, or y-z, plane. These routines are implemented and discussed further in the Multi Layer Fractional Flow Model section. Also, if the reservoir layer thickness is small, and is less than the capillary transition zone between oil and water, the system can further be reduced to a one dimensional homogeneous linear problem. These routines are discussed further in the Single Layer Fractional Flow Model section.
The basic assumptions made when attempting to describe the displacement processes are :
| • | Oil and water are the only mobile fluids in the porous medium, and move in the same direction. |
| • | Water is displacing oil in a water wet reservoir, such that the displacement is an imbibition process, and the movement of the two fluids is described by their relative permeability curves. |
| • | The displacement is considered as incompressible. This assumption implies that steady state conditions prevail in the reservoir with the pressure at any point remaining constant. |
| • | The displacement is considered to be linear. |
Laurie Dake's - The Practice of Reservoir Engineering
Laurie Dake's two textbooks, namely :
"Fundamentals of Reservoir Engineering", Elsevier, 1978-1985
"The Practice of Reservoir Engineering", Elsevier, 1994-2001
are probably the most referenced technical manuals within the discipline of Reservoir Engineering.
Perhaps the most fitting tribute to these books can be found on amazon.com from Malcolm Pye, of the UK's Department of Trade and Industry.
"...This book tells you all you need to know about reservoir engineering.
Chapter 5 is Laurie's masterpiece, 150 pages on waterdrive which could be published as a book in its own right. Drawing on examples from the North Sea, the biggest laboratory ever for the study of waterdrive it demolishes the misconceptions that have grown up over relative permeability curves and stresses the importance of the fractional flow equation in understanding fluid displacement. "
The techniques, presented within these two books, form the basis for the routines contained within this section.
References:
Dake, L., "Fundamentals of Reservoir Engineering", Elsevier Scientific Publishing Company, 1978.
Dake, L., "The Practice of Reservoir Engineering", Elsevier Scientific Publishing Company, 1994.
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