Interpretation of Tests in Fissured and Multilayered Reservoirs With Double-Porosity Behavior: Theory and Practice
Authors: Gringarten Alain C. 
Published: December 2007

Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized as experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering.

Summary
This paper summarizes current knowledge of reservoirs with double-porositybehavior. These include both naturally fissured reservoirs and multilayere dreservoirs with high permeability contrast between layers. The first part presents available solutions to the direct problem (i.e., solutions to thediffusivity equation) that problem (i.e., solutions to the diffusivityequation) that have appeared in the oil and groundwater literature over thepast 20 years. The second part discusses methods for solving the inverse problem--i.e., identifying a double-porosity behavior and evaluating all corresponding well and reservoir parameters.
Several field examples demonstrate various aspects of double-porosity behavior and illustrate how additional knowledge of the reservoir (e.g..fissured vs. multilayered, gas saturation. etc.) can be obtained from numerical values of the reservoir parameters. Practical considerations for planning tests in Practical considerations for planning tests in double- porosity reservoirs also are included.

Introduction
The movement of underground fluids is of interest in many different engineering fields and, consequently, has been the subject of active research over the past 40 years.
Interpretation procedures, however, are well established only for porous fluid-bearing reservoirs considered reasonably homogeneous. Fluid-flow behaviorin heterogeneous formations is still the subject of much debate. It is agreedonly that conventional methods primarily developed for homogeneous reservoirs may be inadequate, and that new specific approaches may be required to providea convincing explanation for some commonly observed flow peculiarities.
There has been no unified approach to the problem, heterogeneous reservoir behavior in the literature is still considered too complex and too diverse tobe analyzed in a systematic and unique way. The main reason is the generalbelief that an interpretation model must closely approximate the actual complexity of the reservoir. The observation of a very large number of well tests in many different formations around the world, however, reveals that the number of possible behaviors during a well test is limited; therefore, only a limited number of interpretation models is required for well test analysis. This is because during a well test, the reservoir is acting only as a filterbetween an input signal, the change in flow rate, and an output signal, the change in pressure, and only high contrasts in physical properties within the reservoir can be highlighted.
In practice, a test reveals only that the reservoir acts as one single medium (homogeneous behavior) or as two interconnected media (heterogeneous behavior). The terms "homogeneous" and "heterogeneous" are related to reservoir behavior, not to reservoir geology. "Homogeneous" means that the permeabilitymeasured in a test and that measured in a core are the same, although theresulting numbers may be different. "Heterogeneous" means that these permeabilities are likely to be different. permeabilities are likely to be different. The Double-Porosity Model
The particular case of heterogeneous behavior where only one of the two constitutive media can produce to the well is called "double-porosity"behavior.
JPT
P. 549