Abstract
The mathematical definition of the reciprocity principle is developed using the concept of the instantaneous Green's function. Investigation of the validity of the principle is extended to cases where pressure-sensitive principle is extended to cases where pressure-sensitive parameters of skin and storage are present at the parameters of skin and storage are present at the wellbores of the test wells. Generally, the reciprocity principle is not valid for wells with skin and storage principle is not valid for wells with skin and storage factors. However, for special cases where these pressure-sensitive parameters fulfill certain carefully laid out pressure-sensitive parameters fulfill certain carefully laid out conditions for the well pair of interest, the principle is perfectly valid. perfectly valid.
Introduction
The reciprocal relationship between two wells within a domain in a porous medium probably was reported first by McKinley et al. A similar observation also was reported by Bruggeman for hydrological systems. Also, recently Falade, in his study of pulse testing in slab reservoirs, reported the reciprocity behavior with the pulsing and responding well pair. pulsing and responding well pair. The reciprocity principle as applied to fluid flow through a porous medium can be stated as follows: the pressure change at an Observation Well A, due to a pressure change at an Observation Well A, due to a stimulus of Strength Q imposed on a Source Well B is identically equal to the pressure change at Well B if Well A were subjected to a stimulus of equal Strength Q for an equal length of time. Thus, in effect, the source well and the observation well can be interchanged readily with essentially the same result.Extension and applications of this generalized theory to well testing in a multiwell field and its intrinsic advantages are obvious. Valuable operational costs involved in a complete well-to-well testing of a field can be reduced significantly by applying the reciprocity principle. This paper tries to explore more in-depth principle. This paper tries to explore more in-depth implications of the reciprocity principle as it affects routine oilwell testing.
Theoretical Development
The mathematical proof of the reciprocity principle can be formulated on a general basis using the concept of instantaneous Green's function. Green's function as applied to the solution of a diffusivity equation recently was highlighted by Gringarten et al. and can be extended easily from the single-well case to that of a multiwell field situation.The generalized pressure response at Point R in an infinite porous medium described as a two-well (or two-domain system) is given as
(1)
If the boundary conditions given at the wellbores are the Neuman type as is usually the case (prescribed flow rate), the normal derivatives of the Green's function will vanish at these boundaries:
(2)
SPEJ
P. 200
A High Compressibility Pressure—Sensitive Structure Based on CB@PU Yarn Network
