A new transient well-testing procedure, which extends "pulse-testing" technology, has been developed for determining the hydraulic diffusivity (K/[ ]) in underground-storage reservoirs. The method depends on the availability of cyclic pressure data from a pair of adjacent and communicating wells: A, the upstream or "forcing-function" well, and B, the downstream or "observation" well.
In general, the pressure fluctuations at well B will exhibit both an attenuated amplitude and a phase lag when compared with those at well A. The theory, which relates the two sets of fluctuations, relies on a solution of the diffusion equation, which governs pressure or potential variations with time and distance in a compressible medium.
To apply the theory to experimental observations, a Fourier analysis is performed on the transient pressures at both A and B. The method has been pressures at both A and B. The method has been tested with field data and indicates good success in predicting the pressures at offset wells.
The use of transient well-testing techniques has become a very important tool in the determination of in-situ reservoir properties. Previously, transient techniques such as interference and pulse tests have been derived and used in varying pulse tests have been derived and used in varying degrees for the determination of formation properties in reservoirs containing slightly compressible fluids. In these procedures, cyclic pressure data, resulting from seasonal and variable inventory, were not involved.
The present method applies to both highly and slightly compressible fluids and is especially designed for gas-storage reservoirs, whether surrounded by an aquifer or not. It involves two adjacent pressure-measuring wells both of which are either in the gas bubble or in the surrounding aquifer.
In the gas bubble, such wells are shut-in all the time and monitor the storage pressures at their respective locations. In the aquifer, the wells are also shut-in and allow observations to be made on water levels. Whether in the gas bubble or in the aquifer, the well-pair must be in pressure-communication with each other.
Fig. 1 depicts the necessary pressure-measuring well-pairs in the gas bubble or in the aquifer. The one-dimensional flow of the single-phase homogeneous fluid between wells A and B (or A' and B') is governed by
where = K/(c), and subject to:
Eq. 2 is the Fourier series approximation for the forcing function (pressures measured at well A or A'). Eq. 3 is the initial pressure distribution in the reservoir at an arbitrary starting time.
The equations are solved using the method of separation of variables.