Effect of Linear Discontinuities on Pressure Build-Up and Drawdown Behavior (1963)

Abstract A detailed treatment is given of the transient pressure behavior of a well located near a linear discontinuity. On either side of the discontinuity, the values of permeability, viscosity, compressibility, and porosity are uniform, but may he different from those on the other side of the discontinuity. These results generalize previously published works which assumed the permeability ratio for media on different sides of the discontinuity was zero, one, or infinity. One application of this material would be to facilitate detection of facies changes or fluid-fluid contacts by transient testing. Solutions, presented graphically, show pressure decline for constant rate fluid production. The range of variables examined includes dimensionless time from 0.1 to 100, mobility ratio from 0.001 to 1000 and specific compressibility ratio from 0.001 to 1000. For dimensionless time less than 0.4, the pressure behavior is essentially that of a well in an infinite reservoir. Thus, reservoir properties near the well may be estimated in the usual manner. Using an overlay technique to match an experimental curve with one of the theoretical curves, it is possible to estimate the distance to a discontinuity by substituting the actual time t and the corresponding dimensionless time tp at which a match occurs into the equation where k,/phi mu c is the diffusivity near the well, and may be estimated from data taken at early time. Because of both the complexity of the solutions and limited computer facilities, well interference problems were not examined extensively. However, it was found that well interference may be masked by the discontinuity in some cases. By superposition of the results of constant rate fluid production, the problem of pressure buildup may be treated. Such results show that for early shut-in times correct values for the transmissibility are obtained from conventional semilog plotting. However, erroneous values of the static reservoir pressure are obtained unless data at large shut-in times are taken. Introduction Transient well testing has yielded estimates of such reservoir parameters as static reservoir pressure, permeability, porosity, and well bore effects. In most tests, it was assumed that the reservoirs were homogeneous and isotropic. Anisotropic media and radial discontinuities were considered. Various studies have been made on multiple-layer reservoirs. Linear discontinuities have been described for problems of one-dimensional flow. In the present paper, a mathematical treatment is given for a well located near a linear discontinuity in an otherwise infinite medium (see Fig. 1). An actual reservoir analogy would be a well in a relatively thin reservoir near a fluid-fluid contact, or a well located in a reservoir exhibiting a sudden change in rock and formation characteristics, such as thickness, porosity, or permeability. A sudden change in porosity or permeability may be caused by clay fill or other types of facies changes. Sudden thickness changes may be the result of such geological formations as buried shore lines and channel deposits. In otherwise uniform formations, a linear discontinuity may be caused by fluid-fluid interfaces such as oil-water contacts, gas-oil contacts, or gas-water contacts.