![]() Substituting this value into the previous equation, When evaluating the wellbore pressure, it is assumed that r = r w. The properties of natural logs can then be used for further simplification. Substituting this equation into the linear diffusivity equation yields: Assuming the error to be negligible, Equation (4) can be reduced to the following: The Ei in the above equation is known as the Exponential Integral and is defined as eitherĮrror associated with the Ei formula. , the dimensionless diffusivity equation becomes: The linear diffusivity equation is given by the equation shown below: The dimensionless linear diffusivity equation can be used to generate pressures at distinct reservoir locations and times. Brit to and Grader determined that pressure response is extremely sensitive to the size, shape, and orientation of the impermeable region. Previous studies have indicated that sealing faults yield to deviation between a well’s pressure response and the homogeneous line-source response. In their paper, they outlined several different techniques to both detect and locate these faults. This study was extended when Tiab and Kumar investigated the pressure transient behavior of a constant producing well located between two parallel sealing faults. Tiab and Crichlow developed a type-curve matching method for interpreting pressure transient curves of a well located inside multiple sealing faults and rectangular reservoir systems. Using the least squares method, he was able to determine many reservoir parameters including: relative distance to the fault, angle between the boundaries, flow capacity, and the initial reservoir pressure. The pressure transient behavior of a well located near two intersecting boundaries was studied by Prasad. This increase is created due to the reduction in production area, from an initial production of 360˚ to a final production of 90˚. After sufficient production, he noticed that the slope of the drawdown curve would become four times the initial value. ![]() In his study, Jones used the reservoir limit test to analyze the performance of a gas well near two orthogonal sealing faults. The theory of images was first applied to multiple boundary reservoirs by Jones. They then presented an equation to calculate relative distance to a fault using pressure drawdown data. Davis and Hawkins identified the features which pressure transient curves must have to produce valid data. This initial study sparked considerable investigation into the identification of petroleum reservoirs using pressure transient testing. By applying the method of images, Horner was able to approximate the distance from a fault using pressure build up data. Horner presented the foundation for pressure transient study of a single well located near a sealing fault. The detection of a linear fluid-barrier (fault) from pressure transient data was first presented by Horner. The identification of theses faults will enable engineers to determine the optimal production strategy of petroleum reservoirs, as well as provide insight on their long-term performance. ![]() ![]() The boundaries present in reservoirs take the form of sealing and non-sealing faults. Pressure transient analysis has been widely used as an industry standard to determine reservoir boundaries.
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