This paper extends a new technique, mown as direct synthesis to the interpretation of the pressure transient behavior of a well located in various multiple-fault systems and within closed rectangular reservoirs. The most important aspect of this new technique is its accuracy because it uses exact analytical solutions to calculate reservoir parameters. The techniques is principally based on the systematic use of the well pressure and its derivative. These functions were employed Co explore the characteristics of well pressure behavior. Characteristic points are obtained at intersections of various straight line portions of the pressure and pressure derivative curves. Characteristic slopes and starting times of these straight lines are also derived. These points slopes and times are then used with appropriate equations to solve directly for various reservoir parameters. A step-by-step procedure for calculating these parameters without type-curve matching is included in this paper. The new technique is applicable to the interpretation of pressure drawdown and buildup tests for a vertical well near several intersecting sealing faults and inside bounded rectangular systems.
Matthews et al.1 presented a method for determining pressure distribution and average reservoir pressure within different bounded geometric shapes. Earlougher et al.2 applied principle of superposition to generate a tabular of the dimensionless pressure distribution for a well located at the center of a bounded square. Ramey and Cobb3 presented a general theory of pressure buildup for a well in a closed drainage shape. Earlougher and Ramey4 presented tables of the dimensionless pressure for different points within several bounded rectangular reservoirs. Tiab and Crichlow5 studied the pressure behavior of a well located within multiple sealing fault systems and closed rectangular reservoirs. They developed a type-curve matching technique based on pressure derivative to find the well location.
Home6, showed that the conventional semi log method sare more accurate than the log-log type curve matching techniques because the log-log axes tend to mask inaccuracies at late time, where 1 mm deviation of a pressure point may mean an actual error of 200 psia. Tiab7–13 introduced first the direct synthesis technique for interpreting pressure transient tests. This technique uses the log-log plots of pressure and pressure derivative versus time to calculate several reservoir parameters without using the type curve matching technique.
The objective of this study is to apply the direct synthesis technique to:
a well near two perpendicular sealing faults,
a well within three perpendicular sealing faults, and
a well located anywhere inside a bounded rectangular reservoir.
The reservoir is assumed to have constant porosity, permeability, and thickness. Fluid viscosity and compressibility remain constant at all pressure, and gravity effects are negligible.
This section considers a single well producing at a constant rate and located between two sealing faults that intersect at a right angle. As shown in Fig. I, a well is at distances b, and by from the boundaries. By applying the principle of superposition in space, three image wells are required to simulate the performance of this system.