Pulse Testing: Mathematical Analysis and Experimental Verification

This paper covers theoretical research on pulse propagation in linear cores saturated with air, and propagation in linear cores saturated with air, and discusses bow pulse tests in these systems can be analyzed to provide a measure of the porosity and permeability of the porous medium. It also covers permeability of the porous medium. It also covers experimental work designed to compare these properties, as calculated from pulse-test data, with properties, as calculated from pulse-test data, with those determined by conventional measurements. The paper shows that, when such pulse data are analyzed correctly, the comparison is very favorable; i.e., permeability values vary no more than 3 percent and porosity values no more than 0.5 percent. We conclude that pulse experiments with linear cores saturated with air give data, which when analyzed by methods based on the diffusion equation, give permeability and porosity values comparable with permeability and porosity values comparable with those obtained by conventional methods. Introduction Pulse testing is a recently developed method for evaluating reservoir storage capacity and fluid transmissibility. Papers have described the basic theory, based on the diffusion equation, and techniques of pulse testing as applied to field operations. Although some of the papers describe field applications, none report laboratory experimental investigations of pulse testing. This paper covers experimental and theoretical research on pulse propagation through porous media. It tests the adequacy of the use of the diffusion equation as a basis for interpreting pulse-test data. Using the diffusion equation, the theory of pulse propagation in a linear porous system and a method propagation in a linear porous system and a method of interpreting the experimental data are derived. A few experiments conducted on long Berea cores saturated with air are described. The porosity and permeability values were determined by gas expansion permeability values were determined by gas expansion and steady-state flow, respectively, and the values were compared with those theoretically calculated from experimental pulse data. The comparison shows that the values determined by the conventional methods compare well with those calculated from the pulse data. MATHEMATICAL ANALYSIS SOLUTION OF APPROPRIATE EQUATIONS The system to be analyzed consists of a Berea core saturated with air. At a reference time, t = 0, air is injected at a constant rate into one end of the core. At time t the injection is terminated and the injection end is closed. The other end is kept closed during and after injection. The equation which describes the above system, when the pressure variation is small, is the diffusion equation. For flow in porous media, the equation is(1) where c = compressibility in 1/atm k = permeability, darcies L = the length of the core in centimeters for thefinite core, and any arbitrary chosen lengthfor the infinite core p = the pressure in atmosphere at t >0 p = the pressure in atmosphere at t >0 pi = the pressure in atmosphere at t = 0 pi = the pressure in atmosphere at t = 0 Deltap = p - pi t = time, seconds tD = dimensionless time given by x = any distance from the inlet end, cm xD = x/L beta = porosity, fraction mu = viscosity, cp We solved Eq. 1 for two cores, finite and infinite, as shown in the Appendix. SPEJ P. 403