Pulse Tests and Other Early Transient Pressure Analyses for In-Situ Estimation of Vertical Permeability
Authors: Hirasaki George J. 
Published: December 2007

Abstract
Formation vertical permeability is often the dominant influence in water or gas coning into a well, in gravity drainage of high-relief reservoirs, and in interlayer crossflow in secondary recovery projects. The advantages of either conducting a projects. The advantages of either conducting a pulse test or analyzing the early transient pressure pulse test or analyzing the early transient pressure response of a constant-rate test compared with previous techniques are simplicity of interpretation, previous techniques are simplicity of interpretation, short duration of test, and minimum interference from conditions some distance from the test well. The pulse test has a further advantage over the constant-rate test in that the rate does not have to be kept constant during the short flow period. Presented are the development of the theory and the curves of the dimensionless response time used in interpreting field data obtained by these techniques. The vertical permeability is determined with the pulse test from the time to the maximum pressure response and with the constant-rate test pressure response and with the constant-rate test from the extrapolated time to zero pressure response from the inflection point. Applications of the techniques to layered systems and to an oil zone with underlying water are demonstrated with results of numerical simulations. The vertical-permeability pulse test has been used to estimate the vertical permeability of a low-permeability zone in the Fahud field, Oman.

Introduction
The formation vertical permeability is often a dominant influence in reservoir recovery processes with vertical fluid flow such as water or gas coning, gravity drainage of high-relief reservoirs, the rising steam process, and displacement by water or gas in a heterogeneous formation. How reliably numerical reservoir simulators can predict the recovery performance of these processes depends upon how performance of these processes depends upon how accurately the significant reservoir parameters are estimated. Furthermore, in simulating a reservoir in two dimensions, the validity of the assumption of vertical equilibrium is based on the value of the vertical permeability. With the previously mentioned recovery processes, the reservoir cannot be modeled as a homogeneous reservoir with a single fluid. A well that has fluid coning or that is producing by gravity drainage will often have a fluid contact intersecting the well and thus dividing the reservoir into zones of differing mobility and compressibility. Reservoir stratification on a microscopic scale will result in a vertical permeability that is less than the horizontal permeability that is less than the horizontal permeability; but stratification on a macroscopic permeability; but stratification on a macroscopic scale will divide the reservoir into zones of differing permeabilities. Thus the design and interpretation permeabilities. Thus the design and interpretation of a vertical-permeability test for most practical reservoir situations will require that the reservoir zonation be represented. Transient pressure techniques for estimating in-situ vertical permeability have been introduced by Burns and by Prats. Both techniques require injection or production at a constant rate from a short perforated interval and measurement of the pressure response at another perforated interval pressure response at another perforated interval that is isolated from the first by a packer. The interpretation technique of Burns required a computer-generated type curve or a single-phase numerical reservoir simulator. This type-curve approach is applicable for an anisotropic, homogeneous, infinite reservoir model, and the numerical simulator with a regression analysis program is needed for finite or layered reservoir models. The technique presented by Prats did not require a computer program because the result of the analysis was presented on a single graph. The horizontal and vertical permeabilities could be estimated from the slope and the intercept of the pressure response and, the appropriate value from the graph. The method of Prats was based on an infinite, anisotropic, Prats was based on an infinite, anisotropic, homogeneous reservoir model.The pulse test and early transient analysis techniques presented here were developed to provide a simple means of interpretation for layered provide a simple means of interpretation for layered systems.