Reservoir description by well test analysis using cyclic flow rate variation

This study concerns the possibility of characterizing the permeability distribution in areally heterogeneous reservoirs through the interpretation of pressure response to cyclic flow rate variations.;A mathematical model was formulated for the pressure behavior due to sinusoidal flow rates in reservoirs with continuously and smoothly varying radial permeability distributions. A correlation between the radius of cyclic influence and the frequency of a sinusoidal flow rate was developed.;A quantitative method was proposed to describe the permeability distribution based on a multicomposite radial reservoir model. The permeability in each zone of the equivalent reservoir was estimated by employing a nonlinear parameter estimation procedure.;The nonlinear parameter estimation in the quantitative analysis applied least-squares as the criterion for defining the objective function to be minimized. Two different techniques were considered: the Gauss-Marquardt method and the singular value decomposition method. In addition, three other procedures for automated well test analysis were proposed and tested on reservoirs with single or double-porosity behavior. These new approaches are robust nonlinear parameter estimation algorithms based on the least absolute value criterion, rather than on the commonly employed least-squares.;The correlation between radius of cyclic influence and frequency of a sinusoidal flow rate was used to design a pulse test flow rate schedule. Several factors affecting the quality and the uncertainty in the estimated permeability distribution were investigated, along with examples including a variety of geometric and permeability distribution configurations. These factors included the type of test, flow rate, total testing time, reservoir zonation and configuration, and permeability distribution.;One type of heterogeneity considered in this study was the case of a reservoir containing an internal circular discontinuity. In order to generate synthetic pressure transient data for this kind of system, the solution for the pressure response was achieved by using the concept of Green's function and by applying the Laplace transformation technique. The solutions obtained include the cases in which the active well is located either inside or outside the circular subregion. (Abstract shortened with permission of author.).