Estimating permeability distribution from 3D interval pressure transient tests

In this paper, the basic features of 3D (spatially r and z and time) interval pressure transient testing (IPTT) are described for the estimation of horizontal and vertical permeabilities and delineation of fracture and fault conductivities using the packer module and observation probe tool combination of the multiprobe wireline formation tester. Mathematical models for the pressure behavior of IPTT tests for using the packer module and the observation probes in multilayer (stratified) formations are presented. The maximum likelihood (ML) method is presented for nonlinear parameter estimation to handle uncertainty in error variances (weights) in observed data. The main advantage of the ML method over the traditional weighted least squares (WLS) is that it eliminates the trial-and-error procedure required to determine appropriate weights to be used in the WLS estimation. As shown by the examples presented in the paper, the ML method provides significant improvement in parameter estimation when working with pressure data sets of disparate orders of magnitude and noise, e.g., pressure measurements for the packer–probe and multiprobe interval tests. d example where eight IPTT tests were conducted in a major carbonate formation is presented for characterization of vertical and horizontal layer permeabilities and vertical communication through the main producing reservoir section. These IPTT tests were conducted with a Formation Tester Dual Straddle Packer and two Probe Modules in a newly drilled well. An IPTT test at each location was interpreted using an appropriate geological model with the packer and probe pressure and flow rate measurements. The interpretation procedure consisted of identification of the different flow regimes followed by history (type curve) matching for the estimation of vertical and horizontal permeabilities for each layer. A detailed interpretation of two of the interval pressure transient tests is presented.