Proposal
The medium scale formation heterogeneity (about 1 foot to 100 feet near-wellbore) cannot be usually resolved well by conventional well test data, particularly in vertical direction. Spatial pressure data sets from the interval pressure transient testing (IPTT) along the wellbore measured by using multi-probe and dual packer-probe wireline formation testers (WFT) provide information about near-wellbore heterogeneity. The objective of this work is to examine the use of spatial 3D (three dimensional) IPTT data acquired by dual packer-probe WFTs and geostatistical information for estimating heterogeneous formation properties (e.g. horizontal and vertical permeability) in both lateral and vertical directions along the wellbore. There has been no systematic study in the literature about resolving heterogeneity in horizontal and vertical permeability and porosity from spatial 3D IPTT data. Throughout, formation property and parameter will be used interchangeably.
In this study, a 3D single-phase single-well (r-T-z) numerical flow model (simulator) was developed to simulate the behavior of IPTT measurements in heterogeneous media. Heterogeneity in formation properties is modeled at the gridblock scale by using geostatistics that allows properties to be treated as random regional variables with certain correlation structures. Horizontal and vertical property distributions conditional to IPTT data sets are estimated by using the inverse problem methodology based on Bayesian probability theorem. For estimation of formation parameters (properties) conditional to IPTT spatial data sets and geostatistical model, we minimize the objective function resulting from the application of the Bayesian probability theorem by using the well-known Levenberg-Marquardt (LM) algorithm. The sensitivity coefficients required in the LM algorithm are efficiently computed by using the adjoint method. We also show maps of sensitivity coefficients of packer interval and observation probe pressures with respect to parameter distributions (e.g., horizontal/vertical permeabilities and porosities) that offer important evidence about near-wellbore heterogeneities, where formation property distributions might be well resolved by interval pressure transient data.Synthetic examples are presented to show the methodology proposed in this work.
