Production Analysis of a Shale Gas Reservoir Using Modified Deconvolution Method in the Presence of Sorption Phenomena

Abstract

When analyzing production data during reservoir characterization, pressure transient analysis requires a constant production rate during the entire production period. However, because of the extremely low permeability of shale formations, the flow regime changes over the long period of production. Therefore, it is rarely possible to acquire production data at a constant rate. In addition, as pressure declines with production in a shale gas reservoir, desorption of gas occurs, leading to nonlinearities due to large changes in gas compressibility, and it should be linearized for the use of deconvolution. In this study, we suggest sorption correction for pseudopressure using material balance equation to linearize the pseudopressure–rate relationship. By using this sorption correction term for pseudopressure in the deconvolution, we carried out pressure transient analysis with production data from a shale gas well to obtain the reservoir characteristics. The results show that, without sorption correction, the pseudopressure decline and its derivative varied depending on the magnitude of the desorption. However, with the correction applied, the curves were almost identical regardless of desorption. In the results of the deconvolution analysis with and without the sorption correction, pseudo-linear and pseudo-pseudosteady state flow periods appeared at different times, which explains the anomalous results in the pressure transient analysis. By implementing those results, we analyzed production data acquired from Fayetteville shale. The results show that the reservoir permeability, stimulated reservoir volume, and fracture half-length depended on the use of sorption correction for pseudopressure.

An improved deconvolution algorithm using B-splines for well-test data analysis in petroleum engineering

“…It is formulated by using 2-order B-splines for representing the derivative of the wellbore pressure p′ u corresponding to the constant unit production rate, and requires numerical inversion of the Laplace transform; and a regularization method is implemented for handling the high levels of data errors. It is worth to mention that although these aforementioned deconvolution algorithms are only valid for linear systems i. e. reservoir models of Darcy's flow with slightly compressible fluid when Duhamel principle holds, they can be also applied to nonlinear systems through the linearized relationship between the defined pseudopressure and the production rate in the cases of gas or multiphase flow (Kim et al, 2015). Onur et al (2006) have presented an investigation of these three deconvolution algorithms, and discussed the specific features associated with the use of each algorithm.…”