An Automatic Fitting Method for Numerical Well Testing Based on a BP Neural Network Surrogate and Differential Evolution Algorithm
TL;DR
The results show that BPADE can fit numerical well-test curves with acceptable accuracy and can reduce manual adjustment during interpretation and can reduce manual adjustment during interpretation.
Abstract
This study develops BPADE, a BP neural-network-assisted differential evolution method, for automatic fitting in numerical well-test interpretation. The method is designed to reduce repeated calls to the oil-water two-phase numerical simulator during parameter inversion. Genetic Latin Hypercube Design is first used to generate samples in the parameter space. The numerical simulator then calculates the objective-function values for these samples, and the BP network learns the relationship between interpretation parameters and pressure-response misfit. To avoid direct inversion of all grid permeability values, sequential Gaussian simulation is used to describe the heterogeneous permeability field with fewer variables. Based on the comparison of reconstruction error and sampling time, 46 conditioning points are selected. The BP structure is also optimized by MSE, MRE, and the correlation coefficient. The final surrogate uses 27 hidden-layer neurons. After training, the BP surrogate is coupled with differential evolution to invert permeability, porosity, skin factor, and wellbore storage coefficient from pressure and pressure-derivative data. The method is tested with one synthetic heterogeneous reservoir case and one field case. In the synthetic case, the mean relative error of permeability inversion is 0.154. The relative errors of wellbore storage coefficient, skin factor, and porosity are 8.9%, 12%, and 11%. In the field case, the errors of permeability, porosity, and wellbore storage coefficient are 0.544%, 2.150%, and 4.00%. The results show that BPADE can fit numerical well-test curves with acceptable accuracy and can reduce manual adjustment during interpretation.