Interpretation of Borehole Strain Measurements Using Surrogate Modeling-Based Optimization

Interpreting strain data measured during well testing requires inverting poroelastic forward models set up to represent an aquifer or reservoir. One approach is to use stochastic methods to conduct the inversion. Subsurface parameters such as elastic modulus, permeability, and geometry of heterogeneities are estimated by searching the parameter space. This is feasible, but cumbersome, requiring more than a week of computation using many hundreds of computer nodes in one of our earlier analyses. This motivated us to consider alternative methods, including an artificial neural network (ANN) as a surrogate model.

We trained an ANN using results from a numerical simulation of the poroelastic deformation of an aquifer caused by pumping or injection. Ultimately, the trained ANN predicts strains and pressures that are similar to those from the poroelastic model, but at a small fraction of the run time. We developed a code that uses an ANN-based surrogate poroelastic model with the multi-objective generic algorithm NSGAII. This code was successfully applied to interpreting strain and pressure data from well tests at the Avant oil field in northeastern Oklahoma. ANN-assisted optimization was able to estimate permeability, elastic modulus, and the size of a permeable lens in the reservoir and generate a suite of parameter sets that match the field data quite well. The inversion using a surrogate model requires 0.4 hour per core to complete, compared to 8.3 hour per core to run the same analysis using the numerical simulator-based optimization if both optimization models are parallelized to 50-core machine to identify multiple scenarios that explain pressure and strain data. The matching quality obtained from the surrogate model was compared to results using the numerical simulator and the average squared difference between the estimated values and the field data were similar. These results indicate that inversion using a surrogate model could be an effective way to streamline the inversion using large poroelastic models with long run times.