History Matching Production and Displacement Data Using Derivative-free Optimization

Geomechanical simulators can be used to predict production-induced subsidence. However, the uncertainty in these predictions depends on the uncertainty in the flow and geomechanical parameters, such as permeability and Young's modulus. In this thesis, we develop a derivative-free optimization procedure for calibrating flow and geomechanical parameters. The method entails the use of the iteratively coupled flow-geomechanics module in Stanford's Automatic Differentiation General Purpose Research Simulator (AD-GPRS) combined with the mesh adaptive direct search (MADS) optimizer. Multiple sets of history matched parameters are generated using the randomized maximum likelihood (RML) procedure.

Both production and displacement (geomechanical) data can be assimilated within our framework. Data types considered in this work include well production data, surface displacement data and well displacement data, and the impact of these different types of data on predictions and parameter calibration is assessed. We first consider a three-layer model with no overburden rock. For this case, we show that assimilating either type of displacement data is useful for calibrating the harmonic average Young's modulus as well as permeability in each layer. Assimilation of either type of displacement data reduces uncertainty in both surface displacement and production predictions. Assimilation of production data, by contrast, improves permeability calibration and reduces uncertainty in production forecasts, but not in displacement predictions. We also show that history matching surface displacement data does not provide calibration of individual layer Young's moduli, though it does enable accurate calibration of the harmonic average Young's modulus over all layers. History matching well displacement data provides calibration of individual layer Young's moduli.

We next consider a more realistic (though two-dimensional) geomechanical model that includes overburden rock and bedrock. For this case we again demonstrate that both surface and well displacement data are useful for reducing uncertainty in surface displacement predictions and for estimating the harmonic average Young's modulus over all reservoir layers. Well displacement data are shown to again enable the calibration of individual layer Young's moduli.