--> Application of Surrogate Models and Derivative-free Optimization in Geothermal Reservoir Modelling

AAPG European Region, 3rd Hydrocarbon Geothermal Cross Over Technology Workshop

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Application of Surrogate Models and Derivative-free Optimization in Geothermal Reservoir Modelling


Numerical models of geothermal reservoirs are valuable tools to understand the processes controlling subsurface flow and to help manage these resources. However, modellers face a number of uncertainties in their efforts to generate reliable predictions. This study addresses uncertainty using geostatistical simulation, in particular using multiple-point statistics (MPS). The main feature of a MPS algorithm is that it relies on a training image, and uses multiple training images to describe spatial uncertainties in subsurface flow problems. MPS was pioneered in the petroleum industry but has received little attention in geothermal. Monte Carlo methods are a traditional approach for uncertainty assessment in many areas of science and engineering. However, Monte Carlo methods can be very computationally expensive since many forward modelling runs are required. Surrogate models are an alternative to Monte Carlo methods. The surrogate is derived from reservoir simulator output, and can be generated from a small number of runs of the simulator. This approximation may then be used to produce fast estimates of the model output for different combinations of parameters gives scope for an optimization algorithm to be applied to the model. This study addresses the problem of global calibration of geological properties in a geothermal reservoir model through the use of surrogate models and adaptive sampling. Efficient solutions were obtained for nonlinear problems, where standard, derivative-based methods may have achieved convergence to low-quality solutions. An important feature of this surrogate model calibration is that it allows the inclusion of both categorical variables and continuous variables in the analysis. This was shown to be a strategy which delivers insight on geological uncertainties from the calibration process. The paper will comment on how the methods applied relate to methods used in petroleum reservoir modelling.