EXPERIMENTS WITH INVERSE MODELLING AND UNCERTAINTY QUANTIFICATION WITH A GEOTHERMAL MODEL

Abstract

A simple method for nonlinear uncertainty quantification of predictions made by a highly parameterized (over 1000 parameters) geothermal model is discussed. The first step of the procedure is to compute a linear approximation to the posterior (post calibration) parameter covariance matrix. This requires computation of a calibration Jacobian matrix by finite differencing. Then many random parameter fields are generated using this matrix. The model is then run using each of these parameter fields and those that do not perform satisfactory against historical natural state and production history observations are rejected. Alternatively, they can be adjusted with relatively small computation cost to satisfy calibration constraints using the same pre-calculated Jacobian matrix as that which was used for calculation of the quasi-linear covariance matrix. If model performance is still not satisfactory, a small number of parameters projections on to identifiable parameter space can be adjusted at comparatively small numerical cost to achieve a desired level of model-to-measurement misfit. Future scenario simulations are then run using all retained (and possibly adjusted) parameter fields. Predictive histograms generated through these runs approximate posterior predictive probability distributions.
The method was tested successfully on a large model of a gassy geothermal system. Of 1400 random parameter fields generated using the quasi-linear covariance matrix, 200 satisfied calibration constraints without the need for further parameter adjustment.