Matching the pre-exploitation or natural state of a geothermal field is often problematic. The natural state is approximated by a steady state, achieved by running a geothermal model forward in time until the system is unchanging. The final simulation time may have to be many millions of years to achieve the goal, and therefore, steady state geothermal model simulations are regularly time-consuming. Furthermore, geothermal steady state models are prone to convergence problems with a steady state not being achieved. These issues may cause the inverse modeling process of matching model results to natural state data to be very time-consuming. We propose a new methodology to aid derivative based inversion of natural state geothermal reservoir models. Model derivatives or sensitivities can be found by running the steady state simulation once and subsequently solving a system of linear equations with the number of right-hand sides determined by either Nm adjustable model parameters or Nd field observations of interest. By contrast, the standard approach for finding model sensitivities is by using finite differencing which requires solving at least Nm+1 nonlinear steady state simulations, each possibly requiring many time-steps. At each time-step the Newton-Raphson solution of the nonlinear equations requires the solution of at least one linear matrix equation making the forward simulations and therefore the inversion computationally intensive. The paper compares these approaches for synthetic steady state inversion problems, using TOUGH2 as the forward simulator. The results show the new methods to be superior to finite differencing in terms of computational time and resources.

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