| Title | ACCELERATING THE SOLUTION OF GEOTHERMAL INVERSE PROBLEMS USING ADJOINT METHODS IN WAIWERA: A PROGRESS REPORT |
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| Authors | B. Gonzalez-Gutierrez, S. Sung, R. Nicholson, J. P. OSullivan1, M.J. OSullivan1 and O.J. Maclaren |
| Year | 2018 |
| Conference | New Zealand Geothermal Workshop |
| Keywords | Inverse problems, Waiwera, geothermal modelling, reservoir simulation, adjoint methods |
| Abstract | Mathematical and computational modelling of geothermal fields plays a key role in effective management of geothermal reservoirs. Central to the management of such reservoirs is the ability to predict future behaviour. In the case of geothermal reservoir modelling, available data consists of noisy temperature, pressure and enthalpy measurements from pre-existing wells. In order to predict future scenarios, however, the real parameters of interest are the underlying permeability structure and the location and/or magnitude of the deep upflow of the reservoir. These parameters are what control the observed and predicted temperature and pressure data. Mathematically, inferring the permeability and/or boundary conditions given temperature and/or pressure measurements is an ill-posed inverse problem. Typically, solving the inverse problem amounts to determining the minimiser of a suitably constructed cost function. Given sufficient computational resources, there are well-defined computational approaches to solving inverse problems; however, these methods can require a large number of simulator runs, and large geothermal simulation models are typically computationally expensive. Adjoint methods provide a method of speeding up the solution of inverse problems, provided model Jacobian information (in particular) is available. Adjoint methods can be adapted to take into account both first derivative and second derivative information of the cost function. When using first derivative information (e.g. steepest descent), the cost to determine each search direction is one forward solve and one additional linear adjoint solve. Here we give an overview of preliminary work on implementing and using the adjoint method to solve inverse problems for geothermal models constructed in the new simulator Waiwera. Waiwera is based on the same robust algorithm as (AU)TOUGH2, with the added benefits of a fully parallel code, additional solvers and, most importantly, easy access to model Jacobians. |