The lumped-parameter model on two-phase and superheated geothermal reservoir

Tank models (also known as “lumped parameter” models) may be used to describe the dynamical response of a geothermal reservoir. In this paper, a generalized combined lumped-parameter model consisting of both two-phase and superheated geothermal fluid is developed. The model is inherently nonlinear and multivariate and therefore it is difficult to compute Hessian matrix (second-order partial derivatives) or Jacobian matrix. We show how the BFGS algorithm, a kind of quasi-Newton method, based on Armijo line search can be used for parameter estimation. Using this algorithm, two different scenarios are matched with data generated by tank model itself.