Study on Lumped Parameter Models for a Two-Phase Geothermal Reservoir with Their Multi-Objective Optimization
Author: Zhen Qin
Year: 2018
Supervisors: Ágúst Vafells , María Sigríður Guðjónsdóttir, XinLi Lu
Abstract
The past decades have increasingly seen the applying of lumped parameter models (LPM) to geothermal reservoir analysis and production planning. Many studies focused on the simulating performance of low-temperature geothermal reservoirs using the lumped-parameter method. A few works had focused on the high-temperature or two-phase geothermal reservoir. Comparing with previous works in lumped parameter modelling that dealt with the two-phase mixture as a single phase by using compressibility, this work presents a new two-phase LPM based on using steam fraction and pressure as two independent variables, since compressibility for the steam-water mixture is extremely sensitive depending on both pressure and steam fraction. In this paper, a generalized, two-phase lumped parameter model is carried out to study the responses, including temperature, pressure as well as the steam fraction of fluid in a high-temperature geothermal reservoir.
The lumped parameter models (also known as “Tank” models) can be used to describe the dynamical response of a geothermal reservoir within a less computational time and achieving a considerable accuracy. This generalized tank model is introduced to represent high-temperature geothermal reservoir in which water and vapor coexist. Besides, a superheated tank model is also included.
With a large scale of object parameters and thermodynamic properties calculated based on steam table, the model is inherently nonlinear and multivariate and therefore it is difficult to compute Hessian matrix (second-order partial derivatives) or Jacobian matrix. In this paper, the quasi-Newton method is introduced first to fit model from several different sets of input parameters. Then the Genetic Algorithm (GA) is carried out to aim at finding the global optimum of input parameters.
Due to the lack of history data from the realistic geothermal field, this model is fitted to the data generated by the model itself. Then a simple lumped parameter model with only 6 tanks is employed to simulate the pseudo history data using both GA and GA+BFGS which is a combination of GA and BFGS. The fitting results show both the accuracy and robustness of LPM. Besides, the analysis of unknown parameters shows their effects on the response of lumped parameter modelling.