NON-LINEAR MODELLING OF A GEOTHERMAL STEAM PIPE

SUMMARY Recent work on developing a non-linear model for a geothermal pipe network system is presented in this paper. Previous methods of modelling are reviewed. Using the mass and energy balance at each node and loop of a pipe network, a non-linear equation set can be established. The equation set is formulated from a conceptual model of the pipe network, which is composed of steam wells and connected pipelines. The well characteristics curves, pipeline frictional characteristic and the different combinations of the connected components all contribute to the pressure and mass flow rate distributions in the system. Some recent numerical experiments on the non-linear model are compared with Italian experience. The results converged satisfactorily. Using this model, the user can change the connection and the characteristic of each individual demand in a network and chose a desired manifold pressure; the simulator will then calculate the balanced mass flow rate and pressure distribution along the defined pipe network. 1 INTRODUCTION Computer modelling of geothermal pipe networks for both design and simulation purposes has been reported. Most of these are linear computing models, which can work well on a tree-like linked simple pipe network. However with more complex practical systems, it is easy to find that both loops of pipelines and a series of nonlinear well characteristics have to be considered. These two factors contribute to the difficulty of the modelling work. Loops in a pipe network can normally be solved using a number of established methods (Stephenson, 1989). However if the pipe network is connected to a number of wells with parabolic like characteristic curves rather than linear curves, even the calculation of a simple network can be a cumbersome process. Convergence of the solution is often very slow because of the trial and error methods used. This paper presents recent development work on a numerical model which uses a non-linear method to simulate a geothermal steam pipeline network. The mass and pressure balance at each node and loop of a pipe network are considered to be under the control of both the connected well and the manifold working point. After setting up a non-linear equation set for the above balance, numerical methods are used to solve for the mass flow and pressure distribution. Convergence of the solution has been satisfactory for the numerical experiments conducted. In this paper, a recent simulation on one of the longest networks at Larderello, Italy, is presented. The simulation results are compared with field measurements and an earlier simulation by Marconcini and Neri (1979). Sensitivity of the simulation to the pipeline loss factor and well characteristics are discussed. Since the non-linear model solves the set of equations describing a network simultaneously, it has good flexibility, making it particularly applicable to looped networks which are much more difficult to solve than a tree-like network. 2 NON-LINEAR MODELLING STRATEGY A non-linear model solves the equation set simultaneously using a numerical method formulated from the conceptual model of the pipe network. A computer code has been developed based on this non-linear modelling strategy. The simulation results for a series of test models have shown a satisfactory convergence of the solution.