GeoSteamNet: 2. STEAM FLOW SIMULATION IN A PIPELINE

A computer program is developed to simulate steam flow in a pipeline as a part of “GeoSteamNet: a computer package for the simulation of steam flow in a geothermal power plant network”. The fluid movement is governed by the following basic principles: the conservation of mass, the linear momentum principle (Newton’s second law or Navier Stokes equations) and the first and second laws of thermodynamics. The second law of thermodynamics defines the direction of a spontaneous process, which is indirectly validated in the algorithm as steam flows from high to low pressure and heat flows from high to low temperature. The nonlinear equations are solved with the Newton-Raphson method. A comparative study on the variation of temperature, pressure and heat loss in a pipeline of length 1000 m, inner diameter 0.3 m and thickness 0.005 m is presented. Three cases are discussed: a) no conduction-convection heat loss, b) an insulation of 0.05 m thickness on the pipeline and c) maximum heat loss (i.e. no insulation). The change in pressure is same in the three cases whereas there is appreciable temperature drop even in the case a. Similarly, there is 36% density change in the case b, which is a restriction to use the Bernoulli’s equation for steam flow simulation. INTRODUCTION Knowledge of numerical simulation of steam flow in a pipeline network of geothermal system is vital for rationalization and optimization of steam used for electrical energy generation (Ruíz et al. 2010). Presently, we are working on two important aspects of the project: a) thermodynamic data of water and b) appropriate algorithm for steam flow in a pipeline. The second aspect will be discussed here. The fluid flow is mostly analyzed by two equations: mass-balance (continuity equation) and momentum balance (Newton’s second law of motion or Navier Stokes equations) in situations where the fluid may be treated as incompressible and temperature differences are small (Mazumdar, 2009). Bhave and Gupta (2006) presented a comprehensive textbook on the analysis of water distribution in a municipal network. The water flow in a pipeline network is successfully modeled with the Bernoulli’s theorem and Hardy Cross method. In the circumstances when flow is compressible (density is not constant), or occurrence of heat flux (temperature is not constant), there is need of at least one more equation: energy balance. Smith and van Ness (1975) presented the derivation of all the three equations for fluid flow. In this article an algorithm is developed to solve numerically the three equations: mass, momentum and energy balance for steam flow in a pipeline. An example is presented for steam flow in a pipeline of 1000 m long for three cases: a) no heat loss, b) heat loss for given characteristics of pipe and insulation of it and c) maximum heat loss (i.e. no insulation). FUNDAMENTAL EQUATIONS The movement of fluid in a system is governed by the following basic principles: conservation of mass, the linear momentum principle (Newton’s second law or Navier Stokes equations) and the first and second laws of thermodynamics (smith and Van Ness, 1975). The second law of thermodynamics defines the direction of a spontaneous process. In the pipeline network of geothermal power plant the steam flows from high to low pressure and heat flows from high to low temperature. Thus the second law of thermodynamics is indirectly validated and will not be considered here. Majumdar (1999) developed a general purpose computer program “Generalized Fluid System Simulation Program (GFSSP)” to compute pressure and flow distribution in a complex fluid network m i-1, Ti-1 , Pi-1 m i, Ti , Pi