A transient geothermal wellbore simulator

Abstract

A new transient geothermal wellbore simulator is presented. It is based on a mathematical model consisting of three conservation equations (mass, momentum and energy) and a slip model describing how the liquid and vapour phases move differently. The three conservation equations are discretised using the finite volume method with thermodynamic variables such as pressure and temperature defined at cell centres and flow variables such as volume flux of liquid and vapour velocity defined at cell boundaries. Implicit differencing in time is used and upstream weighting in space is essential.The three discrete conservation equations are solved together with the slip equation, giving a system of 4N nonlinear algebraic equations to be solved for 4N unknowns for a numerical model containing N blocks. This system of equations is solved using the Newton-Raphson method.For solving difficult transient problems e.g., starting and stopping production in a high temperature well, some subtle modifications of the standard upwinding approach were introduced. The simulator was then able to solve all the test cases we tried, including completion tests, opening and closing of wells (with some high enthalpy cases) and well stimulation by air-lifting and air-compression. The well stimulation simulations used a version of the simulator modified to handle a mixture of water and a noncondensible gas (NCG) by including two mass conservation equations, one for water and one for the NCG.Our simulator appears to be very robust and can solve a wide range of interesting transient flows in geothermal wells.