Heat loss calculation in thermal simulation

An appraisal is presented for four different methods that are usually incorporated in thermal simulators to estimate the rate of heat loss to surroundings. The methods are the analytical solution using a superposition theorem, the analytical solution using a numerical approximation to the convolution integral, the semi-analytical solution, and the numerical solution. This appraisal includes expressing the equations in a form that can be incorporated into a fully implicit simulator, computer programming complexity, and the computer CPU time and memory storage requirements. A steam flood problem is used for the comparison, and the gas recovery, oil recovery, and heat loss performances for a reservoir in one and two dimensions are presented. It is found that the numerical solution is sensitive to grid size in the overburden, the semi-analytical solution is the simplest to program but its prediction is the least accurate, the analytical solution is the most expensive, whereas the analytical-numerical solution combines both accuracy and acceptable storage requirements, and therefore, it is recommended for use in thermal simulation.