Investigation and Implementation of Temperature Field Model for High Temperature Deep Well Utilizing the Element Free Galerkin Method

Abstract In response to the difficulties of calculating the wellbore temperature field using the traditional mesh method, which has high mesh dependence, large calculation scale, and time-consuming, a high-temperature deep well heat transfer model is established based on the element free Galerkin method (EFG). By comparing the mesh method, the Hasan model, and measured values in the Tarim Basin, the applicability, calculation accuracy, and efficiency of the element free method are studied. The influence of the boundary treatment method, scaling parameter, and weight function on the steady-state distribution and transient change of the wellbore temperature is discussed. The research results show that the average relative error in calculating the wellbore temperature during injection is 3.93%, and the maximum relative error is 6.02%. At the same step size, the element free method saves nearly 19 times more time than the mesh method. The penalty function method has more advantages than the Lagrange multiplier method in calculating wellbore heat transfer. When the scaling parameter is less than 2.4 and greater than 1.8, all weight functions can obtain more accurate calculation results when calculating the steady-state distribution of the wellbore temperature field, and when calculating the transient distribution of the wellbore temperature field, the cubic spline (CS), quartic spline (QS), rational, Gaussian, radial basis (RB), and quadratic weight functions are more advantageous. The research results can provide new ideas for the analysis of high-temperature deep well temperature fields and ensure the safety and stability of injection and oil and gas production.