Reproducing kernel method for numerical simulation of downhole temperature distribution

This paper research downhole temperature distribution in oil production and water injection using reproducing kernel Hilbert space method (RKHSM) for the first time. The aim of this paper is that using the highly accurate RKHSM can solve downhole temperature problems effectively. According to 2-D mathematical models of downhole temperature distribution, the analytical solution was given in a series expansion form and the approximate solution was expressed by n-term summation of reproducing kernel functions which initial and boundary conditions were selected properly. Numerical results of downhole temperature distribution with multiple pay zones, in which different radial distance and different injection-production conditions (such as injection rate, injection temperature, injection time, oil layer thickness), were carried out by mathematical 7.0, and numerical results correspond to general knowledge and show that use RKHSM to research downhole temperature distribution is feasible and effective.