Abstract
The propagation of electromagnetic waves within oil production pipes has been studied, taking into account the variation in oil temperature along the pipe. This work shows the development of a simulation model under uncertainties, which is able to simulate the electromagnetic propagation in an inhomogeneous medium by dividing the production pipe into smaller pipe segments, each one approximately homogeneous (constant electrical conductivity). In each segment, the model assumes that the electrical conductivity of oil is a constant and, therefore, the sub pipe is a homogeneous medium. Within each homogeneous medium, the solution is analytically represented by an expansion in basis functions (called modes), that are obtained by the solution of the vector wave equation in a cylinder with lossless walls. Boundary conditions are then applied between adjacent segments to ensure the continuity of both the electric field and the magnetic field, leading into a system of linear equations on the coefficients of the series expansion in basis functions. The solution of this linear system gives the fields in each pipe segment, thus solving the original inhomogeneous problem. In order to account for uncertainties, Monte-Carlo sampling has been used to add small perturbations to pre-defined oil conductivity profiles along the production pipe. The results show that this model can simulate a thousand of scenarios in less than a second, thus making it ideal for use with optimization algorithms which objective function depends on simulating the propagation of electromagnetic waves inside the well.
