With the advancement in fields of science more complex and more coupled phenomena can be explained, calculated and predicted. To solve these problems one has to update the related tools. Since analytical solutions do not exist for all physical processes, solving system of equation numerically has been a readily adopted and proven effective strategy. However, once a new solving strategy is developed, it must be checked for correctness. One way is to compare the output of the new method, to a known analytical solution. This is what this report is aiming to do. We will adopt the Block Conjugate Gradient solving method to a poroelastic Borehole Problem, which is a problem for which analytical solutions exist, to test the effectiveness of the solver.