The Application of Boundary Element Method to Pressure Behaviour Analysis in a Composite Reservoir With Lateral Drilling

Abstract

With the increase of lateral wells, it becomes more and more important to evaluate pressure performance and formation damage in a composite reservoir with lateral drilling. Considering the properties of lateral drilling in a composite reservoir, this paper presents a mathematical model for 3D unsteady flow which is solved using the boundary element method and regional division technique for pressure performance of a lateral drilling well produced at a constant rate or a constant bottomhole pressure. By the reasonable incorporation of pseudo skin factor, dimensionless damaged radius, dimensionless wellbore storage coefficient, and permeability of damaged region, we can get the type curves which can be used to evaluate formation damage caused by lateral drilling. The application to test data for a lateral drilling well in the Liaohe Oilfield in East China shows that the model is reliable and the analysis is valid.

Introduction

During drilling and production, the formation in the vicinity of the wellbore is damaged to some extent due to the invasion of drilling mud and workover fluids. The evaluation of damage in a lateral drilling well is extremely important for the design of the subsequent well completions. However, an applicable method for the evaluation of damage has not been reported in the literature. Considering factors such as permeability, skin factor, and the radius of the damaged region, a 3D unsteady percolation mathematical model based on the physical model has been derived. Finite differential and finite element techniques are not effective in dealing with the intricate boundary conditions associated with this type of problem.
Numerical boundary element method in combination with regional division technique is introduced to solve the flow equations and obtain the numerical solution to the new mathematical model. The boundary element method has three features in handling the mathematical model. First, it lowers the space dimension from 3D to 2D on the boundary curved-surface, which requires less input and computation. Second, it improves precision because the grid partition only involves the boundary and the discreting error comes only from the boundary. The corresponding variables in the region can be directly solved by the differential of the analytical equation. Third, it is convenient for treating the variable at any position in the region. The regional division technique has olved the problem with variable properties as the fluid and formation between the damaged and original formation. The Boundary Element Method, given the above advantages incorporated with the regional numerical simulation, shows promise for applications in simulations. By the reasonable combination of pseudo skin factor, dimensionless damaged radius, dimensionless wellbore storage coefficient, and permeability of damaged region, we can get the type curves which can be used for evaluation of damaged formations caused by lateral drilling. The application to ell test data shows the validity of the model.