A New Method of Numerical Simulation for Perforation Completion of Fracture Formation
Authors: Lian Zhanghua , Meng Yingfeng , Tong Min 
Published: December 2007

Abstract
Based on the photoelectric testing system in this paper, the geometry data of core fracture in reservoir zone was obtained, we inversed the core-fracture data to the borehole wall, and then extended the formation. In this paper, the model of 3D finite-element fluid flow for the fracture formation was established by a series of mathematical and mechanical equations and the fracture coupled with formation. The model included various parameters, which influenced the production ratio (PR) of perforation completion of fracture formation, especially fracture thickness, fracture number, and its orientation, as well as fracture permeability. In light of the model, we analyzed the flow rate in perforation and the distribution of pressure and velocity field around the perforation for four cases: the perforation tunnel is far away, near, cross and parallel the fracture. The paper described the PR curves varying with perforation diameter and length, and fracture thickness, these results provided a new idea for optimum design and PR prediction of perforation completion under fracture. It has a practical engineering meaning for the evaluation of perforation completion of fracture formation.

Introduction
Perforated completion is one of the extensively used methods of oil and gas completion in oil field at home and abroad. Many researchers[1-5] have done a lot of studies in this area for a long time, the main objective is to study various relevant parameters to improve its production ratio. Summarizing the previous researchers' achievement, we can divide the methods into two classifications:experimentation,theoretical method.
Experimentation includes the perforated completion of real models in laboratory, as well as spot logging experimentation. Theoretical methods include formula derivation and finite element method (FEM). The theoretical method is assumed that the fluid flow in the permeable formation can be modeled by potential theory, that is, as a solution to Laplace's equation, subject to particular boundary conditions. FEM directly applies the basic equations of fluid flow and variation principle, and then disperses the perforated completion model. Actually, experimentation and theoretical method are not separated two parts. Various related parameters can be tested by experiment, it provides the modified factors for the theoretical formula, such as the skin factor, drilling damaged factor and completion factor, and so on.
Experimentation is involved some testing apparatus, investment bigger, period longer. Since there are a lot of experimental data[1-5] can be quoted and used for reference at home and abroad. In this paper, we focused on the theoretical FEM to analyze and study the various parameters of the perforated completion, established the models and meshed them. It provides reasonable models for the optimum design of the perforated completion. We use 5 kinds of permeability to simulate the perforated completion model, i.e. first, fracture, second, borehole and perforation tunnel; third, crushed (compacted) zone around the perforation tunnel; fourth, drilling damaged zone formation; finally, undamaged zone formation.