Browsing by Subject "productivity index"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item A mathematical model of the productivity index of a well(Texas A&M University, 2004-09-30) Khalmanova, Dinara KhabilovnaMotivated by the reservoir engineering concept of the productivity index of a producing oil well in an isolated reservoir, we analyze a time dependent functional, diffusive capacity, on the solutions to initial boundary value problems for a parabolic equation. Sufficient conditions providing for time independent diffusive capacity are given for different boundary conditions. The dependence of the constant diffusive capacity on the type of the boundary condition (Dirichlet, Neumann or third-type boundary condition) is investigated using a known variational principle and confirmed numerically for various geometrical settings. An important comparison between two principal constant values of a diffusive capacity is made, leading to the establishment of criteria when the so-called pseudo-steady-state and boundary-dominated productivity indices of a well significantly differ from each other. The third type boundary condition is shown to model the thin skin effect for the constant wellbore pressure production regime for a damaged well. The questions of stabilization and uniqueness of the time independent values of the diffusive capacity are addressed. The derived formulas are used in numerical study of evaluating the productivity index of a well in a general three-dimensional reservoir for a variety of well configurations.Item Gas Deliverability Using the Method of Distributed Volumetric Sources(2010-01-15) Jin, XiaozeProductivity index (PI) is an important indicator of a well?s production capacity. For conventional reservoirs, well productivity is usually calculated using the pressure response of the reservoir in its pseudosteady-state period. There are numerous studies for different well completion schemes which developed correlations for pseudosteady-state productivity index for specific cases, such as horizontal wells and fractured wells. Most of the developed models for complex well completion schemes use some approximations for productivity index calculation and they have some limitations in use. Furthermore, as the petroleum industry goes toward producing lower quality reservoirs like low- and ultra low-permeability reservoirs, the period of transient flow covers a larger part of the well lifetime and these pseudosteady-state productivity calculations become less applicable in prediction of the reservoir?s production behavior. The Distributed Volumetric Sources (DVS) method seems able to fill this gap. Our method is able to predict the productivity index of a general well completion scheme for transient as well as pseudosteady-state flow periods. In this study, we focus on a typical well completion scheme ? vertical well intersected by a vertical fracture of finite conductivity. Parametric study is performed by varying the proppant pack permeability with a linear distribution, varying fracture width with an elliptical distribution and varying fracture height with an elliptical distribution. The details of hydraulic fracture are integrated into the calculation of well productivity. By combining the well productivity with gas material balance, production forecasting of the hydraulically fractured wells could be easily obtained. The result of production forecasting could be used to aid in decision making of choosing the best stimulation treatment. Field examples are presented to illustrate the application of this technology for production modeling the complicated reservoir cases involving fracture stimulation.