Abstract
Abstract
Petroleum well performance and its evaluation are clearly some of the most important functions of modern production engineering. We present a general approach to the issue by employing the field-derived, dimensionless productivity index (J[D]) which we calculate from measured information including the production rate, reservoir and flowing pressures and well and reservoir data.
The dimensionless J[D] is independent of well completion, i.e., it transcends the geometry, whether the well is under radial flow, hydraulically fractured or whether it is vertical or horizontal. The determined J[D]'s are then compared against benchmarks we have developed for optimized production such as the concept of Unified Fracture Design (UFD) or maximized horizontal well performance. We have developed deterministic methods for this analysis and new means to graphically depict the results.
Such evaluations are important in concluding whether the well is underperforming or whether the past engineering could have been improved and by how much. Decisions such as re-fracturing, the redesign and improvement of future treatments and whether to fracture vertical or drill horizontal wells can be readily made.
Introduction
The production (or injection) of an oil or gas well is of fundamental concern in petroleum engineering. There are many well known approaches to tracking the problem, some using analytical mathematical approximations, others, more involved, use numerical simulation schemes. For single well performance, the analytical approximations are often quite adequate and we will use them in this work.
Traditionally the well inflow is derived from Darcy's Law in radial coordinates with added boundaries: the near-well condition is characterized by a skin effect while the outer boundaries can be distinguished as constant pressure (steady state) or no-flow (pseudosteady state.) For radial flow geometry the expressions are quite rudimentary. Irregular drainage shapes and asymmetrical well positions can be accounted for with the use of shape factors. On occasion, transient conditions are assumed with infinite-acting boundaries but such situation is generally of no practical use for the production prediction and evaluation of almost all, but the lowest-permeability reservoirs.
The pseudosteady-state condition is the one most interesting for the forecast of future well performance because it can account for reservoir pressure depletion. The latter requires material balance calculations which relate this depletion to the underground fluid withdrawal.
Well deliverability combines inflow performance, denoted by the inflow performance relationship (IPR), and the flow in the well tubulars providing some of the best known graphical constructions in production engineering. For a comprehensive treatment of these subjects the reader is referred to Economides et al. (1994.)
Beyond the conventional vertical wells, other well configurations and well completions have been introduced over the years. These include slanted or deviated wells, horizontal wells or, more recently, complex well architectures such as multilateral, multibranched, and multilevel wells. The wells themselves are often hydraulically fractured. For all these cases, mathematical approximations have been offered to account for reservoir inflow. These relationships take into account, the well geometry, the well and reservoir-boundary interactions and, even, permeability anisotropy. For hydraulically fractured wells, the fracture dimensions (length and width) and fracture permeability are also used.
At times, as in the case of fractured wells, some investigators (e.g., Cinco-Ley et al., 1978) have replaced the fracture characteristics from well inflow relationships and lumped them together into an equivalent skin effect, a useful approximation for late-time flow performance such as pseudoradial or pseudosteady state.