Abstract
Computer-based numerical simulation can be used as a tool for analysis of fracturing treatments and prediction of postfracturing well performance. The physical problem studied involves fracture mechanics, fluid flow, and heat transfer both in the fracture and in the reservoir. The numerical model predicts fracture extension, length, and width; proppant transport and settlement; fracture closure; cleanup, and postfracturing performance under different producing conditions. The number of physical features that are customarily neglected in fracture designs have been incorporated in the present model. These include stress-sensitive reservoir properties, proper two-phase calculation of leakoff and cleanup, stress-dependent fracture permeability and temperature- and time-dependent fracturing fluid rheology. The utility and a priori predictive capability of the model is illustrated with two examples of fracturing jobs. The first example is a marginal gas well stimulated by a medium-size gelled-water fracturing job. The second example is a massive foam fracture in the Elmworth basin. In both cases, the simulator predicted results that are in good agreement with the observed productivity.
Introduction
Fracturing technology has been developing rapidly in recent years. Both the size and sophistication of field treatments have increased dramatically. The development of low-permeability gas reserves is especially dependent on successful and economical application of fracturing technology. The low-permeability gas sands often have permeability below 1 ud and discontinuous (lenticular) or dual porosity structure. A number of very large treatments have been performed with varied results. Compared with the rapid development of field technology, design and analysis of massive hydraulic fracturing (MHF) treatments have involved traditional methods based on correlations and crude approximations. Design methods used by service companies and industry concentrate on the prediction of fracture shape and proppant placement, and as such do not predict accurately deliverability after the fracturing job. Such methods cannot be used for design optimization, which must be based on accurate long-term production forecasts. In addition, the various aspects of the process are, of necessity, treated separately. Typically, fracture extension, leakoff, fracturing fluid heatup, and cleanup all are determined independently using simplifying assumptions about their mutual influence. The need for production-forecasting tools has been recognized by reservoir engineers who developed analytical and numerical techniques for predicting the deliverability of fractured wells. The most advanced approaches of this type involve conventional finite-difference reservoir simulation techniques and are used for optimization of treatment size. The common weakness of analyses of this type is that the fracture is treated as static and many of the variables controlling deliverability (such as fracture length, conductivity, propped length, and height) must be entered and are typically obtained by the design methods discussed previously. Also, the influence of the fracturing job on the reservoir (such as damage by the fluid) cannot be properly accounted for. The need for tools that would model the entire process in a more rigorous fashion is obvious. Most of the information on the fracturing operations in the field must be obtained indirectly, and production testing yields the basic and most important data. A meaningful tool for analysis of treatments must therefore correctly model the interaction between the fracturing operation and the postfracture behavior. This paper describes development and field application of a comprehensive simulator that treats in an integrated fashion all important aspects of the problem. The correctness of our approach has been confirmed by validation against field data, showing excellent agreement. Our model still simplifies treatment of fracture containment, and ongoing development is directed toward enhancements that will allow a priori optimization of treatments including containment.
General Description of the Simulator
Although the model is general and can be used in other applications, this paper addresses only those features of interest in fracturing treatments. The relevant geometry is shown in Fig. 1. The model simulates two-dimensional (2D), compressible, two-phase flow and heat transfer simultaneously with initiation and propagation of a vertical hydraulic fracture. Once the fracture exists, appropriate equations of two-phase flow and heat transfer in the fracture also are solved.
SPEJ
P. 141^