Abstract
A mathematical model of the fracturing process, coupling the fracture mechanics and fracture propagation with reservoir flow and heat transfer, has been formulated. The model is applicable to fracturing treatments as well as to high leakoff applications such as fractured waterfloods and thermal fractures. The numerical technique developed is capable of simulating fracture extension for reasonably coarse grids, with truncation error being minimized for high leakoff applications when the grid next to the fracture is approximately square. With the aid of the model, a generalization of Carter's propagation formula has been developed that is also valid for high fluid-loss conditions. The capabilities of the model are illustrated by examples of heat transfer and massive-hydraulic-fracturing (MHF) treatment calculation.
Introduction
Induced fracturing of reservoir rock occurs under many different circumstances. Controlled hydraulic fracturing is an established method for increasing productivity of wells in low-permeability reservoirs. The technology of fracturing and the earlier design methods are reviewed by Howard and Fast.1 In waterflooding, injection pressures also often exceed fracturing pressures. This may result from poor operational practices, but it also could be intended to increase injectivity.2 In heavy oils, such as Alberta oil sands, most in-situ thermal recovery techniques rely on creating injectivity by fracturing the formation with steam.3 Fracturing also is being used as a method for deterining in-situ stresses4 and for establishing communication between wells for extraction of geothermal energy.5,6 Finally, fractures may be produced by explosive treatment or induced thermal stresses (such as in radioactive waste disposal).
To date, most of the research has been directed toward the understanding and design of fracture stimulation treatments, with emphasis on predicting fracture geometry.7–11 The influence of fluid flow and heat transfer in the reservoir has been neglected or accounted for by various approximations in these methods. On the other hand, the need for reservoir engineering analysis of fractured wells led to the development of analytical techniques and numerical models for predicting postfracture performance.1 A common feature of all these methods is that they treat only stationary fractures, which therefore must be computed using some of the methods of the first category mentioned earlier.
With the high costs associated with MHF,17–19 and with increasing complexity of the treatments, it is becoming important to be able to understand the interaction of the physical mechanisms involved and to improve the designs.
This paper presents a numerical model of the fracturing process that simultaneously accounts for the rock mechanics, two-phase fluid flow, and heat transfer, both in the fracture and in the reservoir. The model is capable of predicting fracture propagation, fluid leakoff and heat transfer, fracture closure, cleanup, and postfracture performance. Although the detailed calculations of geometry, proppant transport, etc., have not been included, they can be integrated in a natural way within the present model. Because vertical fractures are prevalent except for very shallow depths, the discussion is limited to vertical fracturing. The paper focuses attention on the formulation of the basic model and the numerical techniques in general. Applications to fracturing treatments and the specific enhancements of the model are described in a more recent paper.20
Temperature of rock formation and fracturing fluid during the hydraulic fracturing process
