Thermally Induced Fracturing: Analysis of a Field Case in North Sea
Authors: Charlez P. , Lemonnier P. , Ruffet C. , Bouteca M.J. , Tan C. 
Published: December 2007

Abstract
Thermally Induced Fracturing (TIF) is often observed on injection wells. In this paper a well documented TIF case is presented and analysed. A numerical model is first presented where waterflooding is computed in two steps. In the first step, radial flow is considered and stress changes are computed. Depending on rock characteristics and flow rate the thermal effect (stress decrease) dominates over the pressure effect (stress increase). In the second step, as soon as the fracturing criterion is reached, the model automatically switches to a coupled two-phase flow option where a PKN type fracture has been incorporated. The main features of the model are summarized. To validate the model a field case has been analyzed where bottom hole pressure and temperature have been recorded. From field data it is shown that in the initial stage the height of the fracture varies and is thus different from the pay zone thickness. Use of Perkins and Gonzalez solution together with Prats formula allows to assess height and length evolution of the fracture. From this information, a mean fracture height can be assessed for the test duration. It is then shown that the pressure profile versus time is well given back using the numerical model, thus confirming the previous estimation of fracture dimensions.

Introduction
Waterflooding is still today the most common oil recovery method. It is aimed at improving recovery together with increasing production rate.
Apart from any recovery process, injection of a cold fluid into a warmer reservoir induces thermal stresses, the main effect of which is to relax the hoop stress component over a certain distance. Indeed, the typical hoop stress profile (Fig. 1) around an injection well shows two distinct parts. In the section of the reservoir which has already been cooled, the thermal hoop stress is negative. Consequently, the total hoop stress is relaxed compared to its original value. This relaxation is, however, modulated by the hydraulic component (variation of stress associated with variation of pore pressure), which, depending on the voidage (balance between injection at the considered well and production from adjacent wells), can be either positive or negative. By contrast, in the zone which has not yet been affected by cooling, and for obvious equilibrium reasons, the hoop stress is greater than the original minor geostatic stress ah. Between these two zones, a very thin transition with a very steep stress gradient prevails.
If hoop stress (initially equal to) relaxes below the injection pressure Pinj, a hydraulic fracture will initiate and then propagate until the transition zone (which we will call "stress wall" for obvious reasons) in the vicinity of which it stops. The temperature via the thermal stress thus acts as a propagation regulator. In waterflooding, the resultant back stresses (hydraulic and thermal) can no more be neglected as in classical hydraulic fracturing.
Modelling of Thermal Induced Fracturing (T.I.F.) was initiated during the mid eighties by Perkins and Gonzales. In their paper, they assume that thermal conductivity can be neglected with respect to convection (in practice, this is almost always the case). Consequently, temperature is a step function and the reservoir area can be divided into a cold zone (at fluid temperature Tf) and a hot, undisturbed zone at reservoir temperature TR. Furthermore, as they assume a constant injection flow rate Q, the volume of the cooled zone can easily be calculated at any time t writing the energy balance between injected and received heat. As the fracture propagates, the cold zone initially radial lengthens parallel to the fracture direction. This suggests approximating the cooled region by an ellipsis confocal to the fracture direction (the fracture tip merges with the foci of the ellipsis - Fig. 2). The half-axes a0 and b0 are given by the following formulae:
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