Non-isothermal Gravity Drainage Under Conduction Heating

Abstract Gravity flow plays an important role in thermal oil recovery under a variety of conditions. These include cyclic steam stimulation, conduction heating and formation heating in a fractured system. This paper addresses first the problem of steam heating of a naturally fractured reservoir in terms of a slab or a cylindrical block surrounded by steam. An analytical approach is used, which for the first time considers the transient temperature distribution within a single block. Heat integral method is used to obtain the unsteady-state temperature profile. The temperature distribution is used to calculate drainage rate under gravity flow. The solutions obtained are used to determine the effect of the principal variables involved in particular thermal diffusivity, time, and the geometric size. The application of our approach is extended to conduction heating problems under drag flow in which the heating boundary moves slowly. The criterion used to justify the stationary boundary assumption is Cited. Other potential applications include formation heating below an artificial fracture, and old cyclic steam stimulated reservoirs producing under gravity flow. Introduction Viscosity reduction is known to be the main contribution to higher flow rates in heavy oil recovery using steam1. Heating is achieved by either or both of two heat transfer mechanisms, namely conduction and convection. Field experience and modeling studies have shown that conduction lays the major role in a variety of processes. In naturally fractured reservoirs, steam displaces the heavy oil present in the fracture network to create a steam zone which encompasses matrix blocks containing heavy oil. Heat conduction occurs from steam in the fractures to the heavy oil within the matrix blocks. Conduction causes the mobilization of heavy oil in the vicinity of artificial fractures created by steam injection above parting pressure2. In mature steamdrives with complete override, gravity flow of heated oil by conduction as shown to be the major recovery mechanism3. In this paper, oil flow under conduction heating is modeled for three cases, and the extension of our method for some other cases s explained. Nolan et al. 4 proposed the applicability of steam injection for naturally fractured reservoirs. They solved the beat conduction problem for slabs, and found that temperature of single blocks surrounded by steam rises approximately to steam temperature within a year. Hence, they concluded that heat conduction was the only beating mechanism and performed numerical simulation to study oil recovery under this condition. Dreher et al.5 performed numerical simulation and found that heat conduction plays the major role for heating matrix blocks once steam is injected into naturally fractured reservoirs. Saanan6 analytically studied beat propagation in naturally fractured reservoirs containing impermeable blocks by considering unsteady-state heat conduction between matrix and fracture. His method was analogous to pressure distribution in double porosity systems. Van Wunnik and Wit7 studied stearn injection into the gas cap of a densely fractured reservoir and investigated heat and fluid flow. They considered small matrix blocks and neglected temperature variation within individual blocks. In a companion paper8 steam beating of a single block was studied by considering both conduction and convection terms in the heat equation.