Mathematical Modelling of Transport Processes During Wellbore Heating in Tar Sand and Bituminous Reservoirs
Authors: Karmaker K. , Maini B.B. , Jeje A.A. 
Published: March 2010

Abstract
Enhanced oil recovery (EOR) processes sometimes involve wellbore heating by means of electromagnetic radiation, electrical heating, or steam injection. When a wellbore is heated in tar sands and bituminous reservoirs, many thermo-physical properties of the bitumen and rock matrix can change significantly and thereby alter the fluids and heat flow behaviour.
This paper presents the development of a mathematical formulation that describes the flow behaviours of heat and fluids around a wellbore during the initial period of heating in tar sands and bituminous reservoirs. The model shows that the transient temperature distribution is not affected significantly by convection. However, the pressure distribution exhibits an abnormally high pressure build-up resulting from the relative thermal expansion of in situ bitumen in the region where the temperature is slightly higher than the reservoir temperature. The mathematical model can be used to obtain predictions of pressure-temperature distributions around heated wellbores, well communication time required in the steam assisted gravity drainage (SAGD) process, and well stimulation and absolute permeability improvement resulting from progressive shear dilation in low permeability bitumen and tar sand reservoirs.

Introduction
The recovery of oil from tar sands and bitumen reservoirs is difficult because of the very high viscosity at reservoir conditions. For instance, the in situ viscosity of bitumen in the Athabasca oilsand deposit has been estimated to be more than 106 cp(1). The basic mechanism of thermal recovery processes is to increase the reservoir temperature and thereby reduce the oil viscosity to make it mobile.
Besides the viscosity, other physical properties of the bitumen and rock matrix can also change considerably during formation heating. Based on a study with geomechanical/thermal reservoir simulation, Collins et al.(2) have shown that the injection of high pressure steam into the oil sands during the SAGD process induces stress changes, and these cause an increase in permeability. Laboratory test results have shown that the structural damage to rocks may result from differential expansion of mineral constituents(3). In tight reservoirs, localized fractures might be created due to the expansion of fluids in dead-end pores.
An increase in temperature affects reservoir production mechanisms through changes in the mobility of fluids and interfacial tension. The changes in fluid mobility occur not only due to the expected dependence of fluid viscosity on temperature but also due to changes in the rock properties. It is important while heating a wellbore in a reservoir with a certain type of lithology, to know whether or not such changes in formation physics are likely to occur. In many circumstances, such thermo-physical changes could also induce formation damage and alter the reservoir flow behaviour irreversibly.
The predictions of reservoir flow behaviour and parametric changes for the system require an accurate model for temperature and pressure distributions in the formation during heating. However, such predictive models are still lacking in literature. Particularly in low permeability bituminous reservoirs, the pressure and temperature distributions are interdependent due to the fact that:the thermal expansion of bitumen is an order of magnitude greater than that of reservoir rock matrix; and,the viscosity f bitumen changes dramatically with temperature.