Mathematical Modelling of Transport Processes During Wellbore Heating in Tar Sand and Bituminous Reservoirs

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 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 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 oil-sand deposit has been estimated to be more than 106 cp1. 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 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 showed that the injection of high pressure steam into the oil sands during the SAGD process induces stress changes, and these cause increase in permeability. Laboratory test results3 have showed that the structural damage of rocks may result from differential expansion of mineral constituents. In tight reservoirs, localized fractures might be created due to the expansion of fluids in dead-end pores. An increase in temperature can also affect reservoir production mechanisms through changes in the mobility of fluids, interfacial tension, and many other parameters. It is important, while heating a wellbore in a reservoir with 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 all these parametric changes 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 inter-dependent due to the facts that (1) the thermal expansion of bitumen is an order of magnitude greater than that of reservoir rock matrix and (2) the viscosity of bitumen changes dramatically with temperature. As a result, the relative thermal expansion of bitumen and other fluids present within pores can cause the reservoir pressure to increase remarkably with the increase in temperature.

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