Sensitivity Analysis of the Performance of In-Situ Upgrading for the Recovery of Heavy Oil Using Dimensionless Analysis

The modelling of In-Situ Upgrading of heavy oil is complex as various physical and chemical phenomena need to be represented. In this process, a tight pattern of electrical heater wells is used to bring the formation to a high temperature so that the heavy oil decomposes through a series of pyrolysis reactions into lighter liquid and gas components. The heat propagates inside the reservoir primarily by conduction, but as the chemical reactions advance, the viscosity of the fluid decreases and changes the relative importance of mass and heat convection. Predicting the outcome of the process is challenging as firstly relatively small changes in the fluid compositions can significantly change the thermodynamic properties of the system and secondly there are a large number of parameters that control the behaviour. This paper uses dimensionless scaling to determine the key parameters that control the performance of In-Situ Upgrading. Dimensionless scaling enables us to reduce the number of parameters in the problem and thus simplify our analysis. It also allows us to quantify the relative importance of the various dimensional parameters (permeability, thermal conduction, reaction constants...). We first use Inspectional Analysis (IA) to determine the minimum set of dimensionless numbers needed to characterize 1D In-Situ Upgrading problems applied to bitumen and oil shale, where a heavy liquid or solid reactant decomposes into lighter liquid and gas components by a series of two pyrolysis reactions. This method analyses the underlying physical laws governing the process, expressed in the form of partial differential equations and boundary conditions. Next we study the variability of the Energy Return Over Invested (EROI) with the scaling groups by performing a sensitivity analysis using experimental design. We show that the reduced energy contents of oil and gas, the reduced volumetric heat capacity of the reactant and the Arrhenius number of the chemical reactions are most important for estimating the energy efficiency of the process.