Abstract

New graphical techniques are presented for estimating the diffusivity coefficient (or mass diffusivity) of light gases in highly-viscous bitumens from pressure-decay data. These methods are based on modeling the rate of change in pressureusing the diffusion equation coupled with a mass balance for the gas phase. Analytical solutions of the resulting set of equations, with appropriate initial and boundary conditions, are obtained by Laplace transformation. An inverse solution technique is employed for developing two graphical methods for estimating the diffusivity coefficient from pressure-decay data reported in the literature. The estimated diffusivity coefficients for gas-bitumen pairs at 75–90 °C vary from 2.5 × 10–10 to 7.8 ×10–10 m2/s, and these are in good agreement with literature values. The novelty of the proposed methodology is in its simplicity and in its ability to isolate portions of the pressuredecay data affected by experimental fluctuations. This enables the consideration of only that portion of the data that is consistent with the analytical solution.

Introduction

Due to the rapid decline in conventional oil reserves, bitumens from the vast oil sands reserves in Alberta, Canada, represent an emerging source of hydrocarbons and energy. In 2003, for the first time, the bitumen production surpassed the production of conventional crude oil in Alberta.1 The major obstacle toeconomic recovery and processing of bitumens is their high viscosity, making them essentially immobile at reservoir temperatures. However, the viscosity of bitumens and heavy oils can be decreased dramatically by mixing them with solvents or light gases at high pressures. The decrease in bitumen viscosity is related to the gas solubility. 2 For example, carbon dioxide with a high solubility causes a large reduction in the bitumen viscosity. The decrease in bitumen viscosity results in its improved flow and hydrocarbon recovery factors. In fact, this is the basis of an in-situ recovery technique, known as the VAPEX process.3

Molecular diffusion plays an important role in the recovery rocesses as well as many other reservoir engineering applications. An accurate value of the diffusion coefficient of gases in bitumens is, therefore, essential for calculating the rate of gas dissolution in bitumens and heavy oils. An order of agnitude calculation for diffusion in liquids can be obtained by two theories, the Hydrodynamic theory and the Eyring theory. 4 However, the simplifying approximations involved in these theories may not apply to the complex multi-ring naphthenic and aromatic molecules present in bitumens. Apredictive method, based on the corresponding states thermodynamic framework, for the diffusion coefficient of carbon dioxide in Athabasca bitumen has been reported. 5

The different experimental methods for the diffusivity of gases in bitumens can be broadly classified into the direct and indirect methods. The direct methods, based on the determination of the composition of the diffusing species along the length of the bitumen sample with time, require compositional analysis.6 However, the direct methods tend to be expensive and time consuming. On the other hand, the indirect methods measure thechange in one of the system parameters that varies due to the diffusion without the need to determine the composition.

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