Determination of Gas-Diffusion and Interface-Mass-Transfer Coefficients for Quiescent Reservoir Liquids

Abstract

Summary A physically and mathematically rigorous transient-state equilibrium diffusion model is applied for simultaneous determination of the gas-diffusion and interface-mass-transfer coefficients from pressure de-cline by dissolution of gas in quiescent liquids involving petroleum reservoirs. The short- and long-time analytical solutions of this model are reformulated to enable direct determination of the best-estimate values of these parameters by regression of experimental data. Typical experimental data are then analyzed by means of the present improved methods, and the values obtained are compared with the re-ported values. The present methodology is proven practical and yields unique and accurate parameter values. Introduction Gas-diffusivity and interface-mass-transfer coefficients are important parameters determining the rate of dissolution of the injection gases in oil during secondary recovery, and the rate of dissolution and separation of light gases in reservoir oil and brine, water tables associated with depleted-reservoir gas storage, drilling mud, and completion fluids (Hill and Lacey 1934; O'Bryan et al. 1988; O'Bryan and Bourgoyne 1990; Bodwadkar and Chenevert 1997; Bradley et al. 2002; Liu and Civan 2005). In order to develop proper gas-injection strategies, accurate values of these parameters are required for reservoir simulation and prediction of oil recovery by miscible flooding and the optimization of miscibility for best recovery. Laboratory measurement of gas diffusivity in quiescent liquids is usually accomplished through the measurement of the pressure of gas in contact with certain liquids, such as oil, brine, drilling mud, and completion fluids in a closed PVT cell (see Fig. 1) during gas dissolution in the liquid phase. The accuracies of the available models, including those by Riazi (1996), Sachs (1997, 1998), and Zhang et al. (2000), are limited by the inherent simplifying assumptions involved in the analytic treatment and the subsequent interpretation of such experimental data. As judged by the reported studies, there appears to be no consensus among the available analytical approaches used for diffusivity measurement. In addition, the previous studies focused mostly on the determination of gas diffusivity and did not account for interface-mass-transfer effects. The methodology offered by Civan and Rasmussen (2001, 2002, 2003), and further elaborated in the present paper, allows for both interface mass-transfer effects and for bulk diffusivity. It is a novel and practical approach that determines parameters describing both effects from a given set of pressure-decline data. The best estimate of the coefficient of diffusion of gas species (solute) in a given liquid medium (solvent) is usually inferred indirectly by matching the prediction of a suitable mathematical model involving the species transfer by diffusion to experimental data under prescribed conditions. For this purpose, Sachs (1998) resorts to the numerical solution of the nonlinear model equations incorporating the dependency of the diffusion coefficient on concentration without clearly describing the boundary conditions used in the solution.

Quantification of Density-Driven Natural Convection for Dissolution Mechanism in CO2 Sequestration

“…Other researchers have proposed and developed different mathematical solutions by modeling the interface boundary condition differently. With dependence on how the interface boundary condition is defined, a range of simple to very complex solutions can be expected for this problem Mehrotra 2000, 2002;Civan and Rasmussen 2006;Rasmussen and Civan 2009;Tharanivasan et al 2004;Etminan et al 2010). It is evident that there is not a considerable error in using simple method for determination of diffusion coefficient.…”

Evaluation of interfacial mass transfer coefficient as a function of temperature and pressure in carbon dioxide/normal alkane systems

“…These research works, assumed an equilibrium boundary condition at the gas-liquid interface [6][7][8]; however, some studies put forward the theory of existence of the resistance at interface as a non-equilibrium boundary condition, and this new boundary condition was solved analytically in the form of an infinite Fourier series [9,10]. Employing such boundary condition will be important when a high pressure gas suddenly contacts with a liquid in which gas does not have enough time to reach equilibrium [11].…”

“…4 is replaced with a Robin type boundary condition [11] and mass transfer will be modeled in the presence of interface resistance. Therefore, second boundary condition is:…”

“…As it is obvious, k D expresses the ratio of bulk resistance to interfacial resistance. Low value of k D , indicates significant amount of interface resistance [11,29]. Therefore, Eqs.…”

Temperature Effect on Power for Particle Detachment from Pore Wall Described by an Arrhenius-Type Equation

“…Arrhenius (1889) and Vogel-Tammann-Fulcher-type (Civan 2005) asymptoticexponential equations are frequently used for correlation of the temperature dependence of the various phenomenological parameters. The applications include the correlation of the diffusion coefficient, fluid viscosity, emulsion stability, rock wettability, and particle-particle adherence forces as functions of temperature (Civan and Weers 2001;Civan et al 2004;Civan 2004Civan , 2005Civan and Rasmussen 2006). Khilar and Fogler (2000) correlated the rate coefficient of particle detachment from the pore wall as a function of temperature satisfactorily using an Arrhenius-type (1889) equation.…”