Article pubs.acs.org/jced
Diffusion Coefficients of Carbon Dioxide in Brines Measured Using 13 C Pulsed-Field Gradient Nuclear Magnetic Resonance Shane P. Cadogan,† Jason P. Hallett,‡ Geoffrey C. Maitland,† and J. P. Martin Trusler*,† †
Qatar Carbonates and Carbon Storage Research Centre, Department of Chemical Engineering and ‡Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom ABSTRACT: Tracer diffusion coefficients of CO2 in several brines were measured by 13C pulsed-field gradient NMR at a temperature of 298 K and at salt molalities of up to 5 mol·kg−1. The brines studied were NaCl(aq), CaCl2(aq), Na2SO4(aq), and a mixed brine prepared from seven salts: NaCl, CaCl2, MgCl2, KCl, Na2SO4, SrCl2, NaHCO3. The experimental results are compared with the predictions of a modified Stokes−Einstein relation in which the Stokes−Einstein number is 4 and the hydrodynamic radius of the CO2 molecule in aqueous solution is taken to be 168 pm, as determined in an earlier study of the (CO2 + H2O) binary system at the same temperature (Cadogan et al. J. Chem. Eng. Data 2014, 59, 519−525). This comparison shows agreement to within the experimental uncertainty, independent of salt type and molality. We conclude that the modified Stokes−Einstein relation provides a reliable means of estimating the tracer diffusion coefficient of CO2 in aqueous electrolyte solutions, based on knowledge of the brine viscosity and the hydrodynamic radius of CO2 in pure water at the same temperature.
1. INTRODUCTION Transport properties of CO2 in brines and/or hydrocarbons are of interest in many fields, including chemical and petroleum engineering, earth science, and the biomedical sciences. In particular, diffusion coefficients of CO2 and other species in brines and hydrocarbons are important physical parameters in the fields of carbon capture, utilization, and storage (CCUS) and carbon-dioxide enhanced oil recovery (EOR). For carbon storage in deep saline aquifers, these diffusion coefficients often control the rates of interfacial mass transfer and of heterogeneous chemical reactions involving species in aqueous solution and the porous reservoir minerals. The Peclet number, defined as the ratio of the advection to the relevant diffusion coefficient, is often used to characterize dispersive flow in porous media. The Peclet number of CO2 is typically low far away from the point of injection, and in that regime the transport of CO2 is controlled by molecular diffusion.1 However, the diffusion coefficients of CO2 in brines and other systems relevant to CCUS and CO2-EOR are still largely unstudied. While several investigations have been carried out on the diffusion coefficient of CO2 in water, only two studies have reported values over a range of temperatures and at elevated pressures (>1 MPa).2,3 In the absence of salts, a single diffusion coefficient fully describes the mutual diffusion of CO2 and water in the system. When the CO2 is dissolved in a brine, there are at least three diffusing components: CO2, salt, and H2O. Diffusion can be described in the Fickian formalism by means of the following relations where there is no net molar flux with respect to the coordinate system: −j1 = D11∇c1 + D12∇c 2
(2)
j1Vm,1 + j2 Vm,2 + j3Vm,3 = 0
(3)
Here, ji, ci, and Vm,i are the molar flux vector, concentration, and partial molar volume of component i, the solvent (H2O) is designated as component 3, and Dij are a set of Fickian diffusion coefficients coupling the flux of solute i to the concentration gradient of solute j. Generalization to a system of n solutes in a single solvent involves (n + 1) equations and an n × n matrix of diffusion coefficients which is not generally diagonal. The determination of such a potentially large set of coefficients could be a demanding task, especially in nondilute solutions where the diffusion coefficients depend upon concentration. Furthermore, a formally exact description of a multisolute system may be computationally expensive to incorporate in a large-scale model or simulation. In the present case one of the solutes, CO2, is present only in low concentration. In fact, the mole fraction of CO2 in a brine at saturation is typically only of order 10−2 even at reservoir pressure, and in the experiments reported here, which were carried out at ambient pressure, it was of order 10−4. Under these circumstances, it can be appropriate to consider the tracer diffusion coefficient of the sparingly soluble component in an otherwise spatially uniform brine that is treated as a pseudopure solvent. Such a reduction has been discussed by Garcia-Ratés et al.,4 using arguments based on the Stefan-Maxwell formalism, and also by Cussler.5 Thus, in the remainder of this work, we focus on the diffusion coefficient D11 coupling the flux and Received: October 4, 2014 Accepted: November 15, 2014 Published: November 24, 2014
(1) © 2014 American Chemical Society
−j2 = D21∇c1 + D22∇c 2
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dx.doi.org/10.1021/je5009203 | J. Chem. Eng. Data 2015, 60, 181−184
Journal of Chemical & Engineering Data
Article
Table 1. Composition of the Synthetic Reservoir Brine, Where m Denotes Molality of Salt in Water species m/(kg·mol−1)
NaCl 1.514
CaCl2 0.276
MgCl2 0.080
KCl 0.012
SrCl2 0.004
NaHCO3 0.003
and Na2SO4(aq)] as well as a multicomponent brine, the composition of which is detailed in Table 1. To prepare the 13 CO2-saturated brine solution, a quantity of brine was transferred to a 100 mL borosilicate glass bottle containing a magnetic stirrer bar and closed by an airtight lid fitted with two gas connection ports. One port was connected via a valve to a vacuum pump, while the second led via a manifold to a rubber gas bladder and the valved 13CO2 lecture bottle. Using this apparatus, the brine was first degassed under vacuum and then saturated with 13CO2 at ambient pressure, both operations occurring under stirring. Under these conditions, dissolved CO2 is present primarily in molecular form, and the fraction dissociated is
