Because of the importance of chemical flooding operations, the mechanisms of chemical dispersion and adsorption in porous media are of increasing interest to the petroleum industry. This paper presents a mathematical model for simulating presents a mathematical model for simulating chemical transport phenomena in porous rocks; these phenomena include dispersion and either Langmuir phenomena include dispersion and either Langmuir equilibrium or rate-controlled adsorption. The accuracy of this numerical model was verified by comparing the calculated results with those obtained by analytical solutions for a number of limiting cases. The effects of dimensionless dispersion, adsorptive capacity, flow rate, and kinetic rate groups controlling dispersion/adsorption mechanisms were investigated. The utility of the model was demonstrated further by matching experimental results. When adsorption of a chemical is rate-controlled or time-dependent, core flood data obtained at times much shorter than reservoir residence times can lead to a serious underestimation of chemical requirements for the field projects. Introduction Chemical dispersion and adsorption in porous media are of increasing interest to the petroleum industry because of the increasing importance of chemical flooding operations. While dispersion causes mixing and dissipation of a chemical slug, adsorption can result in a real chemical loss to the reservoir; the ultimate success of a chemical recovery process is controlled by the nature and magnitude of the loss. Although diffusion and dispersion have been studied extensively during the past two decades, publications on the adsorption of chemical recovery publications on the adsorption of chemical recovery agents have been limited. The relatively simple case of adsorption of a gas on a clean, homogeneous, solid surface illustrates the complexity of the adsorption phenomenon. The adsorption can be purely physical, purely chemisorption, a combination of physical, purely chemisorption, a combination of both, or an intermediate type. The adsorption of polymer and surfactant solutions on porous rocks is polymer and surfactant solutions on porous rocks is complicated by the physiochemical properties of the solutions and rocks and by the nature of the pore structure of the rock matrix. Nevertheless, adsorption from dilute aqueous-phase solutions can be described by the Langmuir equilibrium isotherm for a variety of chemicals, including many surfactants and polymers. These chemicals can sometimes exhibit adsorptions that are significantly rate-controlled or time-dependent rather than instantaneous. The classical model for rate-controlled adsorption was proposed by Langmuir. This paper presents numerical solutions to the transport equations for dispersion and adsorption in porous media, considering Langmuir equilibrium porous media, considering Langmuir equilibrium adsorption as well as Langmuir rate-controlled adsorption. The effects of various process parameters on adsorption also were investigated. parameters on adsorption also were investigated. Model Development Transport Equations A chemical transport equation chacterizing dispersion and adsorption of a chemical solution flowing through a porous medium can be derived by a mass balance as follows. 2C q C C 1- CrD ----- - ---- --- = ----- + ---- pr -----.x2 A x t t...................................(1) The dispersion coefficient, D, can be expressed as qD= (---)= u.................................(2)A SPEJ P. 129
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