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Chapter 8Model of reactive transport of an oil-soluble chemicalin porous mediaA physical-mathematical model was developed to describe the injection and reactivetransport of an oil-soluble chemical (OSC) under two-phase conditions in a porousmedium. The model follows from the classical mass balance equations for two-phaseflow and includes the mass fractions for each component and the mass transfer andreaction terms. Numerical calculations were performed to investigate the effect ofthe parameters (flow rate, reaction rate, etc.) on the mass transfer behavior andconcentration profiles. The model was used to simulate the core flow experiments(see Chapter 6), but can also be used to simulate the injection of an OSC in anidealized reservoir, assuming linear flow.8.1 IntroductionIt was found in the bulk phase experiments (see Chapters 2, 3 and 4) and in the coreinjection experiments (see Chapter 6) that the mass transfer of TMOS is predominantlydriven by the hydrolysis reaction of TMOS in the aqueous phase. An important aspectis the solubility of TMOS in water, which is initially poor [24, 34], but the solubilityis increased by the formation of methanol due to the hydrolysis reaction. The rate ofhydrolysis is a strong function of pH, i.e. the rate is minimum at neutral conditions, butit increases in the presence of acid- or base-catalysts. Further, the reaction rates, hencethe mass transfer rates, increase with temperature. In bulk the mass transfer occurstypically on a time scale of hours. The mass transfer in the porous materials is completeon a time scale of less than one hour up to many hours, depending on pH and temperature.The number of existing models for the simulation of reactive transport of an oil-solublechemical in porous media is limited. A network model was presented by Thompsonand Fogler [42] to simulate the injection of TMOS in a porous medium. Their workwas focussed on the displacement behavior on the pore scale and the effect of changingviscosity of the aqueous phase due to the gel reaction. Recently, Valiollahi developed amodel to simulate the placement of TMOS in sandstone based on classical two-phase flowequations [140].The physical-mathematical model presented in this chapter simulates the reactivetransport of TMOS/oil in porous media under two-phase conditions. The model assumeslinear flow and can be used to simulate the injection of an OSC in a simple reservoir. Assuch it can be employed in the design process of a water shut-off treatment in order topredict pressure profiles, gel distribution profiles, etc.113
114 8. Model of reactive transport of an oil-soluble chemical in porous mediaIn this chapter the problem is considered for a homogeneous, water-wet cylinder (core)and is described in one dimension. The core is initially saturated with pure oil and purewater at irreducible water conditions. Two cases were considered; first of all the injectionof a limited amount (or batch) of TMOS-oil solution followed by a shut-in of the system(i.e. no injection of fluids). This case represents the conditions in the core injectionexperiments described in Chapter 6. The obtained mass transfer profiles are comparedwith the experimental profiles. In the second case the solution is injected continuouslythroughout the simulation interval. This case is of interest when a large amount of solutionis placed and/or a low injection rate is employed. In both cases the condensation reactionof the hydrolyzed molecules is neglected. The effect of condensation is, however, assessedqualitatively in one set of simulations by varying the aqueous phase viscosity. The effect ofsolubility was included in the model through the use of a partitioning equation. A simplecapillary bundle model was used to describe the pore-scale diffusion of TMOS betweenboth phases considering the equilibrium concentrations. The effect of main parameters,such as flow rate and amount of mixture injected, on the concentration and saturationprofiles was investigated. In addition, the differential pressure over the core was calculatedfor the case of continuous injection.QS w (z,t)P outz=-L/2zz=L/2Fig. 8.1: Schematic view of porous system (core) in the model. The core has a length L, crosssectionA, porosity ϕ and absolute permeability K abs . The fluids are injected at theinlet (z = −L/2) with a flux Q. In this example the water saturation (S w ) profilerepresents a drainage process. The outlet pressure at z = L/2 is equal to P out .8.2 Theoretical background8.2.1 Problem statementConsider a homogeneous porous cylinder (core) with a length L and cross-section A (seeFigure 8.1). The core has a uniform porosity ϕ and uniform absolute permeability K abs .In the following the problem is described in one dimension, and z represents the spatialcoordinate along the length of the core. The water saturation is given by S w (z, t) and,hence, the oil saturation S o is equal to 1 - S w . The composition of each phase is definedby the mass fraction w X α (z, t), where α represents the phase (w = aqueous phase and o= oleic phase) and X indicates the component (O = oil, W = water, T = TMOS, M =methanol, and SA = silicic acid). The mass fractions are defined such that ∑ X wX α = 1.In the oleic phase only TMOS and oil exist, and in the aqueous phase only water, TMOS,methanol and silicic acid exist.
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TWO-PHASE REACTIVE TRANSPORTOF AN O
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Part ITwo-phase bulk systems7
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170 Bibliography
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