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8.4. Results and discussion 121core injection experiments (see Chapter 6). The parameters that remain fixed throughoutthe simulations are listed in Tables 8.1 and 8.2.In particular, we mention the following parameters. The absolute permeability is 1.6µm 2 , and the porosity is 0.22. The core has a length of 60 mm and a diameter of 14mm. In each case the temperature is 25 ◦ C and the atmospheric pressure, and thus theoutlet pressure, is 1 bar. The residual saturations are S wi = S or = 0.25. The core isinitially always at residual water, and the phases initially consist of pure oil and purewater, respectively. It is noted that the water used in the experiments was heavy water,so that we choose a density ϱ W of 1,100 kg m −3 . The IFT between pure oil and purewater is around 50 mN m −1 [92]. The introduction of TMOS in the oleic phase or thereaction of TMOS in the aqueous phase lowers the IFT significantly (see Chapter 3). Wechoose a constant IFT of σ = 20 mN m −1 .The pore radius r w is an estimate for Bentheim sandstone, based on experimentalvalidation (see Chapter 6). The sorting factors for P c and k rα and the end point relativepermeabilities k rα ′ are chosen arbitrary but are representative for a water-wet porous rock[118]. The exact reaction order of the hydrolysis reaction is unknown, and it is likely tobe sensitive to concentrations and pH [24]. In this model we link the reaction order to thestoichiometry of the hydrolysis reaction (see Eq. 8.18), so that β = 1 and γ = 4. In thefollowing we distinguish between two scenarios. Case A represents the set of simulationsin which a few pore volumes of mixture are injected, followed by shut-in. This case isrepresentative of the core injection experiments discussed in Chapter 6. Case B representsthe set of simulations in which the mixture is continuously injected. The results discussedin the following sections show the sensitivity of the problem to main parameters, such ask and Q.Table 8.2: Fluid properties used in the simulations. The compressibility factors c o and c w representthe average compressibilities of the oleic and the aqueous phase, respectively.The values are based on the compressibilities of pure n-hexadecane and pure water,respectively.parameter description value unitsϱ O density of oil 820 kg m −3ϱ T density of TMOS 1,032 kg m −3ϱ W density of (heavy) water 1,100 kg m −3ϱ M density of methanol 791 kg m −3ϱ SA density of silicic acid a 1,680 kg m −3µ O viscosity of oil 10 mPa sµ T viscosity of TMOS 0.63 mPa sµ W viscosity of aqueous phase 1 mPa sc o compressibility of oleic phase 9×10 −10 Pa −1c w compressibility of aqueous phase 5×10 −10 Pa −1a Silicic acid does not exist in liquid form, however, in order to calculate the density of the aqueousphase an estimate is used based on the conservation of mass.
122 8. Model of reactive transport of an oil-soluble chemical in porous media8.4.2 Case A. Batch injection: exampleThe results of two of the simulations for case A are discussed first. We consider the case offast injection (Q = 1 ml min −1 ) versus slow injection (Q = 0.02 ml min −1 ). The amountof oil/TMOS mixture is two pore volumes (PV). The diffusion constant D is 10 −10 m 2s −1 . The interaction parameter ε 0 is equal to 5×10 3 J mol −1 K −1 and a = 4 (the latter isfour times higher than the parameter α used in the bulk model due to a different scalingin Eq. 8.17). The reaction constant k is based on the reaction constants determined inthe bulk experiments (see Chapter 4), i.e. k = 0.323×10 −3 s −1 (which corresponds to theexperiment without buffer). The total simulation time is 20 hours.The water saturation profiles are shown in Figure 8.3. As the TMOS solution isinjected the TMOS starts to partition between the oleic and aqueous phase in which itreacts to form methanol and silicic acid. Due to the mass transfer the saturation S wincreases and S o decreases. The amount of mixture exceeds (1 - S wi ) × 1 PV and duringinjection not all TMOS transfers instantly from the oleic to the aqueous phase. Therefore,some of the TMOS solution is produced at the outlet between t = 0 and t = t s . Given acertain reaction constant k and amount of PV injected, the flow rate Q has a significanteffect on the degree of change of the S w profiles, as can be observed in Figure 8.3. In casethe injection is relatively fast compared to the reaction rate, the injection of the mixtureresults in uniform S w profiles which increase gradually in the course of time during shut-inup to S w ≈ 0.42. However, in case the injection is relatively slow compared to the reactionrate, the S w profiles during injection start to develop a non-uniform and almost front-likebehavior towards the outlet. During shut-in the ongoing mass transfer of TMOS resultsin uniform S w profiles after several hours. The final saturation is however much higher(S w ≈ 0.48) compared to that in the fast injection case.0.50.50.40.4S w[-]0.30.2t=0timeS w[-]0.30.2t=0time0.10.10-0.03 -0.02 -0.01 0 0.01 0.02 0.03z [m]0-0.03 -0.02 -0.01 0 0.01 0.02 0.03z [m]Fig. 8.3: Water saturation profiles in the example simulations of Case A. Two PV of TMOS/oilwere injected between t = 0 and t = t s . Initially, S w = S wi . The time step betweendifferent solid curves is 0.8 hours. The dashed curve is the saturation profile at t =t s . The reaction constant is k = 0.323×10 −3 s −1 . (left) Q = 1 ml min −1 . (right) Q= 0.02 ml min −1 .Of main interest is the amount of silicic acid which is formed, since this indicates
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TWO-PHASE REACTIVE TRANSPORTOF AN O
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2 1. Introductionproducerbarrierlow
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Part ITwo-phase bulk systems7
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Page 169 and 170: 160 Bibliography[12] B. Vinot, R. S
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172 Summaryand gelation rates. The
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174 Samenvattingwaterfase. De T 1 v
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