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8.4. Results and discussion 125show initial values φ T < 0.20, which is due to a combination of fast mass transfer andincomplete displacement of oil by the oil/TMOS mixture during injection. The lattereffect also leads to the significant differences between the several slices. The plateaus ofφ T between 0.01 and 0.08 are due to incomplete transfer of TMOS between both phases orto the presence of hydrogen in the aqueous phase, which leads to apparently high valuesfor φ T (see Chapter 6).The calculated profiles for the different slices are virtually identical and do not show thenon-uniform behavior found in the experiments. The calculated profiles show a decreasingφ T which starts around 0.20 and goes to zero. Considering the time scale at whichφ T decays we observe the following. For the unbuffered system (A03) and the acidcatalyzedsystem (A05) the calculated rate of decay of φ T agrees well with that observedin the experimentally obtained profiles. However, for the neutrally buffered system (A07)and the base-catalyzed system (A09) the calculated profiles decay much slower than theexperimentally obtained profiles. A modified and refined reaction term will likely improvethe reactive transport model for these systems, but this is left for future studies.0.60.6S wS w0.5w w SA x S ww wSA0.5w w SA x S ww wSA0.40.4value [-]0.3value [-]0.30.20.20.10.10.010 -5 10 -4 10 -30.010 -2 10 -1 10 0 10 1k [s -1 ]Q [ml min -1 ]Fig. 8.7: Calculated final values (at t = 20 hours) for the average water saturation S w , amountof silicic acid wwSA × S w and fraction of silicic acid wwSA . In the simulation the batchsize was 2 PV. (left) variation of k with Q = 1 ml min −1 . (right) variation of Q withk = 0.323×10 −3 s −18.4.3 Case A. Batch injection: effect of main parametersThe effect of the parameters k, Q, D, ε 0 , a and the number of pore volumes injected onthe mass transfer profiles and silicic acid formation was analyzed for the batch injectioncase. First of all, the reaction rate k was varied over two orders of magnitude. Theother parameters were equal to those specified in the example simulation (see previoussection). The effect of k on the final oil saturation (i.e. after 20 hours), averaged overthe core, is shown in the left-hand graph of Figure 8.7. It can be observed that thefinal average S w increases with increasing k, which is due to the enhanced mass transferrate with increasing k. For k > 1×10 −4 s −1 the concentration of TMOS is almost zeroin the oil phase, and the increase of the average S w with k is due to the fact that an
126 8. Model of reactive transport of an oil-soluble chemical in porous mediaexcess of mixture (2 PV) was injected. The average total amount of silicic acid and theaverage fraction of silicic acid in the aqueous phase are given in Figure 8.7 as well. Bothparameters increase with increasing k.0.60.6S wS w0.50.4w w SA x S ww wSA0.50.4w w SA x S ww wSAvalue [-]0.3value [-]0.30.20.20.10.10.00 2 4 6 8PV [-]0.00 2 4 6 8ε 0[kJ mol -1 ]Fig. 8.8: Calculated final values (at t = 20 hours) for the average water saturation S w , amountof silicic acid wwSA × S w and fraction of silicic acid wwSA . In the simulation the batchsize was 2 PV. (left) variation of PV injected. (right) variation of ε 0 .The effect of the injection rate Q on the aforementioned average output parameters isshown in the right-hand graph of Figure 8.7. The rate was varied between 0.02 and 10 mlmin −1 . The final average water saturation decreases with increasing Q. With Q in therange of 0.02 to 0.1 ml min −1 the amount of SA formed is approximately constant. Forvalues of Q greater than 0.1 ml min −1 the amount of SA formed decreases slightly withincreasing Q, given the amount of mixture injected (2 PV).In case of an excess amount of mixture injected the amount of silicic acid formedslightly increases with increasing number of PV injected, the degree of which depends onthe reaction rate k. In this example (k = 0.323×10 −3 s −1 ) the output parameters increasewith an increasing number of PV injected for volumes greater than 1 PV (see Figure 8.8).Obviously, in case less than 1 PV of mixture is injected, not all oil in place is displaced byTMOS/oil so that the amount of silicic acid formed is less than in the previous examples.Similarly, the values for a, ε 0 and D were varied, each within a representative range.The parameters a and D (not shown here) appeared to have a negligible influence on theaverage output parameters. However, the parameter ε 0 has significant influence on themass transfer rate and the average output parameters. It can be observed in Figure 8.8that the final water saturation and the amount of SA formed decrease with increasing ε 0 .8.4.4 Case B. Continuous injection: exampleThe results of one of the simulations for case B are discussed next. The parameters werechosen as follows. The oil/TMOS mixture is injected continuously with a flow rate Q= 0.1 ml min −1 . The diffusion constant D is 10 −10 m 2 s −1 and the reaction constantk is 0.323×10 −3 s −1 . The interaction parameter ε 0 is equal to 2×10 3 J mol −1 K −1 and
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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 155 and 156: 146 Appendix AThe 0.95 Tesla scanne
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Page 159 and 160: 150 Appendix CwhereΩ A (θ) = −2
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Page 165 and 166: 156 Appendix Eand equal to zero in
Page 167 and 168: 158 Appendix EAs the saturations, d
Page 169 and 170: 160 Bibliography[12] B. Vinot, R. S
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Page 177 and 178: 168 Bibliography[127] G. W. Scherer
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Page 181 and 182: 172 Summaryand gelation rates. The
Page 183 and 184: 174 Samenvattingwaterfase. De T 1 v
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178 Dankwoordimmer opgewekte stemmi
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