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Adsorption and Desorption Kinetics and Equilibrium of Calcium Lignosulfonate on Dolomite Porous Media Baojun Bai,*,† Yongfu Wu,† and Reid B. Grigg‡ Department of Geological Sciences and Engineering, Missouri UniVersity of Science and Technology, 129 McNutt Hall, 1400 North Bishop AVenue, Rolla, Missouri 65409, and New Mexico Petroleum RecoVery Research Center, New Mexico Institute of Mining and Technology, 801 Leroy Place, Socorro, New Mexico 87801 ReceiVed: March 29, 2009; ReVised Manuscript ReceiVed: May 31, 2009
Calcium lignosulfonate (CLS) adsorption and desorption on a porous dolomite rock have been studied. Kinetic results showed that both adsorption and desorption are time-dependent processes, not instant. It has been found that adsorption and desorption have a two-step pattern: a fast adsorption/desorption followed by a slow step. Apparent adsorption and desorption rate constants were calculated by a second-order kinetic model. Desorption is an unequilibrated process under normal injection flow rate, and it is much slower than adsorption. Equilibrium results show that adsorption and desorption of CLS onto dolomite can be well fitted by the Freundlich equation over the experimental CLS concentration range and that increase of CLS concentration increases adsorption density. Increasing temperature slightly decreases CLS equilibrium adsorption. Increase of NaCl and CaCl2 concentrations in brine increases adsorption density, but CaCl2 has a much stronger effect than NaCl on the adsorption. Introduction Surfactants have been widely used to enhance oil recovery (EOR) in the oil industry, such as surfactant/micellar flooding, surfactant/alkaline/polymer (ASP) flooding, foam flooding, and surfactant huff-n-puff treatments. However, the costs due to their adsorption loss onto reservoir rocks often exclude the application of those EOR methods in oilfields.1-4 Previous experiments have found that lignosulfonate, a paper industry waste, can be used as a sacrificial agent or a cosurfactant to significantly reduce the expensive primary surfactant adsorption on reservoir rocks. Neale and co-workers described the characteristics of lignosulfonates and their importance to petroleum recovery operations.5 Kalfoglou first reported in 1977 the use of lignosulfonate as a sacrificial agent to reduce the primary surfactant adsorption and found that lignosulfonate reduced the primary surfactant’s adsorption on crushed limestone rock samples by 16-35%.2 Hong and co-workers evaluated lignosulfonate as a sacrificial agent for a surfactant flooding field test in a Glenn Pool reservoir, and their laboratory tests showed that the lignosulfonate could reduce the primary surfactant adsorption by 39%.6,7 Grigg co-workers8-12 and Syahputra et al.13 demonstrated that lignosulfonate could reduce the adsorption of the primary foaming agent CD1045 by 24-60% in Berea sandstone core and 15-29% in Indiana limestone core samples. Both adsorption equilibrium and kinetics are important to properly understand the interactions between chemicals and reservoir rocks and to optimize chemical process for chemical EOR applications. Equilibrium data provide the information of chemical adsorption on rocks, and kinetic data are related especially to the rate of adsorption. Previous publications for lignosulfonate onto different rocks mainly focus on the adsorp* Author to whom correspondence should be addressed. E-mail: baib@ mst.edu. † Missouri University of Science and Technology. ‡ New Mexico Institute of Mining and Technology.
tion equilibrium data, while few have been found in the literature on the kinetics of lignosulfonate adsorption. In fact, chemical adsorption on reservoir rocks usually takes a few days and even quite a few weeks to reach equilibrium.14-18 Research of the adsorption and desorption rates will enable us to understand the mechanisms responsible for surfactant transport through reservoirs and to optimize cost-effective injection strategies for field application. Moreover, surfactant injection is often followed by water or other fluid injection, so it is of major importance to understand surfactant desorption processes. Nowadays, very limited results about lignosulfonate desorption kinetics have been published. Sandstone, limestone, and dolomite are three major types of reservoir rock. The authors previously reported the kinetics and equilibrium data of calcium lignosulfonate adsorption and desorption onto limestone and Berea sandstone.8-12 This paper presents the kinetics and equilibrium of calcium lignosulfonate adsorption and desorption onto dolomite. Experimental Section Materials. Brine. Synthetic brine (2.0 wt %) was used in each test unless otherwise stated. The brine was composed of 1.5 wt % NaCl and 0.5 wt % CaCl2. Lignosulfonate. The lignosulfonate used in this study is Lignosite 100 calcium lignosulfonate (CLS), obtained from the Georgia-Pacific Corporation. The product is a powder produced by sulfonation of softwood lignin. Its basic properties provided by the Georgia-Pacific Corporation are listed in Table 1. Cores. Quarried Lockport dolomite was used in the study. The dolomite is mainly composed of CaMg(CO3)2, and its properties and parameters are shown in Table 2. Experiments. Method for Analyzing Lignosulfonate Concentration. Lignosite 100 sample was dissolved in distilled water for purification. After stirring overnight, the water-soluble samples were completely dissolved in the water except for insoluble impurities. After standby for about 1 week, the water solution was filtrated to remove all insoluble impurities. The
10.1021/jp9028326 CCC: $40.75 2009 American Chemical Society Published on Web 07/02/2009
Kinetics and Equilibrium of Calcium Lignosulfonate
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TABLE 1: Properties of Lignosite 100 properties
descriptions
pH insolubles (wt %) reducing Substances moisture molecular weight calcium (%) chromium (%) iron (%) sodium (%)
2.0-4.0 1.5% max 11% max 8% max 19,200 4.0-5.5 0.02
TABLE 2: Parameters of the Dolomite Core Sample Used in This Study length
diameter
weight
5.70 cm
3.81 cm
150.47 g
pore volume porosity permeability 10.36 cm3
15.9%
24.72 md
TABLE 3: Equations of CLS Standard Curves at Different Salts salt conc distilled water 5% NaCl 10% NaCl 5% CaCl2 10% CaCl2
equation of calibration curve ABS ABS ABS ABS ABS
) ) ) ) )
0.0084 0.0082 0.0086 0.0084 0.0087
× × × × ×
conc conc conc conc conc
+ + + + +
0.0075 0.0019 0.0202 0.0184 0.0113
R2 0.999 0.998 0.996 0.998 0.999
filtrated solution was clear and was put on a heat plate. After all the water was evaporated, purified CLS sample was obtained to make standard solutions for measurement of the UV calibration curve. A spectrophotometer was used to measure the concentration of CLS. CLS has a maximum absorbance in the neighborhood of 283 nm. The 283 nm wavelength was used in all measurements to analyze the CLS concentration. To analyze CLS concentration in brine, a calibration curve of CLS in 2.0 wt % NaCl was measured. CLS was diluted to 300 mg/L or less for a linear relationship between concentration and absorbance at 283 nm. Effect of Salt Type on CLS Absorbance. The absorbance of CLS prepared with different salts and concentrations was measured using a spectrophotometer. Figure 1 shows the influence of salt type on CLS absorbance at the wavelength of 283 nm. Table 3 lists the linear equations fitted to CLS calibration curves for different salts solutions. Effect of pH on CLS Absorbance. The absorbance of 200 mg/L CLS solution was measured at different pH conditions. It was found that pH at the range of 3-11 has negligible effect on the absorbance of CLS. Core Flooding Test. Two dynamic methods, circulation and flow-through experiments, were used in the study of CLS
Figure 1. Effect of salt on CLS absorbance at 283 nm.
Figure 2. Schematic diagram of circulation method.
adsorption and desorption onto porous media. The amount of CLS adsorbed is expressed as the following unit: mass of CLS adsorbed per gram of rock (mg/g). Circulation Method. This method was applied (1) to study the kinetics of CLS adsorption onto dolomite; (2) to measure CLS adsorption/desorption isotherms; and (3) to study the effects of some factors on CLS equilibrium adsorption density onto dolomite, such as salt type and concentration, and circulation rate. Figure 2 shows a flowchart of the circulation experiment. The circulation experimental apparatus consists of (1) a given solution having a known weight in a flask; (2) a core of known pore volume and weight; and (3) a circulation pump. A CLS solution of known concentration and volume was circulated through the core at constant temperature and injection rate. First, brine was circulated through the core at a constant rate. After a designed interval of circulation, brine in the flask was replaced with the same volume of known concentration of CLS solution. After another designed interval of circulation, a sample of solution was removed from the flask for CLS concentration analysis. The cycle of sampling and replacement was repeated several times. The procedures were used for measuring the adsorption kinetics and isotherm. In order to measure desorption kinetics and isotherm, aliquots of solution were removed from the flask and replaced each time with the same volume of CLS-free brine. After each brine addition, the solution was circulated for the same time interval. This was repeated several times. The CLS solution concentration was measured for each removed sample, and the remaining CLS on the core after adsorption was calculated. The adsorption density during adsorption can be calculated using the equation: N
qti )
∑ (Ci-1 - Ci)Vi i)1
1000W
(1)
where qti is total CLS adsorption onto dolomite at the ith circulation, mg/g; W is the mass of dolomite core, in g; Ci is CLS concentration after the ith circulation, mg/L; Vi is total volume of circulated CLS solution including the volumes in the flask, tube, and pore volume of the core, mL; and N is the number of total circulations for each adsorption experiment. For adsorption kinetic experiments, two samples were taken from the flask to analyze CLS concentration at predetermined intervals. For adsorption/desorption isotherm measurements, two samples were taken out for the analysis of concentration and were replaced by equal volumes of CLS (adsorption process) or were replaced by equal volumes of 2.0% brine (desorption process) at predetermined intervals. For experiments of salt type and concentration effect, CLS solution prepared by distilled water was first circulated through the core for 48 h, and then
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Figure 3. Diagram of flow-through method for adsorption measurement.
two solution samples were taken for analysis and a specific amount of salt was added to the solution in the flask. This was repeated several times until the predetermined maximum salt concentration was reached. All circulation experiments were carried out at the circulation rate of 15 mL/h. Flow-Through Method. Figure 3 shows a schematic diagram of the flow-through method apparatus. The source fluid is pumped from a beaker through the pump and into the core holder containing a core. Fluid effluent samples were collected versus time, and the concentrations of CLS were analyzed by using a spectrophotometer. The flow-through method was mainly used to study CLS desorption from porous media in this study. The amount of CLS adsorbed onto the dolomite core during the desorption process was calculated using the following equations:
Di-1 ) Bi /W;
Bi ) Ai - Mi;
Ai ) Ai-1 - Ci-1Vei-1 /1000
Mi ) Ci+1PV/1000 (i ) 2, 3, ... N)
A1 ) D0W + C0PV/1000
(2)
where, Di is CLS adsorption density at step i, mg/g; D0 is CLS adsorption density at equilibrium from circulation result, mg/ g; Bi is mass of the CLS adsorbed on the core, mg; Mi is mass of the CLS left in the pore space and tubing line, mg; Ci is effluent CLS concentration at step i, mg/L; PV is total volume of core pore and tubing lines, mL; Vei is effluent volume at step i, mL; Ai is total mass of the CLS adsorbed on the core and left in the pore space and tubing line at step i, mg; and C0 is CLS concentration before the start of desorption process, mg/L. Core Flooding Test Schedule. Six adsorption/desorption experiments were conducted using dolomite cores. Between every two series of experiments, the core was flushed with 400 mL (∼40 pore volumes) of tetrahydrofuran (THF), then dried using nitrogen flow, and evacuated before being resaturated with 2.0% brine or distilled water. Our lab results showed that the used core cleaned by THF can produce reproducible results, even better than a brand new core. Results and Discussion Kinetics of CLS Adsorption onto Dolomite. Circulation experiments were carried out to investigate the effect of contact time versus CLS adsorption onto dolomite at the initial CLS concentration of 4800 mg/L and a circulation rate of 15 mL/h. The difference between the two experiments is that the core was saturated by a different fluid before the CLS solution was circulated. The adsorption densities as a function of circulation time for the three kinetics experiments are plotted in Figure 4. The adsorption density increases with the elapsed time within the experiment temperature range for 23 and 45 °C. Similar to
Figure 4. Kinetics of CLS adsorption onto the dolomite surface.
the case of CLS adsorption kinetics onto limestone,10 each curve was characterized by a short period of rapid adsorption, followed by a long period of slower adsorption. Comparison of CLS adsorptions onto the dolomite cores saturated with 2.0 wt % brine at the different temperatures shows that the adsorption density was greater at the lower temperature. This indicates that CLS adsorption onto dolomite is an exothermic physical process. Comparison of CLS adsorption densities at the same temperature of the cores saturated with different fluids, distilled water and 2.0 wt % brine, shows that CLS adsorption with distilled water is much lower than that with 2.0 wt % brine, indicating higher salinity increases CLS adsorption and preflushing the core using low salinity brine before injecting CLS will decrease CLS loss in the rock incurred by adsorption. Adsorption Kinetics Models. Three models of adsorption kinetics were used to fit the CLS adsorption rate. Selecting the right model is important to predict CLS transport in porous media and to help design surfactant-based EOR processes. The models, pseudo-first-order equation, pseudo-second-order equation, and intraparticle diffusion, were fitted to find the best one for CLS adsorption onto dolomite. Pseudo-First-Order Kinetic Model for the Adsorption Process. The differential equation for the Lagergren pseudo-firstorder model,19 an equation for adsorption rate of solutes from a solution, is the following:
dqt ) Ka1(qe - qt) dt
(3)
where qe is CLS adsorption density onto dolomite at equilibrium, mg/g; qt is CLS adsorption density onto dolomite at time t, mg/ g; t is time in h; and Ka1 is pseudo-first-order rate constant during the adsorption process. Integrating eq 3 for the initial condition, qt)0 ) 0, the follow equation is obtained:
(
ln
or
)
1 + ln(qe) ) Ka1t qe - qt
(4)
Kinetics and Equilibrium of Calcium Lignosulfonate
qe ) eKa1t qe - qt
J. Phys. Chem. C, Vol. 113, No. 31, 2009 13775
(5)
From eq 5, the plot of (qe)/(qe - qt) versus time is linear on a semilog plot, if the adsorption kinetics is represented by a pseudo-first-order model. It is important to note that the y-intercept of the semilog plot should be 1. Otherwise, the rate is not represented well by a pseudo-first-order model. Equation 4 can be rearranged as the following linear equation:
log
Ka1 1 ) t - log(qe) qe - qt 2.303
(6)
If the data fit to a pseudo-first-order model, a plot of log[1/(qe - qt)] versus t would have a linear relationship from which the adsorption kinetic constant Ka1 and equilibrium adsorption density can be determined from the slope and y-intercept of the plot, respectively, and the y-intercept is log qe. Since qe can be measured experimentally, if adsorption follows a pseudofirst-order kinetic equation, the calculated and measured qe should be the same. Up to now, however, no results have been reported to discuss this adsorption mechanism. Pseudo-Second-Order Kinetic Model for Adsorption Process. The second model describing adsorption kinetics is the pseudosecond-order equation.20,21 The differential equation is
dqt ) Ka2(qe - qt)2 dt
(7)
where Ka2 is the pseudo-second-order kinetic constant of sorption. Integrating eq 7 at the initial condition same as for eq 4, the following equation is obtained:
1 1 ) Ka2t qe - qt qe
(8)
Rearranging eq 8, the following linear equation is obtained:
t 1 1 ) t+ qt qe Ka2qe2
(9)
where the plot of t/qt versus t is a straight line with the slope of 1/qe and y-intercept of 1/(Ka2qe2). Diffusion Model. The intraparticle diffusion model is expressed below,21
qt ) Ka3t1/2 + C
Figure 5. Modeling CLS adsorption kinetics onto dolomite using the pseudo-second-order equation.
TABLE 4: Modeling Results of CLS Adsorption onto Dolomite Using the Pseudo-Second-Order Equation experiment
fitting equation
R2
qe
Ka
distilled water, 23 °C 2.0% brine, 45 °C 2.0% brine, 23 °C
t/qt ) 2.87t + 46.1 t/qt ) 2.58t + 31.4 t/qt ) 2.19t + 25.0
0.986 0.994 0.998
0.348 0.387 0.456
0.179 0.212 0.193
order equation. Table 4 lists the fitting equations, the correlation factors, and the calculated equilibrium density and pseudosecond-order rate constants. The calculated equilibrium adsorption densities listed in Table 4 are 0.348, 0.387, and 0.456 mg/g, which are about 20-25% higher than the adsorption densities shown in Figure 4 (0.263, 0.307, and 0.365 mg/g, respectively) for which the tests were stopped after 48 h. This indicates that CLS adsorption onto dolomite takes a much longer time to reach equilibrium than that onto limestone.9 The adsorption kinetic constants in 2.0% brine are 0.193 and 0.212 at 23 and 45 °C, respectively. This indicates the adsorption rate of CLS onto dolomite increases with increasing temperature. Thus, the required time to reach adsorption equilibrium should be shorter at the higher temperature. Equilibrium of CLS Adsorption onto Dolomite. Experimental Results of Adsorption and Desorption Isotherm. Figure 6 shows CLS adsorption and desorption isotherms onto dolomite at 45 °C for the experiments with 2.0% brine. For the two isotherms, CLS adsorption increased with increased CLS solution concentration. By comparison of the two isotherms, it
(10)
where the plot of qt versus t0.5 will be a straight line if the model is correct with a slope of Ka3. Modeling Adsorption Kinetics of CLS onto Dolomite. CLS adsorption onto dolomite did not reach equilibrium during the test time. The equilibrium adsorption data is thus not available, so the pseudo-first-order model cannot be directly used to fit the results using eqs 7 and 8. Figure 5 shows the results using the pseudo-second-order model to fit CLS adsorption kinetics onto dolomite. The plot of t/qt versus t is a straight line for each experiment, and CLS adsorption kinetics can be well described by pseudo-second-
Figure 6. CLS adsorption and desorption isotherms onto dolomite at 45 °C.
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Figure 7. Concentration change and loss due to adsorption.
Figure 8. Modeling CLS adsorption and desorption isotherms onto dolomite using the Langmuir equation.
can be found that the remaining adsorption density for the desorption isotherm is higher than that of the adsorption isotherm at the same equilibrium concentration, indicating adsorption hysteresis. This might be caused by the attraction forces between pore surfaces of dolomite and CLS molecules. Figure 7 compares CLS initial and equilibrium concentrations and relative loss due to CLS adsorption onto dolomite. The relative decrease of CLS concentration is between 13.6% and 6.1%. The loss percentage decreases with increase of the initial concentration. Modeling CLS Adsorption and Desorption Isotherm. The Langmuir equation is a well-known equation that describes adsorption isotherms.22 The equation assumes (1) monolayer coverage, (2) homogeneous adsorption sites, and (3) that all sorption sites are identical and energetically equivalent. The linear form of the Langmuir model is
TABLE 5: Modeling Results of CLS Adsorption and Desorption Isotherms Using the Langmuir Isotherm Equation
1 1 1 1 ) + qe qmaxKL Ce qmax
(11)
where Ce is the CLS equilibrium concentration, qmax is the monolayer capacity of the dolomite adsorbent, and KL is the Langmuir adsorption isotherm coefficient (L/mg), and a plot of 1/qe versus 1/Ce is a straight line with a slope of 1/(qmaxKL). Figure 8 shows the fitting of the experimental adsorption data to the Langmiur equation (eq 11). Table 5 lists the results. The CLS adsorption isotherm onto dolomite can be described by the Langmiur equation with a correlation factor of 0.964. Correspondingly, the maximum adsorption density is 0.534 mg/g and the Langmiur adsorption constant is 2.3 × 10-4 L/mg. In contrast, the desorption isotherm does not fit the Langmiur equation well. The Freundlich isotherm model is an empirical equation which is used for nonideal adsorption that involves heterogeneous sorption and is expressed by the following equation:23
qe ) KFCe1/n
process
equation
R2
qmax (mg/g) KL (L/mg)
adsorption 1/qe ) 8145(1/Ce) + 1.87 0.964 desorption 1/qe ) 151.3(1/Ce) + 3.15 0.763
0.534 0.317
0.00023 0.0209
TABLE 6: Modeling Results of CLS Adsorption and Desorption Isotherms onto Dolomite Using the Freundlich Equation process
fitting equation
R2
KF
n
adsorption desorption
qe ) 0.001Ce0.666 qe ) 0.0941Ce0.159
0.993 0.941
0.001 0.094
1.502 6.297
Therefore, the plot of log(qe) versus log(Ce) is a linear relationship with the y-intercept of log(KF) and a slope of 1/n. Figure 9 shows the fitting of the adsorption and desorption isotherms using the Freundlich equation (eq 13). Table 6 lists the fitting to the Freundlich equation and corresponding parameters. The CLS adsorption isotherm for dolomite can be described by a Freundlich equation with a correlation factor of 0.993 and a Freundlich constant and heterogeneity factor of 0.001 and 1.502, respectively. The CLS desorption isotherm was also fitted by a Freundlich equation with a relative low correlation factor of 0.941; and the corresponding Freundlich constant and heterogeneity factor are 0.094 and 6.297, respectively.
(12)
where KF is the Freundlich constant (l/mg) and 1/n is a heterogeneity factor. The linear form of the equation is
log(qe) ) log(KF) +
1 log(Ce) n
(13)
Figure 9. Modeling CLS adsorption and desorption isotherms using the Freundlich equation.
Kinetics and Equilibrium of Calcium Lignosulfonate
Figure 10. Effect of salt type and concentration on CLS adsorption onto dolomite.
Effect of Salt Type and Concentration on Equilibrium Adsorption. Two series of experiments were run to study the influence of NaCl and CaCl2 on CLS adsorption onto dolomite. For each experiment, 4700 mg/L CLS solution was circulated until adsorption equilibrium was reached. Then a salt (NaCl or CaCl2) was added incrementally to the circulation solution in a flask until the salt concentration reached the desired maximum. The highest concentrations were 5 wt % for both NaCl and CaCl2. CLS adsorption densities onto dolomite at different NaCl and CaCl2 concentrations are shown in Figure 10. For both NaCl and CaCl2, increasing their concentrations increased CLS adsorption, with the divalent CaCl2 showing a stronger effect on the adsorption. The adsorption of CLS prepared by distilled water is 0.241 mg/g. Adding 0.01 M or 0.059 wt % NaCl increased CLS adsorption density to 0.276 mg/g, and adding 0.01 M (0.11 wt %) CaCl2 increased CLS adsorption density to 0.491 mg/g. The effect of salts on CLS adsorption could be attributed to several mechanisms. An increase in salt concentration may increase CLS adsorption by decreasing the ability of the aqueous phase to dissolve CLS, thus driving the CLS to the interface, or by decreasing electrostatic repulsion between the hydrophilic head groups in the adsorbed layer. Increasing the electrolyte concentration compresses the electric double layer, with the resulting change in adsorption depending on the sign of the charges of the solid surface and CLS. While monovalent inorganic ions change the magnitude of the solid’s surface charge by compression of the electric double layer without changing the sign of the charge, multivalent ions may specifically adsorb to a surface of opposite charge and reverse the sign of the surface charge. Based on the discussion, the effect of NaCl and CaCl2 on adsorption of CLS can be explained as follows: CLS is an anionic surfactant having a functional group with a negative charge in aqueous medium. Adding NaCl or CaCl2 decreases the functional group-group electrostatic repulsion in the adsorbed layer. Increasing salt concentration can compress the electric double layer and thus increase CLS adsorption. On the other hand, the divalent cation, Ca2+, may adsorb onto the rock surface which may reduce more effectively the repulsive interaction between the CLS hydrophilic group and the rock surface with negative charge. This may be the reason that CaCl2 has a stronger effect than NaCl. The adsorbed Ca2+ can make the surface more positive or less negative, thus attracting more CLS by electrostatic interaction. Kinetics of CLS Desorption from Dolomite. Brine of 2.0 wt % was used to flush the core to displace the solution left in
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Figure 11. Adsorption change with time during the desorption process.
Figure 12. Pseudo-second-order model to fit CLS desorption from dolomite.
Figure 13. Pseudo-first-order model to fit CLS desorption from dolomite.
the pore space and tubing line and to desorb the adsorbed CLS at the constant flow rate of 15 mL/h at 23 and 45 °C. Figure 11 shows adsorption density as a function of time during desorption. The adsorption density during the desorption process is characterized by a short, rapid desorption period followed by a longer, slow desorption period.
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TABLE 7: Results of Modeling CLS Desorption from Dolomite Using the Pseudo-Second-Order Equation experiment
equation
Kd2
qr
R2
4794 mg/L, 23 °C 1/qt ) 0.111t + 3.96 0.111 0.0254 0.995 4833 mg/L, 45 °C 1/qt ) 0.063t + 2.75 0.063 0.0139 0.991 4830 mg/L, 23 °C 1/qt ) 0.634t + 4.08 0.634 -0.0233 0.962
Modeling CLS Desorption Process from Dolomite. Most of the previous work reported has been focused on adsorption kinetics with little attention devoted to desorption kinetics. Desorption kinetics models are derived by referring to the definitions of adsorption kinetics. Pseudo-First-Order Kinetic Model for the Desorption Process. Referring to the same definition as adsorption kinetics, the differential equation of pseudo-first-order kinetic model during desorption is defined as
-
dqt ) kd1(qt - qr) dt
(14)
where kd1 is desorption kinetic constant and qr is the residual CLS adsorption density at the end of the desorption process, and the initial condition of qt)0 ) qi with qi as the CLS adsorption density onto dolomite at the beginning of the desorption process. Integrating eq 14 at the initial condition during desorption gives
ln(qt - qr) ) -kd1t + ln(qi - qr)
(15)
If all CLS is assumed to desorb from the limestone, qr ) 0 when t f ∞ and eq 15 becomes
qt ) qi e-kd1t
(16)
Pseudo-Second-Order Kinetic Model for Desorption Process. Similarly, the differential equation of the pseudo-second-order kinetic model during desorption process can be defined as
-
dqt ) kd2(qt - qr)2 dt
(17)
Integrating eq 17 at initial conditions during desorption gives
1 1 ) kd2t + qt qi - qr
(18)
The plot of 1/qt versus t is a straight line with the slope of kd2 and the y-intercept of 1/(qi - qr) if the data fit to the pseudosecond-order desorption equation. The plot of 1/qt versus t shown in Figure 12 indicates that CLS desorption can be well fitted by the pseudo-second-order desorption kinetic model (eq 18). Table 7 lists the fitting equations, the correlation coefficient, and the calculated desorption kinetic constant and residual adsorption density. The residual adsorption is close to zero, indicating that CLS can almost completely desorb from dolomite. If qr is assumed to be zero, the pseudo-first-order kinetic model (eq 16) can be used to fit CLS desorption from dolomite, as shown in Figure 13. Each series of data was fitted by one line in the semilog plot of qt versus t.
Three major types of rock are common in reservoirs, including sandstone, dolomite, and limestone. In our previous work,8-10 we studied CLS adsorption and desorption onto sandstone and limestone. Comparing the adsorption kinetics of CLS on the three porous media, it can be found that all adsorption processes are characterized by a short period of rapid adsorption followed by a long period of slow adsorption, and all kinetics results can be well fitted by the pseudo-second-order equation. However, it took about 2 days for limestone and dolomite to reach adsorption equilibrium while it took about 1 week for sandstone. The difference could be due to the rock compositions and their porous structures. X-ray diffraction of the Berea core demonstrated quartz to be the major component with a small amount of feldspar and clays that coat the pore surface and increase the surface area in the porous media. The compositions of dolomite and limestone are relatively simple. The dolomite contains 54% CaCO3 and 46% MgCO3. Limestone is primarily composed of CaCO3 in the form of the mineral calcite. Comparing the microstructures of three porous media presented in a previous publication,9 the porous structures of limestone and dolomite are almost the same and they are much simpler than that of sandstone. The complex structure of sandstone resulted in longer time for CLS to reach equilibrium than the other two porous media. Comparing the adsorption isotherms of CLS on the three porous media, it can be found that the adsorption increases with the increase of CLS concentration and no plateau was found within the tested concentrations up to 21 800 mg/L for all three porous media.10 All adsorption isotherms can be well fitted by the Langmuir and Freundlich equations. Conclusions This paper reports the studies on the adsorption and desorption of CLS onto dolomite. Based on the results and discussion, some conclusions can be drawn as follows: 1 Both CLS adsorption and desorption onto dolomite are time-dependent. The adsorption and desorption processes have been found to be a two-phase pattern, a rapid sorption process followed by a slow desorption process. 2 CLS adsorption onto dolomite is well fitted to a pseudosecond-order kinetic model and can also be fitted to a diffusion equation during the second period. Even though the plot of log[1/(qe - qt)] versus t is linear, CLS adsorption does not follow a pseudo-first-order kinetic adsorption model due to the poor correlation between the measured and calculated equilibrium adsorption density. 3 Equilibrated CLS adsorption and desorption isotherms onto dolomite can be described by the Freundlich equation in the experimental CLS concentration range. Adsorption isotherms fit the Freundlich equations even better. 4 Increase of NaCl and CaCl2 concentrations increases CLS adsorption density onto dolomite. However, CaCl2 has a stronger effect than NaCl on the adsorption of CLS. 5 Pseudo-first-order and pseudo-second-order kinetic desorption models were applied to fit the experimental data. Except for the first few points, CLS desorption from dolomite can be fitted to both a pseudo-first-order kinetic model and a pseudo-second-order kinetic model. 6 CLS desorption from the dolomite surface is much slower than adsorption onto the dolomite. References and Notes (1) Tsau, J. S.; Syahputra, A. E.; Grigg, R. B. Paper SPE 59365, presented at the SPE/DOE 12th Improved Oil Recovery Symposium, Tulsa, April 3-5, 2000.
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