Ind. Eng. Chem. Res. 2004, 43, 6935-6942
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Kinetics of Ozonation of 2-Mercaptothiazoline in an Electroplating Solution Y. H. Chen,† C. Y. Chang,*,† C. C. Chen,† C. Y. Chiu,‡ Y. H. Yu,† P. C. Chiang,† C. F. Chang,† and J. L. Shie† Graduate Institute of Environmental Engineering, National Taiwan University, Taipei 106, Taiwan, and Department of Environmental Engineering, Lan-Yang Institute of Technology, I-Lan 261, Taiwan
The reaction kinetics of ozonation of 2-mercaptothiazoline (2-MT) in the acid-based electroplating solution of the printed wiring board industry is studied. The substrate prescription of a typical electroplating solution is with [CuSO4‚5H2O] of 200 g‚L-1, [H2SO4] of 60 g‚L-1, [Cl-] of 0.03 g‚L-1, and pH of 0.18-0.42. Multistep reaction kinetics in terms of ozone, 2-MT, and total organic carbons is proposed to describe the ozonation progress of 2-MT. The enhancement effect of chemical reactions on the ozone gas-liquid mass transfer is considered along with the reaction kinetics. The proposed ozonation kinetics is useful for the treatment of 2-MT via ozonation in the electroplating solution of the printed wiring board industry. The removal of the aged organic additives such as 2-MT can assist the recovery and reutilization of the discarded aged electroplating solution. Introduction The discarded aged electroplating solution is one of the major wastewater sources in the printed wiring board (PWB) industry. The substrates (the major chemical species) of the recipe solution are inorganics such as sulfuric acid, copper sulfate, hydrochloric acid, etc., while the minor substances are organics such as 2-mercaptothiazoline (2-MT), which is used as a brightening and stabilization agent.1 Consequently, the characteristics of wasted electroplating solution are high acidity (pH ) 0.18-0.42) and ionic strength. All of the above features make the solution difficult to treat by conventional treatment processes.1,2 The current major method used to treat the waste electroplating solution of the PWB is chemical coagulation, which produces hazardous chemical sludge as a result of its high heavy-metal content such as copper. In Taiwan, the yield of the waste electroplating solution of the PWB is approximately 106 000 CMD, resulting in about 21 000 t of waste sludge/year with 78 wt % moisture.3 Furthermore, in view of the resource recycling, the aged electroplating solution of the PWB has great reclamation and recycling potentials with high copper concentration and electric conductivity. Note that the qualities of the organics in the electroplating solution become low and unreliable to the process after the electroplating and electrophoresis. For this reason, removing the spent organic additives in order to add new additives is one of the key steps for the reutilization process. The chemical structure of 2-MT is composed of an exocyclic mercapto group and a heterocyclic molecule containing sulfur, nitrogen, and carbon atoms. 2-MT has also been used as a biocorrosion inhibitor, an antifungal reagent, and a brightening and stabilization agent in many industrial processes.4 Ozonation is an effective way of removing organics and reducing the total organic * To whom correspondence should be addressed. Tel./fax: +886-2-2363-8994. E-mail:
[email protected]. † National Taiwan University. ‡ Lan-Yang Institute of Technology.
carbons (TOCs) by oxidizing the stream solutions with ozone. Recently, Chen et al.5,6 investigated the decomposition of 2-MT in the aqueous solution by ozonation. Ozonation is found to be effective for decomposition of 2-MT in the aqueous solution. However, the information of 2-MT removal via ozonation in the electroplating solution is still scarce. The kinetics model for 2-MT ozonation is desirable to quantify the concentration variations of ozone, 2-MT, and TOCs, which are critical to the rational design and optimal operation of the ozonation system. Note that the mechanism of pollutant decomposition via ozonation is commonly composed of numerous reaction steps.7-10 The intermediates consequently generated from the destruction of pollutant would react with ozone that can be reflected by the reduction of TOCs. Available models employed for the description of ozonation with pollutant commonly consider only one or two reaction steps.11-13 Accordingly, the reaction kinetics obtained from these models is usually applicable only for the initial period of ozonation. The objective of this study is to investigate and model the ozonation of 2-MT in the electroplating solution of the PWB industry. The multistep reaction kinetics (MSRK) is proposed to describe the concentration variations of 2-MT, TOC, dissolved ozone, and off-gas ozone simultaneously with the consideration of mass-transfer properties. The ozonation experiments of 2-MT with various ozone dosages are performed for the determination of kinetic parameters and model verification. Theoretical Analysis The model with MSRK is proposed to describe the ozonation process of 2-MT in the electroplating solution of the PWB industry. There are three major factors considered in the ozonation model including (1) the gasliquid mass transfer, (2) the ozonation reactions, and (3) the enhancement effect of chemical reactions on the gas-liquid mass transfer of ozone. The mass transfer of ozone from the gas to liquid phase can be described by the two-film model. With the ozone consumption by
10.1021/ie040091z CCC: $27.50 © 2004 American Chemical Society Published on Web 10/01/2004
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chemical reactions, the mass-transfer rate of ozone may be enhanced.14,15 The ratio of the mass-transfer rate of ozone with chemical reactions to that without is designated by the enhancement factor of ozone (ErA). MSRK Model. As ozone (denoted as A) is dissolved in water, it may be consumed via ozone self-decomposition (O3 f 1.5O2) and oxidation with the pollutant (denoted as B) and intermediates (denoted as Ij). Regarding the spontaneous ozone decomposition and ozonation reactions, the pseudo-first-order and secondorder reaction rate expressions, which were successfully employed in other ozonation systems of different pollutants,11-13,16 are adopted, respectively. The assumptions of the MSRK model in the semicontinuous ozonation condition are as follows. 1. The homogeneous conditions with complete mixing of liquid and gas flows are valid in the reactor. 2. A series ozonation mechanism is applicable. 3. Second-order chemical reactions are bimolecular. 4. Henry’s law applies. 5. Reactions in the gas phase are neglected. The governing equation of hold-up gas ozone (CAGi) can be expressed by eq 1. In eq 1, the left-hand-side term
dCAGi/dt ) QG(CAGi0 - CAGi)/VH ErAk0LAa(CAGi/HA - CALb)/G (1) represents the variation of the local gas ozone concentration, while the right-hand-side terms stand for the gas convection and gas-liquid ozone mass transfer, respectively. For the liquid-phase governing equations of ozone (CALb), pollutant (CBLb), and intermediates (CjLb), the chemical reaction terms should be additionally considered as follows.
For ozone dCALb/dt ) ErAk0LAa(CAGi/HA - CALb)/L - kdCALb kBCALbCBLb -
∑kjCALbCjLb
(2)
For pollutant dCBLb/dt ) -kBCALbCBLb
(3)
CTOC/CTOC0 ) (CBLb +
∑RjCjLb + RpCPLb)/CBLb0
(9)
Rj and Rp are the ratios of TOC contributions per mole of intermediate j and of product P to that per mole of pollutant B, respectively. It should be noted that the actual reactions involved may be more complex than the sequential multistep reactions with these simplifying assumptions proposed above in this study. However, the present reaction kinetics model can provide a simplified explanation of the experimental data for practical engineering application. However, of course, the validity of the model must be justified by comparing the agreeability of the model and experimental results as examined in the latter sections. Film Model and Enhancement Factor. Although the surface renewal theory is more appropriate than the film theory to describe the mass transfer in the stirred reactor, the predictions of the enhancement factor ErA (ratio of the mass-transfer coefficient with chemical reactions to that without) based on the film and surface renewal models are closely similar, as indicated by Danckwerts.18 Further, the computation related to the film model is simpler because it involves ordinary differential equations rather than partial differential equations. Thus, we employ the film theory to compute ErA. According to the film model, the value of ErA for ozone absorption can be calculated according to eqs 10-16. Note that the resistance of the ozone gas-liquid mass transfer is mainly contributed by the liquid phase. The concentration of ozone in the liquid film (CALF) at the gas-liquid interface (x ) 0) is in equilibrium with that in the gas phase. Furthermore, the volatilities of pollutant and intermediates are usually neglected. Thus, the concentration gradients of pollutant (dCBLF/dx) and intermediates (dCjLF/dx) in the liquid film at x ) 0 are taken as zero. At the boundary of the liquid film near the bulk liquid (x ) xM), the concentrations of ozone, pollutant, and intermediates in the liquid film are equal to those in the bulk liquid, respectively.
For ozone
For the first intermediate (j ) 1) dC1Lb/dt ) kBCALbCBLb - k1CALbC1Lb
(4)
For the following intermediates (j g 2) dCjLb/dt ) kj-1CALbC(j-1)Lb - kjCALbCjLb
(5)
The concentration of the ozonation product (CPLb), which has a relatively low reactivity toward ozone, is calculated by eq 6.
CPLb ) CBLb0 - CBLb -
The variation of TOC can be estimated by eq 9, where
∑
CjLb
(6)
The governing equation of off-gas ozone (CAGe) in the free space is17
dCAGe/dt ) QG(CAGi - CAGe)/VF
(7)
The initial conditions of eqs 1-7 are
t ) 0, CAGi ) CAGe ) CALb ) CjLb ) CPLb ) 0, CBLb ) CBLb0 (8)
DA d2CALF/dx2 ) kdCALF + kBCALFCBLF +
∑kjCALFCjLF
(10)
For pollutant DB d2CBLF/dx2 ) kBCALbCBLF
(11)
For the first intermediate (j ) 1) D1 d2C1LF/dx2 ) -kBCALFCBLF + k1CALFC1LF
(12)
For the following intermediates (j g 2) Dj d2CjLF/dx2 ) -kj-1CALbC(j-1)LF + kjCALFCjLF (13) The boundary conditions are as follows:
x ) 0, CALF ) CAGi/HA, dCBLF/dx ) dCjLF/dx ) 0 (14) x ) xM ) DA/k0LA, CALF ) CALb, CBLF ) CBLb, CjLF ) CjLb (15)
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The calculation of ErA is as follows:
ErA ) -(dCALF/dx)|x)0/[(CAGi/HA - CALb)/(DA/k0LA)] (16) Computation Algorithm for Solving the MSRK Model. Equations 1-16 represent the governing equations of the MSRK model for predicting the dynamic variations of ozone, pollutant, intermediates, and TOC concentrations. The numerical method with Turbo C program is employed for solving the equations. Equations 10-15 are first solved using the iterative method to obtain the values of CALF, CBLF, and CjLF in the film, yielding the value of ErA from eq 16 at time t. Equations 1-9 are then solved using the fourth-order RungeKutta method to compute the values of the variables in the next time step of t + ∆t from the available values at t. This is followed by the computation of ErA at t + ∆t. The computation is conducted up to the set duration. The grids along x ) 0 to xM and the size of the time step (∆t) adopted in the computer program are 71 points and 0.008 s, respectively. The confidential error range of mass balance for checking the numerical scheme used is less than 10-6. The values of the parameters of the MSRK model are determined by the best fitting of the prediction compared with the experimental data with respect to the determination coefficient (R2). Experimental Section Chemicals. The substrate recipe of the electroplating solution is [CuSO4‚5H2O] ) 200 g‚L-1, [H2SO4] ) 60 g‚L-1, and [Cl-] ) 0.03 g‚L-1. The initial concentration of 2-MT (CBLb0) in the solution is 100 mg‚L-1. 2-MT with the chemical formula of C3H5NS2 purchased from Aldrich (Milwankee, WI) has a molecular weight of 119.21, a melting point of 105-107 °C, and a CAS registry number of 96-53-7. The molecular structure of 2-MT is shown in Figure 1. All experimental solutions are prepared with deionized water. The initial concentration of TOCs (CTOC0) is about 29.1 mg‚L-1. The volatility of 2-MT in the aqueous solution is found to be negligible by the air-stripping tests. Instrumentation. The airtight reactor of 17.2 cm inside diameter is made of Pyrex glass with an effective volume of 5.5 L and equipped with a water jacket to maintain a constant solution temperature at 25 °C in all experiments. The design of the reactor is based on the criteria of the shape factors of a standard six-blade turbine.19 The gas diffuser of cylindrical shape with a pore size of 10 µm is located at the bottom of the reactor. About 3.705 L of solution (VL) is used in each experiment, while the total sampling volume is within 5% of the solution. The stirred speed is 800 rpm to ensure the complete mixing of the gas and liquid phases according to the previous studies.13,16 The generation of ozone from pure oxygen is controlled by the ozone generator (model SG-01A, Sumitomo, Tokyo, Japan) with a gas flow rate (QG) of 0.0324 L‚s-1. The fed (CAGi0) and discharged (CAGe) concentrations of gaseous ozone are measured by the Seki model SOZ6004 UV photometric analyzer (Tokyo, Japan), which is calibrated by the KI titration method. The Orbisphere model 3600 liquid ozone monitor with a membranecontaining cathode sensor is used to measure the dissolved ozone concentration (CALb) in the aqueous solution. A circulation pump is used to transport the
Figure 1. Molecular structures of 2-MT and some possible intermediates and a simplified scheme of decomposition of 2-MT via ozonation.
liquid from the reactor to the sensor and reflow it back with a flow rate of 0.18 L‚min-1 during the ozonation. The concentrations of 2-MT (CBLb) are analyzed using high-performance liquid chromatography (HPLC) system, with a 250 × 4.6 mm column [model BDS C18 (5 µm), Thermo Hypersil-Keystone, Bellfonte, PA] and a UV/visible detector (model 1706, Bio-Rad, Hercules, CA) at 275 nm. The HPLC effluent with a flow rate of 1.0 mL‚min-1 has a composition of 73.5 mM [CH3(CH2)3]4N(HSO4)/CH3CN of 74:26. The injection volume of the solution for the analysis is 20 µL. In addition, the concentration of TOCs (CTOC) is analyzed by the TOC analyzer (model 700, OI Corp., College Station, TX). Properties of an Electroplating Solution. The pH value of the electroplating solution is about 0.25. The variation of pH during the experiments is found to be very slight because of the high acid concentration. The physical properties and mass-transfer parameters in the reactor are summarized in Table 1. The density (FL) and viscosity (µL) of the electroplating solution are apparently greater than those of the aqueous solution because of the high inorganic contents. On the other hand, the surface tension (σL) of the electroplating solution is only slightly higher than that of water. The fraction of holdup gas (G) under the operation conditions is estimated to be 3.26% and 1.71% for the electroplating and aqueous solutions, respectively, by the volume-expanding method employing G ) VH/(VH + VL). The Sature diameter of the bubbles (dbs) has the normal distribution of the average value of 0.729 mm by analysis of the photographs of the bubble images. The specific area of the gas-liquid interface (a) can be calculated from the known G and dbs with a ) 6G/dbs. The dimensionless Henry’s law constant of ozone [HA ) He/RGT ) 102.1 atm‚L‚mol-1/(0.082 atm‚L‚mol-1‚K-1 × 298 K) ) 4.18 M‚M-1] determined from the experimental data of ozone
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Table 1. Physical and Mass-Transfer Properties of Electroplating and Aqueous Solutions in the Stirred Reactora item
units
density, FL viscosity, µL surface tension, σL fraction of hold-up gas, G Sature diameter of bubbles, dbs specific area of the gas-liquid interface, a Henry’s constant of ozone, HA liquid diffusion coefficient of oxygen, DO liquid diffusion coefficient of ozone, DA mass-transfer coefficient of oxygen, k0LO mass-transfer coefficient of ozone, k0LA power consumption for agitation, PmGg
kg‚m-3 cP N‚m-1 % mm m-1 m2‚s-1 m2‚s-1 m‚s-1 m‚s-1 W
electroplating solution
aqueous solution
1130 1.64 0.0733 3.26 0.729b 269c 4.18 1.6× 10-9 e 1.3× 10-9 e 1.02× 10-4 f 8.80× 10-5 f 4.76
999 0.924 0.0718 1.71 0.476c 216d 4.18 2.5× 10-9 2.0× 10-9 1.28× 10-4 1.15× 10-4 f 4.27
a T ) 25 °C, superficial gas velocity ) 1.39 mm‚s-1, stirring speed (ω) ) 800 rpm. b Number of bubbles counted ) 134, relatively standard deviation ) 19%, volume-to-surface mean bubble diameter dbs ) ∑nkdbk3/∑nkdbk2. c Computed by the relation of a ) 6G/dbs. d Computed from a in an electroplating solution of 269 m-1 according to eq 10 of Calderbank20 as follows: a ) 1.44(P 0.4 0.2 mG/VL) FL (uG/ ut)0.5/σL0.6 m-1. e Computed from the value of the diffusion coefficient (D) in an aqueous solution according to eq 5 of Wilke and Chang,21 which is D ) 7.4 × 10-8T(χMW)0.5/(µLVS0.6) cm2‚s-1. f Computed from the oxygen mass-transfer coefficient (k0LO) in an aqueous solution of 1.28 × 10-4 s-1 based on the surface renewal theory (k0L). g PmG ) 2πω(τ - τf).
dissolution experiments is found to be similar in both the organic-free water solution and the organic-free electroplating solution. The volumetric mass-transfer coefficient of oxygen (k0LOa) in the aqueous solution is measured as 0.0268 s-1 by oxygen aeration. Moreover, the a value in the aqueous solution is calculated as 216 m-1 by employing eq 10 of Calderbank.20 The diffusion coefficients of oxygen (DO) and ozone (DA) in the electroplating solution are estimated according to eq 5 of Wilke and Chang.21 The molar volume of ozone in the Wilke and Chang equation is taken as 33.1 cm3‚gmol-1. The values of mass-transfer coefficients of oxygen (k0LO) and ozone (k0LA) can be accordingly computed based on the surface renewal theory (Table 1). The power consumption for solution agitation (PmG) depending on the viscosity is measured as 4.76 and 4.27 W in the electroplating and aqueous solutions, respectively. In addition, the reaction rate constants of ozone self-decomposition (kd) in the electroplating (pH ) 0.18-0.42) and aqueous (water with a pH of 6-7) solutions were determined as 0.0036 and 1.45 × 10-4 s-1, respectively.13,16 kd in the electroplating solution is greater than that in the water system because of the high ionic strength.16 The diffusion coefficients of 2-MT (DB) and intermediates (Dj) are taken as 7.77 × 10-10 m2‚s-1 for the modeling.22 Experimental Procedures. The semibatch experiments of 2-MT ozonation are carried out to investigate the concentration variations of 2-MT, ozone, and TOCs with three different fed-ozone dosages. Before the ozonation processes are started, the ozone-containing gas is bypassed to the photometric analyzer to ensure stability. A part of the gas stream at the preset flow rate is directed into the reactor when the ozonation system is ready to start. Samples are drawn out from the reactor at desired time intervals in the course of ozonation. The residual dissolved ozone in the samples is removed immediately by stripping with nitrogen. The experimental apparatus employed in this work is shown in Figure 2. Results and Discussion The dynamic variations of CBLb, CTOC, CALb, and CAGe in the course of 2-MT ozonation are simultaneously monitored for the investigation. Furthermore, the MSRK model adopting schemes with various reaction steps is
Figure 2. Experimental apparatus sketch: s, ozone gas stream; - -, experimental solution; -‚-, isothermal water. Components: (1) oxygen cylinder, (2) drying tube, (3) ozone generator, (4) flowmeter, (5) three-way valves, (6) stirrer, (7) reactor, (8) sample port, (9) liquid ozone sensor, (10) pH sensor, (11) circulation pump, (12) thermostat, (13) gas ozone detector, (14) KI solution, (15) vent to hood.
employed to simulate the concentration variations. The normalized concentrations in dimensionless forms are θBLb ()CBLb/CBLb0), θALb [)CALb/(CAGi0/HA)], and θAGe ()CAGe/CAGi0). Variations of θBLb, ηTOC, θALb, and θAGe. As shown in Figure 3, the elimination rate of θBLb increases with higher fed-ozone concentration (CAGi0). The times required for the complete decomposition of 2-MT with CAGi0 ) 40 mg‚L-1 (6 min) is about one-third and half of those with CAGi0 ) 10 (20 min) and 20 mg‚L-1 (10 min), respectively. Further, the pseudo-first-order reaction rate expression can be proposed as θBLb ) e-kB,Appt with kB,App ) 0.0162CAGi0 min-1 (where CAGi0 is in mg‚L-1) from the experimental data. The value of kB,App in the electroplating solution is about the same as that in the aqueous solution ()0.0167CAGi0 min-1).5 Figure 4 shows the variations of the removal efficiency of TOCs [ηTOC ) (CTOC0 - CTOC)/CTOC0] under different experimental conditions. The CAGi0 value also accelerates the mineralization rate correspondingly. Obviously, the mineralization rate decreases with the ozonation time because the subsequent intermediates have lower reactivities toward ozone. As observed in the case of CAGi0 ) 40 mg‚L-1, the value of ∆ηTOC/∆t decreases to
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Figure 3. Time variations of θBLb for 2-MT ozonation in an electroplating solution of a semibatch system. θBLb ) CBLb/CBLb0. Symbols: experiments. Lines: prediction based on five-step reaction kinetics. O and -‚-: CAGi0 ) 10 mg/L. 4 and - -: CAGi0 ) 20 mg/L. 0 and -‚‚-: CAGi0 ) 40 mg/L.
Figure 5. Time variations of θALb for 2-MT ozonation in an electroplating solution of a semibatch system. θALb ) CALb/(CAGi0/ HA). Symbols: experiments. Lines: prediction based on five-step reaction kinetics. Notations are the same as those specified in Figure 3.
Figure 4. Time variations of ηTOC for 2-MT ozonation in an electroplating solution of a semibatch system. ηTOC ) (CTOC0 CTOC)/CTOC0. Symbols: experiments. Lines: prediction based on five-step reaction kinetics. Notations are the same as those specified in Figure 3.
Figure 6. Time variations of θAGe for 2-MT ozonation in an electroplating solution of a semibatch system. θAGe ) CAGe/CAGi0. Symbols: experiments. Lines: prediction based on five-step reaction kinetics. Notations are the same as those specified in Figure 3.
lower than 0.012%/min when ηTOC > 24%, indicating the slow progress of the mineralization. It is worth noting that ηTOC in the electroplating solution is about 24% at 240 min, which is significantly greater than that in the aqueous solution of 16%.5 The noteworthy enhancement for the mineralization of 2-MT ozonation in the electroplating solution may be caused by the catalytic effect of copper ions.23,24 As shown in Figure 5, the variations of θALb can be divided into three stages. In the first stage (with ηTOC < 7%), θALb remains nearly undetectable. In this regime, the rate of ozonation reaction with the original pollutant B is very fast (Figure 3) so that the ozone transferred from the gas phase is consumed immediately in the solution. Then θALb starts to increase rapidly with the ozonation time in the transient regime (with 7% e ηTOC < 17%). The accumulation of dissolved ozone is attributed to the case in which the consumption rates of dissolved ozone are smaller than its gas-liquid masstransfer rate because of the lower reactivities of the refractory intermediates in the reacted solution. Finally, θALb gradually approaches the constant value of about 0.79, which seems to be independent of CAGi0. Meanwhile, the consumption of ozone mostly comes from the self-decomposition reaction. This ozone-rich regime (with ηTOC g 17%) representing the steady state of
dissolved ozone has the theoretical value of 1/(1 + kdVL/ QGHA + kdL/k0LAa) of 0.80. Figure 6 shows that θAGe increases consistently from the beginning to reach the steady state, indicating that the ratio of ozone transferred from gas-to-liquid phases to that in the feed gas [)ErAk0LAa(θAGi - θALb)(VL + VH)/ HAQG] decreases with the ozonation time. This is due to the smaller values of ErA (as illustrated in Figure 8) and θAGi - θALb in the later time. Evidently, θAGe increases faster with a higher CAGi0 value; however, it also has the same steady value of about 0.90 close to the theoretical value of 1 - 1/(1 + QGHA/kdVL + QGHAL/ k0LAaVL) of 0.92. Simulation of Ozonation Based on MSRK. Before the MSRK model was applied to the ozonation system of 2-MT, the model was simplified to simulate a different set of experiments of ozonation of poly(ethylene glycol) performed by Li et al.13 Good agreement was achieved, supporting the validity of the utilization of the present model. The kinetic parameters can be obtained by achieving the best fitting for the experimental data in the simulation with MSRK models with various steps of reactions. As a result, the corresponding values of the parameters and R2 are summarized in Table 2. This indicates that θBLb and ηTOC can be satisfactorily predicted when the
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Table 2. Ozonation Kinetics of 2-MT Adopting Schemes with Various Reaction Steps in an Electroplating Solution reaction step 2 3 4 5
kinetic parameter kB ) 165 000 M-1‚s-1, k1 ) 1.5 M-1‚s-1 kB ) 165 000 M-1‚s-1, k1 ) 24 000 M-1‚s-1, k2 ) 1.55 M-1‚s-1 kB ) 165 000 M-1‚s-1, k1 ) 24 000 M-1‚s-1, k2 ) 3500 M-1‚s-1, k3 ) 1.55 M-1‚s-1 kB ) 165 000 M-1‚s-1, k1 ) 24 000 M-1‚s-1, k2 ) 3500 M-1‚s-1, k3 ) 10 M-1‚s-1, k4 ) 1.55 M-1‚s-1
factor of TOC contribution
R2 value for predicted results θBLb ηTOC θALb θAGe
R1 ) 0.92, RP ) 0.7 R1 ) 0.96, R2 ) 0.935, RP ) 0.74
0.957 0.983
0.918 0.939
