2437
Ind. Eng. Chem. Res. 1991,30, 2437-2444
Strong Acid Equivalent Control of pH Processes: An Experimental Study Raymond A. Wright,* Masoud Soroush, a n d Costas K r a v a r i s Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan 48109
The control of pH is widely recognized as a difficult problem. The strong acid equivalent approach for control of pH processes consists of defining an equivalent control objective, the strong acid equivalent, and using a linear control law in terms of this new control objective. The strong acid equivalent is calculated on-line from pH measurements given a nominal titration curve of the process stream. A laboratory system has been built to implement this method. Experimental results for the hydrochloric acid-sodium hydroxide and acetic acid-sodium hydroxide systems are given. The results demonstrate the performance of the strong acid equivalent control method. 1. Introduction
The control of pH is a classic and difficult nonlinear control problem encountered in the chemical process industry. It is well established in the literature that standard linear PI or PID control provides poor performance for pH processes. Results for laboratory-scale pH control systems have been reported by several researchers using a variety of adaptive and/or nonlinear control methods. Gustafsson (1985) gives experimental results for the sulfuric acid-sodium hydroxide-sodium carbonate system using the reaction invariant control method developed in Gustafsson and Waller (1983). The same chemical system is also studied by Hall and Seborg (1989) and Girardot (1989), who also use the reaction invariant control for a two-tank neutralization along with level control. An adaptive optimal quadratic PI feedback controller is used for a strong acid/strong base system in Buchholt and Kummel (1979). Williams et al. (1990) investigate a system consisting of sulfuric acid-hydrochloric acid-acetic acid-sodium acetate-sodium hydroxide mixed in city water using a process-model-based controller that considers the wastewater as a single fictitious acid of unknown concentration and updates the parameters on-line. Direct comparison of the result9 given in these papers is difficult if not impossible due to the different chemical systems, concentration levels, and physical process equipment employed. In general, they all show the difficulties encountered in controlling pH processes. In this paper, the strong acid equivalent approach first introduced by Wright and Kravaris (1991) will be implemented for a laboratory-scale pH experiment. The strong acid equivalent of a mixture of electrolytes arises naturally from the chemical equilibrium relations in a pH process. The regulator problem, when reformulated in terms of the strong acid equivalent, becomes a linear and nonadaptive control problem. On-line estimation of the strong acid equivalent based on the minimal-order model of Wright and Kravaris (1991) is straightforward and requires no information other than a nominal titration curve of the process stream. A linear controller with error in terms of the strong acid equivalent is then used to complete the control structure. In this paper, results will be given for an experimentalimplementation of this control algorithm. This work begins with a brief necessary review of the minimal-order model for pH processes and the resulting model-based nonlinear-in-pH controller. The components and characteristics of the experimental apparatus will be given next. The hydrochloric acid-sodium hydroxide system will then be studied. The specific mathematical *Author to whom correspondence should be addreased at The Dow Chemical Company, 1400 Building, Midland, MI 48667.
model and quantities necessary to program the controller for this system will be presented first, followed by the experimental results. The acetic acid-sodium hydroxide system will similarly be examined. The experimental results for these systems will show that the nonlinear control algorithm based on the strong acid equivalent can be successfully implemented for simple acid/base systems in a laboratory setting. 2. Titration-Curve-Based Model for pH Processes
The standard approach for modeling pH processes involves ion balances and chemical equilibrium relations (see McAvoy et al. (19721, Gustafsson and Waller (19831, and Wright and Kravaris (1991)). This general model is unobservable and uncontrollable in a systems theory sense. A minimal-order model, which has the same input/output behavior as the original detailed model, was rigorously derived by Wright and Kravaris (1991). This reducedorder model facilitates controller synthesis for pH processes. Consider a general pH process as shown in Figure 1. When a sample of the process stream is titrated with the same agent as in the titrating stream, a standard titration curve, as shown in Figure 2, results. The inverse of this curve, i.e., its reflection about the 45' line, results in the plot shown in Figure 3. This function, T(pH), is equal to A(pH) + 5ai(pH)ci i=l
T(pH) = -
n
A(pH) + Cai(pH)ai
(1)
ill
where A(pH) = 10-pH - K,lOpH
(2)
ci and ai are the total ion concentrations of the process stream and titrating stream, respectively, and ai(pH) are functions of pH and the dissociation constants, as shown in Table I, with the understanding that 1 1 -=O or - = ( ) K.ji Kbji if the j t h dissociation for an acid or a base, respectively, is strong. T(pH) may be obtained through the formulas given in Table I if the acids and bases present in the process stream are known, or it may be obtained experimentally from titration data taken from samples. The steady state value of the titrating stream flow rate is then given by u, = ~ ( P H , ) (3) where the subscript s denotes steady state.
08SS-5885/91/2630-2437$02.50/00 1991 American Chemical Society
2438 Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 Table I. Definitions of ei(pH), c,, and ai for Common Acids and Bases total ion concn of ith ith ionic species species (ci or a i )
ai(~H) 1
anion of monoprotic acid, HA
[HA1 + [A-I
anion of diprotic acid, H2A
[H2A] + [HA-] + [A2-]
anion of triprotic acid, H3A
[HSA] + [HZA-] + [HA2-] + [A3-]
cation of monohydroxyl base, BOH [BOH] + [B+] cation of dihydroxyl base, B(OH)2 [B(OH),]
+ [BOH+] +
P2+1
strong acid equivalent. By definition the strong acid equivalent of a mixture of electrolytes is given by n
Y = -Cai(pH,,)(total ion concn of ith species) (4) i=l
v
P+u
X .
-b
Figure 2. Titration curve of inlet stream.
where pH,, is the desirable value of pH that the system is to be brought to. Notice from Table I that ai(pH) is -1 for a monoprotic strong acid and +1 for a monohydroxyl strong base. Physically, this corresponds to the hydrogen or hydroxyl ion, respectively, associated with each acid or base molecule always being dissociated in solution. When only these chemical species are involved, the total ion concentrations are directly combined and the result reflects the actual state of the solution and, therefore, the amount of titrating agent required to bring the solution to its set point. When a weak monoprotic acid is involved, the ai(pH)will range between -1 and 0 depending on the acid’s pK, and the desirable final pH. When the ai(pH) is close to -1, the acid is nearly all in ionic form. When the ai(pH) is close to 0, the acid is nearly all in molecular form. A similar discussion holds for more complex acids and bases. Overall, ai(pHSp)may be viewed as a conversion factor relating the strength and concentration of a chemical species to a monoprotic strong acid at the desirable final pH, pH,,. From (l),it can be seen that it is this weighted sum of concentrations which determines the amount of titrating reagent required to bring the system to pH,,. The minimal-order model for the pH process may now be written in deviation variable form as
v-= dY‘
,
dt
-(1 + T(pH,,))FY’-
where U’=
u - I”r(pH,,)
(6)
The quantity, Y’, which is the state of the dynamic model, is the strong acid equivalent of the effluent stream in deviation variable form. The quantity PH
Figure 3. Inverse of the titration curve in Figure 2.
Another key notion in developing and interpreting the minimal-order model for pH processes is the one of the
n
Cai(pH,p)ai
(7)
i=l
is the negative of the strong acid equivalent of the titrating
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2439 pH EXPERIMENT PI CONTROLLER
T I
PROCESS smng Acid Equivalent
-
I
Figure 4. Nonlinear control structure using measurement of pH and on-line estimation of the strong acid equivalent.
stream, which is known because the chemical composition of the titrating stream is known. For most applications, including the experimental ones considered in this paper, the titrating stream is much more concentrated than the process stream, and therefore the process flow rate is much larger than the titrating stream flowrate, Le., u -
I
-O.1 -0.3:”. 0
to prevent any bypass flow through the reactor. An agitator was used to ensure proper mixing, and baffles were added to prevent a vortex from forming. The effluent stream tube was much larger in diameter than the inlet stream tubes and was raised to the desired liquid level in the tank before leading to a 55-gal polyethylene collection drum. In this way, constant volume could be maintained. A pH electrode was submerged in the tank near where the effluent stream exited. The signal from the electrode was sent to the control computer. According to the manufacturer, the particular electrode used should show 95% of a step change in pH within 10 s. For control purposes, the sensor dynamics were neglected in the control algorithm and were therefore another source of model uncertainty. The control computer received the pH measurement signal, implemented the control law, and sent the flow rate signal to the metering pump on the titrating stream. The control algorithm of the previous subsection based on the strong acid equivalent (eq 10) was used with the only chemical information being a nominal titration curve of the process stream. 4. Hydrochloric Acid-Sodium Hydroxide System
A system consisting of hydrochloric acid (HCl) titrated by sodium hydroxide (NaOH) was selected for study. The set point value of the pH is 7. This system, consisting of only a strong acid and a strong base, is the pH process that is the most nonlinear. The gain at pH equal 7 is the highest possible for any pH process. The inverse titration curve of the process stream titrated by the reagent of the titrating stream is given by 10-pH - 10(pH-14) - C1 (13) T(pH) = - 10-pH - 10‘pH-14) + az where c1 is the concentration of [Cl-] in the process stream and azis the concentration of [Na+]in the titrating stream. Substituting (13) into the output map of (5) results in y‘ = A(pH) = 10-PH - lo(PH-14) (14) which is independent of c1 and az.Thus, Y’ or the strong acid equivalent can be directly calculated from the effluent pH measurement. The function Y‘ = A(pH) is plotted in Figure 6. The function T(pH) is plotted in Figure 7 for both values of the process stream acid concentration. Notice the high degree of nonlinearity of this system and the large gain of the process at the neutralization point. The process parameters for all runs of this chemical system are summarized in Table 11. For each experi-
.
, 4
.
,
.
6
,
e
.
,
lo
.
,
1
.
t2
l4
PH
PH Figure 6. Plot of strong acid equivalent versus pH for strong acid/strong base system.
,
2
Figure 7. Initial T(pH) curves for both inlet acid concentrations for strong acid/strong base system.
2 4 1
v
o l . , . , . , . , . , . , . l 0 Joo goo 9 0 0 m 0 1 5 0 0 8 0 0 2 x M lime (4 Figure 8. Response of pH to a tripling of inlet acid concentration in the HCl-NaOH system, with t-domain poles at 0.8. Table 11. Process Parameters for the HC1-NaOH System = 0.3 N F = 1 L/min V=lOL c1 = 0.03 N (in acid feed tank 1) T=6s c1 = 0.01 N (in acid feed tank 2)
mental run, the system is first brought to an effluent pH as close as possible to 7 from an arbitrary initial condition while pumping from acid feed tank 1. The proposed control algorithm is used during this startup period. The feed is then switched from acid feed tank 1 to acid feed tank 2 and the controller tries to reject the process stream acid concentration disturbance in the presence of the model uncertainty noted previously. Both step increases and step decreases in acid concentration are studied. Discussion of Results. Results of experimental runs for this system with both closed-loop poles set equal and placed at 0.6, 0.7, 0.8, and 0.9 are available in Wright (1990). The results of these runs show the classic performance/robustness tradeoff. For the sake of brevity, only the results with closed-loop poles at 0.8, which gave the best response of the four pole locations tried, will be shown here. The response to a tripling of the process stream acid concentration is shown in Figures 8-10. Figure 8 shows the pH response, Figure 9 the response of the strong acid equivalent, and Figure 10 the corresponding titrating stream flow rate. The response obtained when the process stream acid concentration goes from 0.03 to 0.01 N is likewise shown in Figures 11-13.
Ind. Eng. Chem. Res., Vol. 30, No. 11, 1991 2441
5 0 0 6 0 0 9 0 0 t 2 o o M x ) 1 8 w 2 x x )
0
r m e (s)
Figure 9. Response of strong acid equivalent to a tripling of inlet acid concentration in the HCI-NaOH system, with z-domain poles at 0.8.
*
O
Figure 12. Response of strong acid equivalent when the inlet acid concentration of the HCl-NaOH system is reduced to one-third ita initial value with z-domain poles a t 0.8.
I 100
0
0
300
900
600
l5W
UOO
2 2100
1800
Time (s)
24 1
l 0
.
, 300
.
, 600
.
,
.
900
,
wo
! 0
.
, 300
.
, 600
.
, 900
,
, 1200
,
, 1500
,
, 1800
. 2
Time (s)
Figure 10. Titrating stream flow rate after a tripling of inlet acid concentration in the HCl-NaOH system, with z-domain poles at 0.8.
O
o
.
,
.
Mx)
,
. !a00
] 2100
Tme (s)
Figure 11. Response of pH when the inlet acid concentration of the HCl-NaOH system is reduced to one-third ita initial value, with z-domain poles at 0.8.
The small oscillations of pH around 7 evident in both responses are due to the sensitivity of the system at the neutralization point. As would be expected from (13) or Figures 7 and 8, small changes in concedtration lead to large changes in pH. Local changes would be expected
Figure 13. Titrating stream flow rate when the inlet acid concentration of the HC1-NaOH system is reduced to one-third its initial value, with z-domain poles a t 0.8.
from the effects of mixing and the placement of the pH electrode. This sensitivity is a fundamental limitation of the system that would be apparent using any control algorithm. The fluctuations are slightly more pronounced in the step-decrease responses than in the step-increase responses. This is due to a difference in sensitivity. When the process stream acid concentration is 0.01 N, an incremental change in the titrating stream flow rate has a more significant effect than when the process stream concentration is 0.03 N. It is important to note, however, that the fluctuations are not evident in the plots of the strong acid equivalent and therefore the flow rate of the titrating stream. For the strong acid/strong base system, such changes in pH represent only a small change in the true acid demand being placed upon the system. This supports the intuitive notion given by Wright and Kravaris (1991) that the strong acid equivalent is a more direct measure of the true state of the process than is pH. 5. A c e t i c Acid-Sodium Hydroxide S y s t e m A system consisting of acetic acid (CH,COOH) titrated by sodium hydroxide (NaOH) was chosen to study the performance of the controller when buffering is present. The set point value of the pH for all experimental runs is 7. The inverse of the titration curve of the process
2442 Ind. Eng. Chem. Res., Vol. 30, No. 11,1991
42 1
-0.1
0
2
4
6
8
12
lo
l4
01 0
ZOO
I
I
400
600
800
1
IO
Time (s)
PH Figure 14. Initial T(pH) curves for both possible inlet values of the acetic acid-sodium hydroxide system.
Figure. 15. Response of pH to a tripling of inlet acid concentration in the CH,COOH-NaOH system, with z-domain poles at 0.7.
Table 111. Process Parameters for the CH&OOH-NaOH System F = 1 L/min L Y ~= 0.3 N V=lOL c1 = 0.03 N (in acid feed tank 1) c1 = 0.01 N (in acid feed tank 2) T=6s pK, = 4.75
stream titrated by the reagent of the titrating stream is given by 10-pH
- 10(pH-14) -
C1
where c1 is the total ion concentration of the acetic acid in the process stream and a2is the total ion concentration of the sodium hydroxide in the titrating stream. This function is plotted in Figure 14 for both values of the process stream acid concentration. Notice the effect of the buffering in the acidic region when compared to Figures 6 and 7. Also notice that this function is not symmetric about pH 7. The process parameters for all runs of this chemical system are summarized in Table 111. The conduct of each run is the same as was detailed for the HC1-NaOH system. Again, both step increases and step decreases in process stream acid concentration are studied. However, since the titration curve is not symmetric about 7, it would be expected that the nature of the stepincrease responses would be different from that of the stepdecreme responses. The only information encoded in the controller is the initial T(pH) curve of the system. Discussion of Results. Results of experimental runs for this system with both closed-loop poles set equal and placed at 0.6, 0.7, 0.8, and 0.9 are available in Wright (1990). The results of these runs show the classic performance/robustness tradeoff. For the sake of brevity, only the results with closed-loop poles at 0.7, which gave the best response of the four pole locations tried, will be shown here. The response to a tripling of the process stream acid concentration is shown in Figures 15-17. Figure 15 shows the pH response, Figure 16 the response of the strong acid equivalent, and Figure 17 the corresponding titrating stream flow rate. The response obtained when the process stream acid concentration goes from 0.03 to 0.01 N is likewise shown in Figures 18-20. These two runs also show the effect of the asymmetry of the titration curve. Due to the buffering in the acidic region, tripling the process stream acid concentration has
Figure 16. Response of strong acid equivalent to a tripling of inlet acid concentration in the HCl-NaOH system, with z-domain poles at 0.7.
20
0: 0
I
200
400
600
000
-1
1000
Time (s) Figure 17. Titrating stream flow rate after a tripling of inlet acid concentration in the CH,COOH-NaOH system,with z-domain polea at 0.7.
a much smaller effect on pH than reducing the process stream acid concentration to one-third of its original value. Thus, a small deviation in the acidic region requires a much larger change in the titrating stream flow rate than the same deviation in the basic region. It is this buffering
Ind. Eng. Chem. Res., Vol. 30,No. 11, 1991 2443
QoQ
'"I
1 2
O! 0
I
I
200
400
I
600
800
I
1000
Tme (s) Figure 18. Response of pH when the inlet acid concentration of the CH,COOH-NaOH system is reduced to one-third ita initial value, with z-domain poles at 0.7.
Figure 20. Titrating stream flow rate when the inlet acid concentration of the CH3COOH-NaOH system is reduced to one-third ita initial value, with t-domain poles at 0.7.
information other than a nominal process stream titration curve. The results for both the HCl-NaOH and CH3COOH-NaOH systems show that the proposed control method can reject disturbances in the presence of model uncertainty. Acknowledgment Financial support from The Dow Chemical Company is gratefully acknowledged.
-8.0
0
200
400
600
800
1000
T i e (s)
Figure 19. Response of strong acid equivalent when the inlet acid concentration of the CH,COOH-NaOH system is reduced to onethird ita initial value with z-domain poles at 0.7.
or, more precisely, sudden changes in the amount of buffering that have traditionally caused difficulties for pH controllers. It is interesting to note the differences in the responses of this chemical system and the HC1-NaOH system. The first noticeable difference is that the CH,COOH-NaOH system does not have the small fluctuations about pH 7. This is due to the buffering of the system, which requires a larger difference in concentrations to signScantly change the value of the pH. For this system, the mixing effects produce only about a 0.05 deviation in pH. Also, note that the length of the runs is shorter. For all values of the poles, the system was able to reject the step process stream acid disturbance in much less time for the CH,COOH-NaOH system than for the HC1-NaOH system. This is also a result of the buffering, which makes this system much less sensitive. The controller, based on a nominal process stream titration curve, thus provides more aggressive control action for the same value of the poles than in the strong acidlstrong base system. 6. Conclusions
The algorithm for pH control based on using the strong acid equivalent has been implemented for a laboratoryscale pH process. The algorithm requires no chemical
Nomenclature A = anion of acid A = term depending on pH in general titration curve equation ai = function of pH that appears as a coefficient of ith ionic total ion concentration ci = total ion concentration of ith species in process stream, g-mol/L F = flow rate of process stream, L/s [H+]= hydrogen ion concentration in effluent stream, g-mol/L K,i = ith dissociation constant of acid Kbr= ith dissociation constant of base K , = proportional controller gain K, = dissociation constant of water, n = number of species P1,P2= t-domain closed-loop poles pH = -log [H+] PKG = - log K, PKb, = - log Kbi t = time, s T = sampling period of the controller T = inverse of standard titration curve u = control variable, flow rate of titrating stream, L/s V = volume of CSTR, L xi = total ion concentration of ith species in effluent stream, g-mol/L Y = strong acid equivalent of a mixture of electrolytes, gmol/L Y' = strong acid equivalent in deviation variable form Greek Symbols = total ion concentration of ith species in titrating stream,
ai
TI
g-mol/L = reset time, s
Subscripts s = steady-state value sp = set point value Registry No. HCI, 7647-01-0; NaOH, 1310-73-2; CH3COOH, 64-19-7.
Ind. Eng. Chem. Res. 1991,30,2444-2449
2444
Literature Cited Buchholt, F.; Kummel, M. Self-Tuning Control of a pH-Neutralization Process: Automatica 1979, 15,665. Girardot, D. M. Control of pH Based on Reaction Invariants. Master's Thesis, University of California a t Santa Barbara, 1989. Gustafsson, T. K.An Experimental Study of a Class of Algorithms for Adaptive pH Control. Chem. Eng. Sci. 1985, 40 ( 5 ) , 827. Gustafsson, T. K.;Waller, K. V. Dynamic Modeling and Reaction Invariant Control of pH. Chem. Eng. Sci. 1983,38 (31, 389. Hall, R. C.; Seborg, D. E. Modelling and Self-Tuning Control of a Multivariable pH Neutralization Process, Part 1: Modelling and Multiloop Control. Proceedings of the American Control Conference, Pittsburgh; 1989; p 1822.
McAvoy, T. J.; Hsu, E.; Lowenthal, S. Dynamics of pH in a Controlled Stirred Tank Reactor. Znd. Eng.Chem. Process Des. Deo. 1972, I I (l),68. Williams, G. L.;Rhinehart, R. R.; Riggs, J. B. In-Line ProcessModel-Based Control of Wastewater pH Using Dual Base Injection. Znd. Eng. Chem. Res. 1990, 29,1254. Wright, R. A. Equivalent Output Formulations of Nonlinear Control Problems. Ph.D. Dissertation, The University of Michigan, 1990. Wright, R. A,; Kravaris, C. Nonlinear Control of pH Processes Using the Strong Acid Equivalent. Ind. Eng. Chem. Res. 1991,30, 1561.
Received for reuiew January 15, 1991 Reuised manuscript receiued June 4, 1991 Accepted June 25, 1991
SEPARATIONS Extraction of Zinc from Sulfate Solutions with Bis(2-ethylhexy1)phosphoric Acid in the Presence of Tri-n-0ctylphosphine Oxide Ruey-Shin Juang* and Yaw-Tsong Chang Department of Chemical Engineering, Yuan-Ze Institute of Technology, Nei-Li, Taoyuan, 32026 Taiwan, ROC
The extraction of zinc from 0.5 M (Na,H,Zn)S04 aqueous solution with bis(2-ethylhexy1)phosphoric acid (D2EHPA, HR) dissolved in kerosene has been studied a t 25 "C. The distribution data have been treated both graphically and numerically. The composition of the extracted species was determined to be ZnR2(HR) and ZnR2(HR)2and the extraction constants of these species were also estimated. Finally, the effect of the presence of tri-n-octylphosphine oxide (TOPO) on the above extraction system was quantitatively analyzed by considering the greater interactions between D2EHPA and TOPO molecules in the organic phase. Introduction Bis(2-ethylhexy1)phosphoricacid (abbreviated as D2EHPA or simply HR) has been shown to be an effective extractant in the hydrometallurgical processes for the separation and purification of a number of metals. It is able to extract the first-row transition metals such as copper, cobalt, nickel, and zinc, as well as uranium and rare earths in the familiar nuclear fuel processing, in a wide range of operating conditions (Kimura, 1960; Baes, 1962; Sat0 et al., 1978; Johnston, 1988). In metal extraction systems tri-n-octylphosphine oxide (TOPO) is sometimes intentionally added as a phase modifier in order to overcome the third-phase formation or to prevent emulsion (Ritcey and Ashbrook, 1984). In combination with DSEHPA, it has well-known synergistic effects on the extraction of UOZ2+and several other rareearth metals (Rublev, 1983). Papers that examine the effect of TOPO on the extraction of the first-row transition metals with acidic organophosphorus extractants has seldom been seen. Sabot and Bauer (1979) studied the extraction of Ni and Co(I1) from perchlorate medium with a kerosene solution of bis(2-ethylhexy1)dithiophosphoric acid and TOPO. They found that Co(I1) extraction increases by increasing the *To whom all correspondence should be addressed.
concentration of TOPO, whereas Ni extraction is practically unaffected but a weak decrease in fact is observed. Paatero et al. (1990) studied the extraction of Cu(I1) from perchlorate medium with a chloroform solution of TOPO and bis(2,4,4-trimethylpentyl)phosphinic acid (BTMPPA or HA, the main component of the commercial extractant Cyanex 272, American Cyanamid Co.). They found that the presence of TOPO slightly decreases the extractability than with BTMPPA only. Danesi et al. (1984) observed that the as-received Cyanex 272 extracts more Ni than BTMPPA since Cyanex 272 contains the alkylphosphine oxide impurities with branch alkyl chains. This is a general agreement that Ni is extracted as an octahedral complex where the two HA2- bidentate anions occupy four coordination sites and the two sites are occupied by water molecules and/or undissociated dimer (HA),. Hence, the phosphine oxide molecules would displace the hydration water in the complex, making the complex more lipophilic. However, these authors did not give a quantitative explanation about this extraction behavior. The effect of TOPO on the extraction of zinc from sulfate solutions with D2EHPA has not yet been fully investigated. In this paper the equilibrium behavior of the extraction of zinc from sulfate solutions with DPEHPA alone and a mixture of DPEHPA-TOP0 dissolved in kerosene were studied, respectively.
0888-5885f 91f 2630-2444$02.50f 0 0 1991 American Chemical Society
