Determination of the effective diffusion coefficient for gold(III) on a macroporous resin XAD-2 impregnated with triisobutyl phosphine sulfide

Reactive & Functional Polymers 41 (1999) 27–35 www.elsevier.com / locate / react

Determination of the effective diffusion coefficient for gold(III) on a macroporous resin XAD-2 impregnated with triisobutyl phosphine sulfide J. Serarols a , J. Poch a , M.F. Llop b , I. Villaescusa b , * a

` ` ` ´ Santalo´ , s /n, i Matematica Aplicada, Universitat de Girona, Escola Politecnica Superior, Av. Lluıs Department d’ Informatica 17003 Girona, Spain b ´ ´ ` ´ Santalo´ , s /n, 17003 Girona, Spain Department dEnginyeria Quımica , Universitat de Girona, Escola Politecnica Superior, Av. Lluıs Received 13 July 1998; accepted 11 November 1998

Abstract In this work the experimental and numerical techniques employed to estimate the diffusion coefficient of gold(III) in a macroporous particle of resin XAD-2 impregnated with triisobutyl phosphine sulfide (TIBPS) have been described. Batch and column experiments were performed in order to get the necessary experimental results to determine the effective diffusion coefficient, De . In the studied initial metal concentration range (39.3–196 mg / dm 3 ), De was found to increase with increasing the initial feed concentration from 1.28 3 10 28 to 6.40 3 10 28 m 2 / h.  1999 Elsevier Science B.V. All rights reserved. Keywords: Gold(III) extraction; Amberlite XAD-2 resin; Solvent impregnated resin; Effective diffusion coefficient; Mathematical model

1. Introduction In recent years increasing interest in environment protection, economy of energy, as well as process optimisation and the continuous progress in fundamental chemistry have produced an important development of new chemical separation techniques. The need of more specific systems for dilute metal recovery from both ecological and economic aspects has led to the development of the synthesis of new ex*Corresponding author. Tel.: 134-72-418-416; fax: 134-72418-399. E-mail address: [email protected] (I. Villaescusa)

tractants, exchangers and adsorbents. These products have improved significantly the selectivity and efficiency of a large number of separation process techniques such as extraction with solvents, supported liquid membranes, precipitation, etc. Among these new products, Solvent Impregnated Resins (SIR) have been postulated as a new technological alternative for problems associated with metal separation and recovery. The use of polymeric materials impregnated with selective extraction reagents offers many advantages over the use of liquid– liquid extraction, due to characteristics of the solid phase [1]. SIR were introduced in hydrometallurgical

1381-5148 / 99 / $ – see front matter  1999 Elsevier Science B.V. All rights reserved. PII: S1381-5148( 99 )00020-6

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J. Serarols et al. / Reactive & Functional Polymers 41 (1999) 27 – 35

applications by Warshawsky [2,3]. Some authors have studied the recovery of different metals using Amberlite XAD-2 resins impregnated with different commercial extractants [4– 6]. Recently, the extraction of Au(III) with triisobutyl phosphine sulfide (TIBPS) impregnated in Amberlite XAD-2 resin has been carried out [7]. The application of these systems to the industrial scale requires a suitable technology for its optimal use. Due to the good contact of liquid–solid and the high mass transfer coefficients attained with the fluidised bed, this technology has been applied for Au(III) selective recovery from diluted aqueous solutions with the impregnated resin TIBPS / XAD-2 [8,9]. Gold extraction process with the extractant TIBPS seems to occur via a solvation mechanism, where AuCl 3 ? 2TIBPS is postulated to be the predominant species [10]. Hence, the extraction process with the impregnated resins TIBPS / XAD-2 can be considered similar to the adsorption process of a solute on an adsorbent. This kind of process has already been studied both in fixed and fluidised beds [11,12]. Nevertheless, for predicting an extraction process, it is necessary to develop a good mathematical model that relates the different parameters and variables of the system. A mathematical model has to describe the mass transfer steps that take place in a process: external, at the surface and internal mass transfer. The exact mechanisms of intraparticle transport are unknown a priori for most adsorption processes. This usually causes difficulties in finding the correct model for design and scale up. The relative importance of pore and surface diffusion in adsorption mass transport is dependent upon the adsorbate–adsorbent system used and must be evaluated experimentally. To simplify the determination of adsorption diffusivity, a common approach is to combine pore and surface diffusivity into a single intraparticle diffusivity, the apparent or effective diffusivity. In this work, we have determined the effective diffusion coefficient for gold(III) inside the solid particle of XAD-2 Amberlite resin im-

pregnated with triisobutyl phosphine sulfide (TIBPS) for different initial gold concentrations in the aqueous solution (39.3–196 mg / dm 3 ).

2. Theoretical

2.1. The homogeneous solid diffusion model The model used to describe the diffusion is the homogeneous solid diffusion model (HSDM) [13]. Several authors have used this model to describe adsorption processes [14,15]. The governing equations of the present model have been derived based on the following assumptions. 1. The resin is of uniform particle size. The resin beads have been selected with a narrow mesh size range. The particles are also assumed to be spherical in shape. The diameter of the particles is the arithmetic mean of the sizes of the sieves passing and retaining the particles. 2. The cross-sectional area of the adsorber is constant. 3. The entire adsorption system is at a uniform concentration at any given time. 4. The adsorption process is sufficiently rapid so that a local equilibrium is established at the particle surface between the gold concentration in the solution and the adsorbed phase. 5. The mass transfer resistance in the laminar boundary layer surrounding an individual adsorbent particle is negligible. To ascertain this, a high flow rate was used. It should be noted that the diffusion coefficient determined in this manner is the effective value that implicitly incorporates the effects of deviations from the idealised transport model. Notably, the model does not take into account the non-uniform intraparticle pore structure, molecular diffusion in the liquid-filled pores and steric interactions. Therefore, the parameter

J. Serarols et al. / Reactive & Functional Polymers 41 (1999) 27 – 35

value extracted is referred to as the effective diffusivity. The unsteady state material balance equation around a spherical shell of a polymer particle, at position r, can then be written as:

S

≠q 1 ≠ ≠q ] 5 ]2 ] De r 2 ] ≠t r ≠r ≠r

D

(1)

D #1

(5)

where A, B, D are experimental parameters. In order to choose the better isotherm model the experimental data must be correlated.

2.3. Algorithm for estimating effective diffusivity, De

The initial and boundary conditions are: q(r, 0) 5 q0 0 , r , R ≠q r 5 0, ] (0, t) 5 0 t . 0 ≠r r 5 R, q(R, t) 5 f(C, t) t . 0

AC q 5 ]]] 1 1 BC D

29

t 5 0,

(2)

The function f(C, t) is the isotherm equation which relates the adsorbate concentration at the particle surface to the liquid phase concentration. The equation can be of any general form. The first step to determine De is to obtain the adsorption isotherm equation that fits our experimental data.

2.2. Isotherm equations In the literature there are different empirical expressions to define the isotherm equation [16]. The representation of the adsorption isotherm can be based on models with two, three or more parameters [11]. Some of them are the following: Freundlich and Heller Isotherm q 5 KC

1 /B

(3)

where q is adsorbate concentration in the particle, C concentration in liquid phase, K, B are empirical constants dependent on the nature of solid and adsorbate. Langmuir Isotherm bC q 5 q0 ]]] 1 1 bC

(4)

where q0 and b are empirical constants. They are related to the maximum capacity of adsorption and the speed of adsorption, respectively. Redlich and Peterson Isotherm

Mass balance requires that the decrease of gold concentration in the solution is equal to the increase of gold adsorbed on the resin. The overall material balance for the closed adsorption system can be written as: R

3W V [C0 2 C(t)] 5 ] R3

E (q(r, t) 2 q )r dr 2

0

(6)

0 3

where V is the volume of gold solution (dm ), C0 is the initial concentration (mg Au(III) / dm 3 ), C(t) is the concentration measured after a given time t (mg Au(III) / dm 3 ), W is the amount of resin in the column (g), R is the average radius of the beads (m), q is the adsorbed concentration (mg Au(III) / g XAD-2) and q0 is the adsorbed concentration at t50 (mg Au(III) / g XAD-2, in this work q0 50). Therefore, the sum of square of errors (SSE) i.e., the difference between the adsorbate gain on the resin and adsorbate loss from the solution, at a particular value De is:

O fV(C 2 C(t )) N

SSE 5

0

i

i 51

R

3W 2] R3

E (q(r, t ) 2 q )r dr 4 2

i

0

2

(7)

0

where i51, 2, 3, . . . , N are the N sampling points, C(t i ) is the concentration measured at the sampling point i and q(r, t i ) is calculated with the diffusion model. The optimum value of De has been estimated by minimising SSE.

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J. Serarols et al. / Reactive & Functional Polymers 41 (1999) 27 – 35

3. Experimental

3.1. Reagents and solutions of Au( III) Stock solutions of Au(III) were prepared from solid HAuCl 4 ?3H 2 O (Aldrich) in a 0.5 mol / dm 3 NaCl solution. The pH in all gold solutions was pH 2. NaCl and HCl (Merck A.R.) were used to adjust the ionic strength and the pH of the gold solutions. Triisobutyl phosphine sulfide (TIBPS) provided as Cyanex 471 by American Cyanamide Co. was purified by recrystallisation from ethanol–water mixture. Ethanol (Merck A.R.) was used without further purification. Amberlite XAD-2 purchased from Rohm and Haas was washed as described elsewhere [7]. The characteristic parameters of the resin can be seen in Table 1. An organic solution of TIBPS of 1300 mg / dm 3 in 66% ethanol–water mixture was used as impregnation solution following the same procedure used in the same work mentioned above. After the impregnation the extractant content into the resin is 16 mg TIBPS / g XAD-2.

3.2. Experimental procedure 3.2.1. Batch experiments Amounts of 0.2 g of impregnated resin were contacted with 20 cm 3 of Au(III) solutions of different concentration (36.6–185.0 mg / dm 3 ) until the equilibrium was reached. In a previous work, the equilibrium time was found to be 1 h. After filtration of the resin the gold concentration in the remaining aqueous solution was determined by atomic absorption spectrometry. Table 1 Characteristic parameters of the resin Property

Value

Particle diameter Sphericity Surface area Pore diameter Particle porosity Particle density

630–890310 26 m 0.7 330 m 2 / g 90310 210 m 0.41 1020 kg / m 3

For each different gold concentration a total of eight contacts were done. In some experiments the gold adsorbed in the resin was stripped with a 1.0 mol / dm 3 thiocyanate solution in order to verify the mass balance. The results were used to obtain the isotherm. All the experiments were performed at room temperature.

3.2.2. Column experiments The column consisted of a 10-cm glass tube with an internal diameter of 4 mm. For each experiment 0.2 g of impregnated resin was introduced into the column. Two pieces of glasswool were used to keep the resin packed. A volume of 100 cm 3 of gold(III) solution of different initial gold concentration (39.3–196.0 mg / dm 3 ) contained in a recipient continuously agitated was passed through the column at a flow rate of 2 cm 3 / min. The exit gold solution was recycled back to the column until the reservoir gold concentration became almost constant. Samples of 0.5–2.0 cm 3 of the reservoir solution were taken every 5 min and the gold concentration was analysed by atomic absorption spectrometry. The amount of gold adsorbed on the resin was determined by mass balance. All the experiments were performed at room temperature. The experimental set up is shown in Fig. 1.

4. Results and discussion In Table 2, the constants (A, B, D) and the correlation coefficients (R 2 ) corresponding to the three isotherm models used in this work are shown. It can be observed that the Langmuir isotherm fits better the experimental data. In addition, from the theoretical point of view the concentration q cannot increase indefinitely because the resin has a saturation point and this fact is taken into account in the Langmuir isotherm equation. It must be pointed out that it is of great importance for De determination to get a good equilibrium equation. As this equation is a boundary condition in the diffusion

J. Serarols et al. / Reactive & Functional Polymers 41 (1999) 27 – 35

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Fig. 1. Experimental set-up.

Table 2 Fitting results of the isotherm equation

Equilibrium equation R2 Constants A B D

Redlich

Freundlich

Langmuir

AC q 5 ]] 1 1 BC D

q 5 AC 1 / B

AC q 5 ]] 1 1 BC

0.8712 11.8997 5.0644 0.5640

0.8415 5.8849 4.3975 –

0.9377 0.7298 0.0287 –

model, it has a determinant influence on De calculation. In Fig. 2 the gold concentration in the liquid phase versus the gold concentration on the impregnated resin found after the different contacts with the studied initial gold concentrations are plotted. When identical values were obtained indicating that the resin has reached saturation these values were not taken into

Fig. 2. Isotherm data for different initial concentration of gold (C0 ) and Langmuir fit.

J. Serarols et al. / Reactive & Functional Polymers 41 (1999) 27 – 35

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account. The best fit by the Langmuir isotherm that is also plotted in Fig. 2 is represented by 0.7298C q 5 ]]]] 1 1 0.0287C In Fig. 3 the experimental versus the fitted values of q are presented. As can be seen, the experimental data fit quite well a line with slope near unity. That confirms the fitness of the isotherm equation. The optimum value of De has been estimated by the generalised reduced gradient method (GRG) [17]. For this, it is necessary to calculate first, q(r, t) by using the model of diffusion (Eqs. (1) and (2)). Afterwards, we must calculate the integral of the right hand side of Eq. (6) in order to calculate the total adsorbate on the resin. Finally, the calculation of SSE (Eq. (7)) i.e. sum of square differences between the adsorbate loss from the solution (experimental values) and the adsorbate gain on the resin (calculated values) must be done.

Eq. (1) has been integrated by using the method of lines with cubic Hermite polynomials by calling the IMSL subroutine DPDES [18]. The total loading on the resin has been calculated by integrating the right hand side of Eq. (6), by quadrature Simpson method [19]. The De for the five different gold initial concentrations used in the column experiments were calculated. The results of the calculations are given in Table 3. These results show that the effective diffusion coefficient is a function of the solution concentration. The diffusivity in-

Table 3 Effective diffusion coefficient De C0 (mg / dm 3 )

De (10 28 m 2 / h)

39.3 78.6 118.0 157.0 196.0

1.2837 2.9922 4.2028 5.6070 6.4022

Fig. 3. Relation between experimental and simulated values of equilibrium adsorbed quantity (q).

J. Serarols et al. / Reactive & Functional Polymers 41 (1999) 27 – 35

creases when increasing the initial gold concentration. Other authors who studied different adsorption systems [14,16] found the same effect. With the diffusion coefficient calculated, it is possible now, using the differential Eq. (1) that describes the diffusion, to calculate the adsorbed concentration in the resin. In Fig. 4, q has been plotted as a function of the time t. The full line represents the total adsorbate concentration of

33

Au(III) in the XAD-2 estimated by diffusion model. The ticks represent the total adsorbate concentration of Au(III) in the XAD-2 of experimental results. In Fig. 4, the experimental and calculated q corresponding to the initial gold concentrations of 39.3 and 78.6 mg / dm 3 have been plotted as a function of time t. In the same figure, the tridimensional plots show the evolution of gold adsorption from the surface to the inside of the

Fig. 4. The surface represents the adsorbate concentration of Au 31 in the XAD-2 at any place (r) at any time (t). The full line represents the total adsorbate concentration of Au(III) in the XAD-2 estimated by diffusion model. The ticks represent the total adsorbate concentration of Au(III) in the XAD-2 of experimental results. (a) C0 539.3 mg / dm 3 . (b) C0 578.6 mg / dm 3 .

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J. Serarols et al. / Reactive & Functional Polymers 41 (1999) 27 – 35

particle. As can be seen, the model describes the gold uptake in the resin at any time and particle radius. If we compare the experimental and the estimated by the model values, it can be observed that there exists a deviation in the edges. The same effect was found for the other initial gold concentrations studied. This is probably due to the fact that we assumed De is constant during the process without taking into account the influence on diffusivity due to the loss of gold in solution and the increase of gold adsorbed on the SIR. This fact could be corrected by considering the diffusion coefficient variable in function of q [14] or studying separately the surface and pore diffusivity [12,15]. Nevertheless, both options would give an additional difficulty to the diffusion equation resolution and possibly the benefits obtained would not be in accordance with the difficulty added. The significance of this study is that the results obtained in this work can be applied in future studies to develop models capable of accurately describing the gold adsorption on the XAD-2 resin impregnated with TIBPS for both fixed and fluidised bed processes.

Notation A,B,D,K C C0 De q q0 r R t V W

Isotherm parameters Gold concentration in liquid phase (mg Au(III) / dm 3 ) Initial concentration in liquid phase (mg Au(III) / dm 3 ) Effective diffusion coefficient (m 2 / s) Gold concentration in the particle (mg Au(III) / g) Initial gold concentration in solid phase (mg Au(III) / g) Radial position inside particles (m) Particle radius (m) Time (s) Sample volume (dm 3 ) Resin weight (g)

Acknowledgements The assistance of Mr. Lieven Dieussaert with the laboratory work is gratefully acknowledged.

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