The dynamic simulation of carbon-in-pulp systems: A review of recent developments

Minerals Engineering, Vol. 4, Nos 7-11, pp. 667-681, 1991 Printed in Great Britain

0892-6875/91 $3.00 + 000 © 1991 Pergamon Press pie

THE DYNAMIC SIMULATION OF CARBON-IN-PULP SYSTEMS: A REVIEW OF RECENT DEVELOPMENTS J.S.J. VAN DEVENTER and V.E. ROSS" Department of Metallurgical Engineering, University of Stellenbosch, Stellenbosch 7600, South Africa * Present address: De Beers Diamond Research Laboratories, PO Box 916, Johannesburg 2000, South Africa

ABSTRACT Despite major advances in the practical use of the carbon-in-pulp (CIP) process, the dynamics of this process are still poorly understood by operating staff. Moreover, the many features of existing models for the CIP process are frequently not appreciated by production personnel. It is the aim of this paper to review and compare existing empirical and fundamental models, and to identify areas for further development work. Empirical methods, such as the classic and widely used Fleming & Nicol model, are conceptually simple but rather limited in their applicability. Also, it is sometimes impossible to attach any practical significance to the values of their parameters. On the other hand, the more rigorous fundamental models are computationally more complex, but more generally based. Most of these models involve the simultaneous solution of initial value or boundary value problems. In pulps with a low concentration of gold or silver, a simple film diffusion model may be adequate. However, if the process is characterised by incomplete leaching, severe preg-robbing, fouling of the carbon by organics and inorganic precipitates, competitive adsorption by base metal cyanides, or high loadings of gold or silver, then a more complex model may be required. This paper explains how these phenomena could be accounted for in material balance equations. Relatively simple models, however, could be used to study the interaction between the leaching, adsorption, elution and regeneration sections with a view to determine optimal operating conditions. As in the case of adsorption models, much scope still exists for R&D on elution and the development of simulation models for desorption. The transport phenomena associated with the pre-treatment step in AARL elution deserves special attention in this regard. Furthermore, very little work has been published on the modelling of the regeneration step in a CIP circuit. With the development of knowledge-based system (KBS) modelling, new avenues have been opened to the simulation o / c o m p l e x adsorption processes. Keywords Activated carbon, adsorption, elution, regeneration, modelling, knowledgebased system. INTRODUCTION

During the last 15 years, much progress has been made on carbon-in-pulp (CIP) technology for the extraction of gold in South Africa, the U.S.A., Canada and Australia. Nevertheless, the fundamental understanding of factors influencing both the adsorption and elution processes has lagged far behind practical developments. Most research in this area has 667

J. S. J. VAN DEVENTER and V. E. Ross

668

focused on the behaviour of gold cyanide [1,2], while very little attention has been given to fundamentals affecting the adsorption of other metal cyanides and species fouling the carbon [3,4]. Owing to this lack of basic understanding, many simulation procedures used by production staff and design teams for CIP adsorption and elution plants have been based on empirical or semi-empirical models. Despite the wide=spread application of the CIP process, the dynamics of such plants are still poorly understood by operating staff. Moreover, the many features of existing models for the CIP process and the advantages associated with the use of simulation packages are frequently not appreciated by production personnel. It is the objective of this paper to review and compare existing empirical and fundamental models, and to identify areas for further development work. The discussion will not focus on the mathematical characteristics of the models, but rather on the practical implications of applying such models. In this way it is hoped to bring dynamic simulation models to the attention of more practising engineers. The paper will firstly review the various types of existing kinetic models. Process related factors to be considered when formulating a mathematical model will be discussed with reference to the adsorption of gold onto activated carbon. Furthermore, non-ideal behaviour in CIP plants such as incomplete leaching, competitive adsorption, preg=robbing, fouling or inadequate mixing will be explored in modelling terms. The state of the art in the modelling of elution and regeneration processes will also be reviewed. Finally, it will be explained how a knowledge=based approach could be used to simulate the dynamics of CIP plants. The methodology of parameter estimation will be reviewed for all kinetic models. It should be emphasised that the focus of this paper is not on the numerous physico=chemical phenomena affecting the CIP process, but rather on the methodology employed to incorporate such phenomena in simulation models. KINETIC MODELS FOR ADSORPTION During the early stages of model development for the CIP process most authors [5=9 ] proposed semi-empirical models which did not have any conceptual basis, but which were found to simulate data reasonably under special circumstances. For example, Nicol et al. [8] proposed that: dq/dt = knC

(1)

Dixon et al. [7] and Menne [5] suggested a rate equation that leads to a Langmuir isotherm: dq/dt = kaC(q + - q) - kdq

(2)

Such a rate expression based on the Langmuir isotherm, as used by Carrier et al. [10], has the limitation that other forms of isotherms which may be dictated by the pulp-carbon system, cannot be used. Several other authors [11-14] have suggested the use of a simple film transfer mechanism due to its linear characteristics and ease of inclusion in a system of equations: - d C / d t = Apkf(C - Cs)

(3)

These more empirical equations are usually applicable under special process conditions only [15,16]. Both the kinetic and equilibrium behaviour of the activated carbon should be characterised mathematically if predictions are to be made of adsorption behaviour. In most CIP plants where the concentration of gold in solution is low, and where low loadings on the carbon are achieved, the rate of adsorption is controlled by film diffusion, especially in the last adsorption stages. However, as loadings increased in the initial stages, or in some calcine treatment plants where the concentration in solution and the loadings on the carbon are high, intraparticle diffusion becomes rate=controlling. Models incorporating diffusion in the pores are normally more complex and require more computer time to solve than

Dynamicsof carbon-in-pulpsystems

669

simpler models based only on film diffusion. With the development of improved and faster microcomputers it has become possible to solve the more complex intraparticle models with relative ease [17-20]. In the case of the more rigorous models, it is essential to consider the rate processes governing the adsorption of metal cyanides onto activated carbon, namely:

(1) (2) (3) (4) (5)

Film resistance in the layer of liquid surrounding the particle. Transformation from the dissolved to the adsorbed state. Liquid phase diffusion from the dissolved to the adsorbed state. Surface diffusion along the pore walls. Diffusion from the larger pores into smaller pores.

The phenomenon of surface diffusion is usually modelled by assuming that the carbon particles can be treated as equivalent spheres: aqlat = D(azqlar 2) + (2DIr)(aq/ar)

(4)

It can also be assumed that no accumulation occurs at the external surface of the adsorbent, so that the boundary condition becomes: (OqlOr)lr= R =

(kf/aD)(C-Cs)

(5)

Van Deventer [18] explained how partial differential equations such as Eq. (4) could be transformed into an ordinary differential equation by use of a quadratic driving force expression and a quadratic transformation of the loading q. These model equations could then be solved by use of Runge-Kutta and backwards-difference methods. In an earlier paper [21 ] it was explained how the parameters of such a more fundamental model could be used to evaluate activated carbons. Unfortunately, analytic solutions of most of these systems are not straightforward, if not impossible. Whereas most models assume that the adsorption reaction itself is instantaneous and does not control the rate of adsorption, Brinkmann and King [22] assumed a combined pore diffusion and reaction mechanism, and derived an analytical solution. It has been shown that, if intraparticle diffusion is to be considered, extruded carbon or carbon which has been regenerated repeatedly, can be modelled adequately by ignoring diffusion in the micropores. This simplifies the estimation of parameters, but does not give a meaningful reduction in the computational time. The main problem with the inclusion of intraparticle diffusion is the calculation of the concentration and loading at the liquidcarbon interface. With all present models this is necessary, except when the effect of either film transfer or intraparticle diffusion is neglected. A procedure which will be more efficient computationally will be the use of only film diffusion at low concentrations and loadings, and only intraparticle diffusion at higher loadings and concentrations. It may take months for the carbon to reach a true equilibrium when in contact with a solution [15]. While this is impractical in experimental work a pseudo-equilibrium may be used, as long as the loadings attained in tests are higher than those in the plant to be simulated. At low concentrations of gold in solution the initial part of a loading isotherm appears to be linear, which simplifies calculations. However, at higher loadings, and in some ores at low loadings this may not be the case, so that empirical forms such as the Freundlich or Langmuir isotherms should be used. SYSTEMS OF EQUATIONS An equation for leaching has to be included in a CIL model. Much more work needs to be done before a leaching model could be formulated to account for changes in pulp density, mixing conditions and the chemical conditions of the pulp. Todtenhaupt et al. [23] described the design of agitators for the large ERGO CIL plant in South Africa, and give

670

J . S . J . VAN DEVENTERand V. E. Ross

specific correlations for the suspension of solids and mass transfer. These type of correlations are specific to the mixer-vessel combination, and are difficult to scale-up. Coefficients of film diffusion measured in small scale batch tests cannot be used as such in large-scale plants. Appropriate correlations of the mass transfer, given as the Sherwood number, in terms of a dimensionless function of the Schmidt and Reynolds numbers, should be incorporated in the design algorithm. As described by Van Deventer [4,16,19] and Stange et al. [13,24], the carbon in each stage of a CIP/CIL plant will exhibit a distribution of ages and therefore a distribution of loading. This will be caused by the transfer of carbon, during which a fraction of the carbon will remain in the tank while new carbon with a lower loading will be added. For the purpose of calculation this distribution could be discretised, so that mass balance equations for the loading onto the carbon should be written for each loading fraction. However, Van Deventer [4,19] showed that the modelling of a cascade was fairly insensitive to the number of discrete fractions selected. The liquid phase material balance for gold in stage i of a CIP cascade is written as [19]: L

eV(dCi/dt) = EQ(Ci-1-Ci) - (6kf/dpa) i~ 1(C i -C s i j)wi j

(6)

In this equation the continuous distribution of loading on the carbon in a stage was discretised into a total of L loading fractions, so that the accumulation term for each individual fraction j should be considered. If an adsorption column is simulated the mass balance equation for the liquid phase should be written for a differential element, and this equation can then be integrated simultaneously with the equations for diffusion into the carbon [20,25]. If the liquid is well distributed and plug flow can be assumed, radial dispersion can be neglected. It is also possible to divide the column theoretically into a number of well-mixed reactors and then to use the same procedure described for a cascade of perfectly mixed stages. The continuity equation for adsorption at any position in a column is: Q(0C/0x) + eA(0C/0t) + {6kf(1-~)A}(C-Cs)/d p = 0

(7)

Van Deventer and Jansen van Rensburg [20] applied this equation together with a bidisperse surface diffusion model to simulate the dynamic behaviour of a countercurrent moving bed adsorption column. RESIDENCE TIME D I S T R I B U T I O N S The majority of models for the simulation of CIP/CIL circuits have all assumed perfect mixing in the stages. This is not necessarily true, as bypassing, leakages and areas of dead volume may be encountered. The efficiency of mixing could change as the nature of the ore and thus the rheology, changes and this will influence the residence time distribution in the plant. Although measurements of the flow in a stage could be made to assess the efficiency of mixing, it will be difficult to relate this to the residence time distribution. A better diagnostic tool to assess mixing in the tank is to inject tracers such as radioactive isotopes or lithium chloride in the feed to a stage, and to measure the outflow concentration of the tracer with time. The problem in CIP circuits is that standard tracers such as fluorescine cannot be used as this will also be adsorbed by the activated carbon. An increasing number of tanks enhances the probability that a particle will spend sufficient time in a tank. The positioning of the inlet and outlet, together with the type of agitation, will determine whether a particle will find it easy to short-circuit. If settling of solids occurs, the effective volume of the tank will decrease, and so the average time of reaction. However, a dead volume could be encountered in a tank without settling if two regimes of circulation occur. Tests on leaching pachucas on the Witwatersrand in South Africa

Dynamics of carbon-in-pulp systems

671

indicated that the effective volume was close to 90% [26]. It is advised that the mixing efficiency of a plant should be assessed by tracer tests when changes are made to the reactor configuration, or when a drastic change occurs in the nature of the ore. A simple and industrially relevant model of an agitated stage is one in which fluid circulates between an ideally mixed reactor and a stagnant volume. The real mixed stage could also be divided theoretically into two smaller ideally mixed reactors in parallel. In the simulation of adsorption and leaching behaviour in a CIP/CIL plant each of these theoretical stages can then be modelled by conventional methods. The philosophy is therefore to divide the operation of the real plant into sub-sets of simple theoretical reactors, to model each of these separately, and then to reconstitute the different models. ESTIMATION OF PARAMETERS The more complex a model becomes, the more parameters are usually involved, and the more difficult it becomes to estimate parameters independently. If the different subprocesses are independent, it is usually more simple to estimate kinetic and equilibrium parameters individually. In many cases, however, the parameters have to be estimated simultaneously, so that a good regression programme should be used. In any case, a valid model will be of such nature that each of the parameters will govern a specific regime, so that they will be relatively insensitive in other areas. Equilibrium parameters can be estimated from the end points of a well-planned series of batch experiments [4,16]. Film transfer coefficients can be estimated from the initial data in a batch experiment, and then scaled-up by use of appropriate correlations, or measured from the unsteady-state data measured in a real CIP plant after transfer of carbon. Carrier et al. [10] used this technique for the estimation of all their model parameters, which is perhaps not that accurate because the loadings after transfer are the furthest removed from equilibrium. Jansen van Rensburg and Van Deventer [25] discussed the estimation of parameters in the case of adsorption in columns. It is important that the chemical conditions in the pulp, as well as the pre-treatment of carbon, should be the same in both the small-scale tests and the large-scale plant to be simulated. It has been argued before that small-scale continuous tests are necessary in order to obtain a quantitative estimation of the fouling behaviour of the carbon. If a wellplanned series of batch tests are run for sufficiently long times, and the appropriate poisoned pulp is used, then sufficiently accurate predictions of the continuous operation could be made. It is strongly recommended that such batch tests should be run in parallel with the large-scale plant to provide an early warning of changes in the adsorption behaviour of the pulp or the carbon. Little work has been done on the estimation of parameters for a leaching model to be used in conjunction with a CIP model. If some leaching is expected to take place during adsorption, then the leaching behaviour of the ore should be determined in a separate batch experiment using the same chemical conditions as during adsorption. OPERATING CONSIDERATIONS The optimal operating strategy for a CIP/CIL plant will depend very much on the dynamic interaction between the carbon and pulp. Most published models have been solved at steady state conditions for defining the optimal operating strategy [10,14,16,27,28]. Owing to frequent disruptions, emergency maintenance and changes in the feed rate and characteristics of the pulp from the mills or thickener, few plants operate at ideal steady state conditions. Therefore, it is not accurate to prescribe operating strategies which are optimal for all plants. Furthermore, it is difficult to generalise about the dynamic influence of preg-robbing or fouling agents on optimal operating strategies. The overall optimal operating and design philosophy will be determined by economic as well as technical factors.

672

J . S . J . VAN DEVENTERand V. E. Ross

Bailey [2] discussed two methods of periodic transfer of carbon: (1) Carbon is transferred from the first tank and then sequentially down the bank until regenerated carbon is added to the last tank (sequential d o w n - b a n k transfer). (2) Regenerated carbon is added to the last tank and then carbon is transferred sequentially upstream until loaded carbon is transferred from the head tank (sequential u p - b a n k transfer). Method (I) temporarily denudes one stage of carbon, which creates long transfer times, effectively reduces the number of stages available for gold recovery, and results in significant loss of gold, which increases significantly if the activity of the carbon is reduced. Method (2) temporarily doubles the carbon which returns to normal as the batch is transferred. This creates more mixing of the carbon and a flatter loading profile, but according to Bailey [2] this is preferable to an increased loss in the tailings. Hence, method (2) is preferred to method (1). The next question is whether it is better to use periodic or continuous transfer of carbon. Nicol et al. [27] showed that for a system where film diffusion is controlling at low loadings, frequent small transfers are not as efficient as one single transfer. This may be explained in terms of the higher concentration gradient in solution for an increase in the fraction of carbon transferred. On the other hand, Van Deventer [4] showed that under conditions of intraparticle diffusion control, fractional transfer of carbon did not exert any significant influence. According to Stange et al. [28], a carousel type of operation, in which the pulp feed to each tank is rotated, appeared to be preferable to any other method of carbon transfer. Although it is difficult to monitor and control the concentration of carbon in the different CIP stages, the on-line instrument developed by Mintek [29] will be most useful in this regard. As will be shown in the next section, the distribution of carbon across a CIP/CIL cascade could affect the efficiency of gold extraction. Simulators such as those by Nicol et al. [27], Bailey [2], Carrier et al. [10], Stange et al. [28] and Van der Walt [14] could be utilised to determine the economically optimum number of pre-adsorption stages, CIP or CIL stages, concentration of carbon in the cascade, residence time of pulp, and the extent to which gold should be eluted from the loaded carbon. EFFECTS OF L E A C H I N G AND P R E G - R O B B I N G If the leaching of gold ore occurs simultaneously with the adsorption of gold onto carbon, another term has to be added to the material balance equation for the solution phase, and an equation has to be added to describe the material balance of the leaching component in the solid ore phase. Despite the many papers on the chemistry of gold leaching, little is known about the rate controlling phenomena involved in the dissolution of gold from its ores. No fundamental equations exist for simulating the leaching of gold in CIP/CIL. This is the reason why Van der Merwe et al. [30] used a knowledge-based approach to model the leaching of gold and the simultaneous consumption of oxygen and cyanide in batch reactors, cascades of CSTR's and countercurrent columns. Woollacott et al. [12] reviewed the use of various empirical and semi-empirical expressions for the leaching of gold, but used the Mintek expression in a CIP/CIL simulator [27]: - dg/dt

=

kg(g - g®)2

(8)

This expression was also used by Nicol et al. [27] and Van der Walt [14] in the simulation of CIL circuits. Nicol et al. [27] indicated that the optimum distribution of carbon in a CIP plant is an even distribution, i.e. the carbon concentration in the vessels should be the same. The studies by Stange et al. [28] and Van der Walt [14] revealed that, although this may be the case for plants in which no leaching occurs, it is definitely not true for CIL plants. Stange et al. [28] showed that, for a specific case, it was highly advantageous to distribute the carbon so that the stages at the pulp effluent end of a CIL cascade contain more carbon than the stages at the feed end. The phenomenon of preg-robbing has received very little attention from either a modelling or experimental point of view. In fact, many operators of especially CIL plants do not

Dynamics of carbon-in-pulp systems

673

recognise that they have a preg-robbing problem. Johns and Mathews [11] explained an experimental technique whereby the rate of gold adsorption by carbonaceous material in ashed woodchips could be determined. Van der Walt [14] modelled the phenomenon of preg-robbing by ore constituents on the same basis as the adsorption of gold by activated carbon, and used a film transfer mechanism as a first approximation. This means that a second accumulation term should be added to the material balance equation for gold in the solution phase, and the same accumulation term should be added to the material balance equation for gold in the solid ore phase. COMPETITIVE ADSORPTION AND FOULING Organics such as flotation reagents, lubricating oils and kerosine are commonly found in gold plant circuits, and foul the activated carbon. Thermal regeneration selectively removes these organics and recovers most of the original pore structure and activity. According to Bailey [2], special care must be taken on gold plants to avoid the common mine practice of draining oil into ore passes underground or into the process plant. La Brooy et al. [31] provided an excellent review of the effects of a variety of organics on activated carbon, but unfortunately used only an empirical model to interpret their data. The relatively slight deactivation caused by small organic solvent molecules contrasts the significant deactivation caused by larger organic molecules with molecular masses around 150-1000, such as frothers, collectors and natural organics. These organics may effectively block the pores of carbon, while very large molecules like grinding aids and flocculants are probably unable to enter the pores. In most CIP/CIL plants the efficiency of extraction decreases from the last to the first stage as the carbon is poisoned by organic and inorganic species, and as detrimental coatings form on the superficial surface of the carbon. This fouling of carbon is taken into account in existing models by using different kinetic and/or equilibrium parameters in different stages. Ideally, the modelled loading capacity should decrease as the carbon becomes poisoned. Petersen and Van Deventer [32] observed that, at low loadings of organics on the carbon, the reduction in the rate of adsorption of metal cyanides appeared to be a kinetic influence, which could be caused by pore blocking. The decrease in the intraparticle diffusivity was quantified by fitting a dual resistance model to the profiles for the adsorption of gold or silver cyanide. This model was also applied to the simultaneous adsorption of gold or silver cyanide and humic acid. However, at higher loadings on the carbon, a profound effect on the equilibrium loadings of gold and silver cyanide was observed, which indicated a mechanism of poisoning. Base metals such as copper, nickel, cobalt, iron and zinc are often leached in CIP/CIL circuits. While copper and nickel cyanides could load strongly on carbon, cyanide complexes of the other base metals have little effect on the activity of the carbon. When copper is present as the Cu(CN)32" and Cu(CN)43" complexes, it is only weakly adsorbed on carbon. On acidification or lowering of the cyanide level, Cu(CN)2" is formed which is strongly adsorbed, resulting in an increase in the rate of free cyanide destruction and subsequent improvement in gold loading. One problem in the modelling of multicomponent adsorption is the definition of a suitable multi-species isotherm [16,33]. Most of the empirical isotherms have too many parameters, which makes computation extremely difficult during regression of data. Furthermore, the ideal adsorbed solution (IAS) theory which is based on the single-species isotherms and works satisfactorily in the case of non-polar organics, cannot be used for metal cyanides [33]. Little research has been conducted on the mechanism of competitive adsorption. In previous papers [32,33] it was shown that multi-component Freundlich isotherm expressions could be used to model the simultaneous adsorption of metal cyanides, or metal cyanides and humic acid. The form of this expression is:

674

J . S . J . VAN DEVENTERand V. E. Ross N

qt = AtCt [ C t +k~IBtkCk]nI"I

(9)

k#l

It is possible to rewrite these equations in a linear form so as to facilitate the estimation of the competition coefficients Btk from a linear plot. For example,

f(C1) = {(AIC1/ql)I/(nl "I) -CI} = B12C2

(I0)

In the field of water-treatment various efforts have been made to group species together which have similar adsorption affinity. This approach is not very practical in a CIP system where f e w of the fouling agents are clearly defined. Nieuwoudt [34] showed how a "tracer" component occurring naturally in the pulp was selected to model the poisoning of the carbon. The selection of such a tracer is still a problem, as this could be different for different types of ore and fouling conditions. In some cases nickel, silver, copper, or the total organic content could be measured and modelled as a second adsorbate besides gold. As the gold adsorbs the tracer component also adsorbs, so that the effective loading capacity of the carbon is decreased. An alternative strategy is to measure the loading of gold from the pulp, as well as from a pure synthetic solution at the same pH and level of free cyanide. If poisoning occurs, the pseudo-equilibrium measured will be lower in the pulp. A competitive adsorption model is then fitted to the adsorption data, and the equilibrium parameters for a fictitious fouling agent estimated. The fictitious fouling agent has the effect of decreasing the adsorptivity of the carbon as adsorption of the gold and foulants proceeds. Whereas the presence of divalent cations like calcium and magnesium could enhance the adsorption of gold cyanide, the simultaneous precipitation of calcium or magnesium carbonates has an inhibiting effect on adsorption. Most research in this regard has been done on calcite formation, and very little work has been done on the effect of magnesium which is so common in the pulps on the Eastern Goldfields of Western Australia. Bailey [2] stated that the presence of calcium carbonate did not affect the equilibrium capacity of activated carbon. He showed that calcium had a detrimental effect on the activity of carbon in different plants. No detailed report has been published on the modelling of the fouling of carbons by these precipitates. Petersen and Van Deventer [35] demonstrated that the rate of intrusion of fine silica and alumina particles into the matrix of activated carbon and ion-exchange resins was fast, and dependent on the concentration of particles in the slurry. It was found that the presence of fine particles had no effect on the equilibrium loading of silver cyanide on either resin or carbon. The reduction in the rate of adsorption appeared to be a kinetic influence, and could be attributed to two effects, viz: (a) pore blocking, and therefore retarded diffusion into the adsorbent particles, and (b) temporary blinding of the adsorbent surface. Petersen and Van Deventer [35] defined an availability factor O in the film transfer expression so as to reduce the effective external area of the adsorbents: (ll)

d C / d t = -kfApO (C-Cs)

It appeared as if O approached an asymptotic value at higher concentrations of inert particles in the slurry. The decrease in O was significantly more than the corresponding decrease in voidage fraction in the slurry. MODELS FOR E L U T I O N Little work has been published on the modelling of the elution of gold cyanide from activated carbon. The first attempt in this direction was the modelling of Zadra elution by Adams and Nicol [36]. Although these authors claimed that they could simulate the Zadra process successfully, they did so after assuming that: (a) a single average mass transfer coefficient was used to describe the intraparticle diffusion; (b) the equilibrium between the

Dynamicsof carbon-in-pulpsystems

675

gold on the carbon and that in solution was described by a single linear isotherm; (c) the elution conditions were assumed to remain constant during the course of the process. The assumption of a linear isotherm will be applicable only under conditions of low solution phase concentrations, as was the case for the continuous stirred tank reactor in which Adams and Nicol [36] performed their tests. These authors presented an extension of their model to describe elution in a column, but provided no experimental evidence for the applicability thereof. According to Van der Merwe and Van Deventer [37], the main reasons for the lack of modelling efforts on the AARL elution process are: (a) the poor insight into the mechanism of the pre-treatment process; (b) the evolution of the composition of the eluate during the elution cycle; (c) the apparent complexity of the opposing effects of high ionic strength and high cyanide concentrations. Van der Merwe and Van Deventer [37] showed how an intraparticle-film diffusion model with a shifting equilibrium could be used to simulate AARL elution curves. The equilibrium adsorption expression was found to be a function of mainly the pre-treatment conditions, concentration of spectator cations, temperature, pH, and the deactivation of the carbon surface caused by the degradation of cyanide. An interesting general observation was that the exponent in the Freundlich expression was inversely proportional to the pre-exponential parameter. In further work, Van der Merwe [38] showed that an equilibrium approach to modelling could be used in the case of weak adsorption, i.e. where severe pre-treatment conditions were used. Under such conditions, kinetic influences were irrelevant, so that the velocity of flow through the column did not affect the elution behaviour. When the influence of pre-treatment was less profound, so that the equilibrium of adsorption was higher, a kinetic approach was required to model elution data. Despite the fact that the elution model of Van der Merwe [38] is versatile and generally applicable, many questions regarding the modelling of elution still remain unanswered. MODELS FOR REGENERATION Numerous publications have appeared on the kinetics of the decomposition of organics adsorbed on activated carbon. It is clear that the duration and temperature of regeneration should be determined by the nature of the organics adsorbed on the activated carbon. Hence, it is possible that regeneration conditions could differ dramatically between plants. Few papers, however, have appeared on the modelling of regeneration in industrial plants, or on the interrelationship between regeneration conditions and the adsorptive capacity of the carbon. Van Deventer & Camby [39] regenerated spent carbon from a CIP plant, as well as carbon loaded with phenol, in a small fluidized bed and measured the loading characteristics of the reactivated carbon by adsorption of silver cyanide. It was observed that the temperature, rather than the duration beyond 10 minutes, affected the adsorptive behaviour of the activated carbon. By fitting a kinetic model to batch adsorption data, Van Deventer & Camby [39] showed that an increase in the temperature enhanced the equilibrium adsorptive capacity, the transformation of micropores into macropores, and the rate of transport in the micropores. The diffusivity in the macropores increased only at higher temperatures. It was possible at temperatures higher than 700°C to increase the loading capacity above that of the virgin carbon. KNOWLEDGE- BASED SIMULATION From the preceding discussions it is evident that the CIP process is in many respects illdefined, which means that existing fundamental equations are not applicable under all conditions. Reuter & Van Deventer [40-42] explained how a knowledge-based system (KBS) approach could be used to simulate such ill-defined processes. The basis of the adsorption model is batch concentration-time data, and the corresponding loading-time

676

J. S. J. VAN DEVENTER and V. E. Ross

curve that covers the adsorption profile up to the equilibrium loading [40-42]. From this curve and the corresponding concentration-time data, the rate variable k[q(t)], which is defined here to be a function of only the loading q(t), may be determined. This rate variable is subsequently used to predict the change in concentration and carbon loading at any carbon concentration Me, and at any initial concentration at the prevailing chemical process conditions. Equations (12) and (13) give the rates of change in the solution and carbon phases respectively caused by adsorption: dC/dt=-(Ctl/C~2)k[q(t)]C

=

r1

(13)

d q / d t -- alk[q(t)]C = r 2 where:

(12)

ktq(t)] = -2(Cn, 1-Cn)/6t(Cn*l+Cn) ~1 = (Mt/Mc)I a 2 = (Mr/Me) 2

Equations (14) and (15) give the corresponding rates of change in the solution and ore solids phases respectively caused by leaching: d C / d t = k[g(t)]g(t) dg/dt=-Bk[g(t)lg(t)

=

r3 =

(14) re,

(15)

where: k[g(t)]= 2(gn+l-gn)/6t(gn.l+gn) 13 = ( M r / M s ) Although these models do not suggest a mechanism for the reaction under consideration, the transformed kinetic data represent a finger-print of that reaction. Consequently, the model can be used as a basis to describe the reaction under all possible conditions, given that the mechanism does not change. This basic finger-print curve and its associated shallow and deep level knowledge, defined as objects, are termed the pivot-data, or the standard condition. These pivot-data serve as a reference with which other curves are compared, and which can subsequently be used for fault-diagnosis or process identification. Any condition that differs in whatever way from this standard condition or the pivot-data, is considered to be non-standard. Consequently, any change in the profiles of k[q(t)] or k[g(t)] should be considered as the combined effect of different deviations from the standard condition, and therefore as taking all interactions into account. The changes in the leaching, adsorption or other reactions may be caused by changes in the mineralogy and chemistry of the ore, deactivation of the adsorbent, or changes in the concentration of reagents. It is convenient to express deviations from the pivot-data or standard parameters as percentages, which are estimated through experience, directly from the plant or from experimental data. The kinetic equations (12) to (15) can be incorporated into suitable process models which describe continuous flow systems. Equations (16) to (18) that define the change of concentration in the solution, loading on the carbon and element content (gold in this case) in the ore were published previously [42]. Ideal flow is assumed in the formulation of these models, although in the KBS non-ideal flow in the form of short-circuiting [Ci.l= ~Ci_l+ (1-~)Ci.2] and dead volume [Vact=Vtotat-Vdead] can be incorporated. The theoretical values of the dead volume and bypass streams can be obtained from tracer tests, or can be estimated by comparing real plant behaviour with that predicted from an ideal flow model. d C i / d t = (Qp, in/Vact)Ci-1 - (Qp,out/Vact)Ci + r 1 + r 3

(16)

d q i / d t = (mCCc/MCCc,t)[qi+l-qi ] + (mC°c/MC°c,t)[qi.l-qi] + r 2

(17)

d g i / d t = (Qp, in/Vact)gi-1 - (Qp,out/Vact)gi + r4

(18)

Dynamics of carbon-in-pulp systems

677

Depending on meet, MCCc ,, mC°c and Me° c t any type of carbon transfer mode, ranging from a low periodicity to'~ontinuous, co-cu~'rent to counter-current or a combination of these may be simulated. Reuter and Van Deventer [40] showed how the same philosophy of integrating KBS and dynamic material balance equations could be used to simulate the adsorption of gold or silver cyanide on activated carbon in fixed beds or periodic countercurrent columns. O P P O R T U N I T I E S FOR F U R T H E R RESEARCH

The review has shown that many aspects concerning the modelling of adsorption onto activated carbon have been researched thoroughly, while the incorporation of physicochemical phenomena in such models have received less attention. Furthermore, the simulation of elution and regeneration processes has not been developed to the same extent as that for adsorption. Consequently, ample opportunities exist for the development of more advanced models, and for the mathematical description of phenomena affecting the CIP process. The following aspects deserve further attention, and have been identified on the basis of the literature survey: One major problem encountered in the scale-up of leaching and adsorption processes from laboratory batch tests to large-scale continuous flow mixed reactors is the estimation of film transfer coefficients for large-scale tanks. The published information on dimensionless correlations for film transfer coefficients is extremely sparse. The relationship between the pore size distribution of an activated carbon and the values of the macropore and micropore diffusion coefficients is not clear. Little quantitative information is available about factors affecting the intraparticle diffusivities. Moreover, little experimental information is available to evaluate the relative importance of surface 'versus pore diffusion. No phenomenological models are available to describe the rate of leaching of gold in CIL reactors. The processes of leaching, preg-robbing and adsorption on carbon are interrelated, which means that the estimation of true parameters cannot be conducted independently for the two processes. The nature of the fouling of carbon by organics, solids and inorganic precipitates is not well-understood, and very little quantitative modelling work has been published in this regard. At present the influence of chemical conditions in a CIP plant on the adsorption of gold cyanide cannot be taken into account adequately in fundamental models, so that a knowledge-based approach is the only alternative. Very little is understood about the nature of interaction between adsorbates (both metal cyanides and organics) during competitive adsorption. Consequently, models for multi-component equilibrium adsorption of metal complexes are all empirical and have limited validity. The incorporation of such equations in simulation models for CIP plants results in computationally complex computer programmes. Further research into the nature of competitive adsorption in CIP cascades could assist in streamlining the simulation of non-ideal behaviour in cascades. More clarity is required regarding the optimal conditions governing the operation of CIP or CIL cascades. The literature has revealed conflicting results for the effects of the carbon distribution across the cascade, and the mode of carbon transfer between stages. This is caused by the fact that different models have been used, which are all simplified representations of reality. It is recommended that a general dynamic model incorporating all the major effects should be used in a comprehensive sensitivity analysis to elucidate this problem.

678

J. S, J. VAN DEVENTER and V. E. Ross

Recent work on the modelling of elution of gold cyanide from loaded carbon has shown that the fundamentals of the process are still poorly understood. Much more research is required before reliable predictions could be made from limited testwork. Moreover, no modelling work has been conducted on the multi-component desorption of metal complexes from loaded carbon. Despite extensive research on the decomposition of organics adsorbed on carbon, few modelling studies have been published on the regeneration of spent carbon in industrial kilns. It is not yet possible to relate quantitatively the effect of operating conditions in a regeneration kiln to the adsorption characteristics of the carbon in a CIP plant. CONCLUSIONS Simple empirical models for adsorption appear to be valid only under very specific conditions. When gold cyanide reveals low loadings on the carbon and low concentrations in solution, so that the driving force across the external film is rate controlling, a simple film diffusion mechanism can be used. However, when high loadings of gold on the carbon, fouling or pore blocking of the carbon, and steep concentration gradients across the external liquid film are encountered, intraparticle diffusion has to be taken into account. In such instances, the relative diameters of the adsorbates and pores, as well as the distribution of pore size, will determine whether a single diffusivity or a bi-disperse approximation should be used. For most practical situations, a film diffusion approach appears to be adequate. Little work has been published on the modelling of competitive adsorption, preg-robbing and fouling of carbon. Usually, the identities and concentrations of the competitive species are unknown, so that a lumped approach has to be followed whereby a single "tracer" species is selected to represent the overall effect of the competitive species. Organic foulants present on the carbon at low loadings affect only the intraparticle diffusivity of gold or silver cyanide, while an equilibrium effect is more prominent only at higher loadings of organics. The pre-treatment of loaded carbon, as well as the elution pattern of cations, are the major phenomena to be considered in the modelling of the elution of gold cyanide from an AARL column. Under severe conditions of pre-treatment, the dynamics of elution are determined mainly by the adsorption equilibrium and the flow conditions in the column. It was shown that the flexibility of a knowledge-based system (KBS) could be combined with the dynamic characteristics of a set of simple ordinary differential equations so as to give realistic simulations of leaching, CIP and CIL plants. A KBS is especially useful to answer "what-if" questions and to perform fault-diagnosis and process identification. LIST OF SYMBOLS A At Ap

Btk CS

g,gi,gn

g®

Flow area of column [mz] Pre-exponential factor in Freundlich isotherm. Total external surface area of carbon particles [m 2] Competition factor for the effect of component k on 1. C , C i , C n Concentration in a batch reactor, concentration in stage i and data point n respectively [ppm]. Solution phase concentration at the liquid-carbon interface [ppm]. Average diameter of carbon particle [m]. Surface diffusivity [mZ/s] Ore grade in a batch reactor, grade in stage i and grade data point n respectively [g/toni. Refractory gold in ore [g/ton].

Dynamics of carbon-in-pulp systems

k ka, kd kf kg kn L Me,Mr,Ms met c

MCCc, t

nt,nl q,qi,qn q÷

Qp,in

r

rl... r 4

R t

V Vact

wij x

0 o"

679

Rate variable as a function of y(t) and g(t) [h-l]. Parameters in Langmuir rate equation. External film transfer coefficient [m/s]. Rate constant for empirical leaching expression. Empirical constant in Eq.l. Number of discrete loading fractions in a stage. Mass concentration of carbon, liquid and solids respectively [g/l]. Mass flow rate of the carbon counter-current and me°c for co-current flow [kg/h]. Mass of carbon being transferred counter-current and Mete, t co-current [kg]. Exponent in Freundlich isotherm. Carbon loading in a batch reactor, loading in stage i and loading data point n [mg/kg]. Parameter in Langmuir isotherm. Pulp flowrate in and Q, out out of a stage [m3/h]. Radial variable in carb~h particle [m]. Rate equation [ppm/h]. External radius of carbon particle [m]. Time variable [h]. Volume of liquid phase in reactor. Active stage volume [m3]. Mass of carbon in stage i in discrete loading fraction j, or voidage in column. Distance variable along column length. Volumetric fraction of pulp that is liquid. Surface availability factor. Apparent density of carbon [kg/m3]. Fraction of pulp short-circuiting reactor stage.

REFERENCES

I. . . .

.

6. .

8.

.

Nicol M.J., Fleming C.A. & Paul R.L., The chemistry of the extraction of gold, in: Chapter 15, The extractive metallurgy of gold in South Africa, 2, (ed.) G.G. Stanley, Johannesburg, S. Afr. Inst. Min. Metall., 831-905 (1987). Bailey P.R., Application of activated carbon to gold recovery, in: Chapter 9, The extractive metallurgy o/gold in South Africa, 1, (ed.) G.G. Stanley, Johannesburg, S. Afr. Inst. Min. Metall., 379-614 (1987). Van der Merwe P.F. & Van Deventer J.S.J., The influence of oxygen on the adsorption of metal cyanides on activated carbon, Chemical Engineering Communications, 65, 121-138 (1988). Van Deventer J.S.J., Factors influencing the efficiency of a carbon-in-pulp adsorption circuit for the recovery of gold from cyanided pulps, Proceedings of GOLD 100, Vol. 2: Extractive Metallurgy of Gold, (eds.) C.E. Fivaz & R.P. King, Johannesburg, S. Afr. Inst. Min. Metall., 85-95 (1986). Menne D., Predicting and assessing carbon-in-pulp performance, 14th International Mineral Processing Congress, Toronto, (17-23 Oct. 1982). McDougall G.L. & Fleming C.A., The extraction of precious metals on activated carbon, Ion exchange and sorption processes in hydrometallurgy, (eds.) M. Streat & D. Naden, Society of Chemical Industry, London, 56-126 (1987). Dixon S., Cho E.H. & Pitt C.H., The interaction between gold cyanide, silver cyanide and high surface area charcoal, AIChE Symposium Series 74, no. 173, 75-83 (1978). Nicol M.J., Fleming C.A. & Cromberge G., The absorption of gold cyanide onto activated carbon. I. The kinetics of adsorption from pulps, J. S. Afr. Inst. Min. Metall., 84, no. 2, 50-54 (1984). Williams D.F. & Glasser D., The modelling and simulation of processes for the absorption of gold by activated charcoal, J.S.Afr. Inst. Min. Metall., 85, no. 8, 237243 (1985).

680

10,

11, 12. 13. 14. 15. 16. 17. 18. 19. 20.

21. 22. 23.

24. 25. 26. 27. 28.

J . S . J . VAN DEVENTERand V. E. Ross

Carrier C., Hodouin D. & Courchesne M., Dynamic simulation of the CIP gold recovery process, Proceedings of an International Symposium on Gold Metallurgy, (eds.) R.S. Salter, D.M. Wyslouzil & G.W. McDonald, Pergamon Press, Toronto, 309325 (1987). Johns M.W. & Mathews I.D., Recovery of gold from ashed woodchips, J, S. Afr. Inst. Min. Metall., 90, no. 1, 1-10 (1990). Woollacott L.C., Stange W. & King R.P., Towards more effective simulation of CIP and CIL processes. 1. The modelling of adsorption and leaching, J.S.Afr. Inst. Min. Metall., 90, no. 10,275-282 (1990). Stange W., Woollacott L.C. & King R.P., Towards more effective simulation of CIP and CIL processes. 2. A population balance-based simulation approach, J.S.Afr. Inst. Min. Metall., 90, no. 11, 307-314 (1990). Van der Walt T.J., Parametric sensitivity analysis of abnormal behaviour in the dynamic simulation of carbon-in-pulp plants, Final year thesis (in Afrikaans), University of Stellenbosch, South Africa, 240 (1989). Van Deventer J.S.J., Kinetic models for the adsorption of gold onto activated carbon, Proceedings of MINTEK 50, 2, (ed.) L.F. Haughton, Council for Mineral Technology, Randburg, South Africa, 487-494 (1984). Van Deventer J.S.J., Kinetic model for the adsorption of metal cyanides on activated charcoal, Ph.D. Thesis, University of Stellenbosch, South Africa, 337 (1984). Van Deventer J.S.J., Modelling of the adsorption of gold on activated carbon in a periodic countercurrent cascade of continuous stirred tank reactors, Institution of Chemical Engineers Symposium Series, no. 87, 619-626 (1984) Van Deventer J.S.J., Kinetic model for the reversible adsorption of gold cyanide on activated carbon, Chemical Engineering Communications, 44,257-274 (1986). Van Deventer J.S.J., Parametric sensitivity study of adsorption in a periodic countercurrent cascade of stirred tanks, Separation Science and Technology, 22, no. 7, 1737-1759 (1987). Van Deventer J.S.J. & Jansen van Rensburg, P., Computer program for the design of a countercurrent moving carbon bed used for the recovery of gold from solutions, Proceedings of APCOM '87, 2: Metallurgy, (eds.) R.P. King & I.J. Barker, Johannesburg, S. Afr. Inst. Min. Metall., 197-207 (1987). Van Deventer J.S.J., Criteria for selection of activated carbon used in carbon-inpulp plants, Reagents in the minerals industry, (eds.) M.J. Jones & R. Oblatt, Inst. Min. Metall., 155-160 (1984). Brinkmann E.A. & King R.P., A kinetic model framework for combined diffusion and adsorption processes, Proceedings of APCOM '87, Vol. 2." Metallurgy, (eds.) R.P. King & I.J. Barker, Johannesburg, S. Afr. Inst. Min. Metall., 189-195 (1987). Todtenhaupt P., Forschner P., Grimsley D. & Lases A.B.M., Design of agitators for the ERGO carbon-in-leach plant, Proceedings of GOLD 100, Vol. 2: Extractive Metallurgy of Gold, (ed.) C.E. Fivaz & R.P. King, Johannesburg, S. Afr. Inst. Min. Metall., 195-207 (1986). Stange W. & King R.P., A population balance approach to the modelling of the CIP process, Proceedings of APCOM '87, Vol. 2: Metallurgy, (eds.) R.P. King & I.J. Barker, Johannesburg, S. Afr. Inst. Min. Metall., 209-221 (1987). Jansen van Rensburg P. & Van Deventer J.S.J., Simulation of adsorption of metal cyanides in packed beds of activated carbon, Proceedings of Extraction Metallurgy '85, London, Inst. Min. Metall., 289-307 (1985). Smith S.W. & De Jesus A.S.M., Nuclear-technical applications in gold extraction metallurgy, Proceedings of GOLD 100, Vol. 2: Extractive Metallurgy of Gold, (ed.) C.E. Fivaz & R.P. King, Johannesburg, S. Afr. Inst. Min. Metall., 429-434 (1986). Nicol M.J., Fleming C.A. & Cromberge G., The absorption of gold cyanide onto activated carbon. II. Application of the kinetic model to multistage absorption circuits, J. S. Afr. Inst. Min. Metall., 84, no. 3, 70-78 (1984). Stange W., Woollacott L.C. & King R.P., Towards more effective simulation of CIP and CIL processes. 3. Validation and use of a new simulator, J.S Afr. Inst. Min. Metall., 90, no. 12, 323-331 (1990).

Dynamics of carbon-in-pulp systems

29.

30. 31.

32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42.

681

Hulse N.D., Fitzgerald B. & Ohlson de Fine M.J., The measurement of the carbon concentration in the adsorption vessels of a carbon-in-pulp plant, Proceedings of MINTEK 50, 2, (ed.) L.F. Haughton, Council for Mineral Technology, Randburg, South Africa, 495-500 (1984). Van der Merwe I.W., Van Deventer J.S.J. & Reuter M.A., Knowledge-based computer simulation of gold leaching in batch and continuous systems, Proceedings 14th CMMI Congress, Edinburgh, Inst. Min. Metall., London, 147-160 (1990). La Brooy S.R., Bax A.R., Muir D.M., Hosking J.W., Hughes H.C. & Parentich A.,Fouling of activated carbon by circuit organics, Proceedings of GOLD 100, Vol. 2: Extractive Metallurgy of Gold. (ed.) C.E. Fivaz & R.P. King, Johannesburg, S. Afr. Inst. Min.Metall., 123-132 (1986). Petersen F.W. & Van Deventer J.S.J., The influence of pH, dissolved oxygen and organics on the adsorption of metal cyanides on activated carbon, Chemical Engineering Science, to appear in 1991. Van Deventer J.S.J., Competitive equilibrium adsorption of metal cyanides on activated carbon, Separation Science and Technology, 21, no. 10, 1025-1037 (1986). Nieuwoudt I., Dynamic model for the competitive adsorption of metal cyanides on activated carbon in batch reactors, M.Eng. thesis, University of Stellenbosch, South Africa, 289 (1988). Petersen F.W. & Van Deventer J.S.J., Inhibition of mass transfer to porous adsorbents by fine particles and organics, Chemical Engineering Communications, to appear in 1991. Adams M.D. & Nicol M.J., The kinetics of the elution of gold from activated carbon, Proceedings of GOLD 100, Vol. 2: Extractive Metallurgy of Gold, (ed.) C.E. Fivaz & R.P. King, Johannesburg, S. Afr. Inst. Min. Metall., 111-121 (1986). Van der Merwe P.F. & Van Deventer J.S.J., Generalized simulation of Zadra and AARL elution columns, Proceedings of 14th CMMI Congress, Edinburgh, Inst. Min. Metall., 161-171 (1990). Van der Merwe P.F., Fundamentals of the elution of gold cyanide from activated carbon, Ph.D. Thesis in preparation, University of Stellenbosch, South Africa, (1991 ). Van Deventer J.S.J. & Camby B.S., The influence of regeneration conditions on the adsorptive behaviour of activated carbon, Minerals Engineering, 1, no. 2, 157-163 (1988). Reuter M.A. & Van Deventer J.S.J., A knowledge-based system for the simulation of batch and continuous carbon-in-pulp systems, Proceedings: Extraction Metallurgy '89, Inst. Min. Metall., London, 419-443 (1989). Reuter M.A. & Van Deventer J.S.J., A knowledge-based system for the simulation of batch and continuous carbon-in-leach systems, Proceedings: APCOM '90, TUBDokumentation, vol. 51, no. 1, Berlin, 343-356 (1990). Reuter M.A., Van Deventer J.S.J. & Van der Merwe I.W., The application of knowledge-based systems to the simulation of gold extraction processes, Minerals Engineering, 4, no. 2, 103-119 (1991).

M£ 4 : 7 / 1 1 - D