COMSOL 6.4 - Gold Recycling Through Oxidative Dissolution

Gold Recycling Through Oxidative Dissolution

Recovery of precious metals in recycling of electronics, or extraction from ore, is usually performed through leaching of the metal into an aqueous phase. Precious metals require the use of an oxidant and, often, a complexant. In the case of gold, the cyanide anion CN- forms a soluble complex with gold(I) (that is, Au(CN)-2), that is so stable that molecular oxygen becomes a viable oxidant. The process is known as gold cyanidation, and it has — unsurprisingly — been studied extensively for the past century. Research into finding less toxic complexants is ongoing, but due to the availability of kinetic parameters, this model sticks to using cyanide.

The model studies the oxidative dissolution of this noble metal in an air saturated cyanide solution. The system encompasses three phases: a gaseous phase (air), an aqueous phase, and a solid gold phase. The system is assumed to be homogeneous on a macroscopic scale, for example fine particulate matter dispersed in water, which is continuously agitated by a stream of air bubbles.

Model Definition

Since this problem is not limited by mass transport in the bulk, it will be modeled in a 0D component. The rate limiting step is that of a surface reaction, and corresponds to a problem where diffusion is not a rate limiting step. Since the evolution of available surface area during dissolution depends on the geometry of the particles, the model includes two cases: flakes and spheres (see Figure 1), each in its separate 0D component.

Figure 1: The two cases studied, flakes (to the left) and spheres (to the right).

Liquid phase

In each component, two Reaction Engineering interfaces will be added, the first one will describe the liquid phase, in which the following reaction is added:

The rate of reaction is, according to Ref. 1:

(1)

where A is total exposed surface area of gold, V is the volume of the liquid, kAu is a parameterized rate constant, and c' is the product between the adsorption coefficient of cyanide on gold (Kads), the concentration of aqueous dioxygen, and the concentration of cyanide to the power of three:

(2)

Assume that the starting material is monodisperse; that is, that all particles are of the same size. The total amount of gold per unit of volume (the so called loading) is set equal in the two components, and the thickness of the flakes is set such that initial surface areas of the two cases are equal. Since the system is assumed to be well mixed, the concentration of oxygen is set to be in equilibrium with the partial pressure in the gas phase.

Gas Phase

The second Reaction Engineering interface will represent the gas phase (air). Add two species: O2 and N2, but only the former will participate in any reactions. A global constraint, requiring Henry’s Law for O2 to be fulfilled at all times, is added, and since the system is considered to be a batch reactor (where oxygen can be depleted), introduce an additional constraint, enforcing mass conservation of the total amount of oxygen.

Differences Between the Components

In the first component, the dissolution of flakes is modeled. Here assume that the total surface area exposed remains constant throughout the reaction (the flakes are assumed to be utterly oblate) up to the point that the last bit of solid has been consumed, at which point the available surface area is assumed to drop to zero. In order not to introduce a discontinuity in the available surface area, assign a smoothed stepping function which rapidly falls around the point at which depletion occurs.

In the second component, describing dissolution of spheres, the surface area exposed does vary during the course of the dissolution process (the surface area is proportional to the mass loading of gold to the power of two thirds). Since the surface area naturally goes to zero as the amount of solid gold declines, it is possible to do away with the smoothed stepping function, but as the solver approaches the end of the reaction, care is taken to avoid evaluating the fractional power of a negative number.

Results and Discussion

The result of the time integration is shown in Figure 2.

Figure 2: Time evolution of concentrations and partial pressure of oxygen for each of the two particle cases.

The initial conditions are the same for both studies, and also the initial rates of change are the same for the two components. But as the spheres dissolve, their total surface area decreases, leading to a slower leaching compared to the flakes. After some time the leaching process in the system with flakes stops runs out of solid gold and all reactions stop, whereas this quantity in the system with spherical particles is still asymptotically approaching zero.

Reference

1. G. Senanayake, “Kinetics and reaction mechanism of gold cyanidation: Surface reaction model via Au(I)–OH–CN complexes,” Hydrometallurgy, vol. 80, pp. 1–12, 2005.

Chemical_Reaction_Engineering_Module/Ideal_Tank_Reactors/gold_recycling

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Right-click and choose .

Click

In the tree, select > .

Click

Liquid phase

Add a interface, which will correspond to the liquid phase.

In the window, under click .

In the window for , type Liquid phase in the text field.

Locate the section. Find the subsection. In the Vr text field, type V_liquid.

Locate the section. In the T text field, type T.

Locate the section. From the list, choose .

Global Definitions

Parameters 1

Read in a set of parameters to be used in the model (V_liquid being one of them).

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file gold_recycling_parameters.txt.

The first component describes a system with dispersed gold flakes dissolving in a liquid, while maintaining a constant interfacial area to the liquid phase. Read in variables describing this behavior into the variables section of .

Definitions

Variables 1

In the window, under right-click and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file gold_recycling_variables_flakes.txt.

Liquid phase (re)

Define a reaction describing the overall dissolution process, where gold is oxidized by molecular oxygen into a gold(I)dicyanide complex.

Reaction 1

In the toolbar, click

In the window for , locate the section.

In the text field, type Au(s) + CN- + O2(aq) + H2O => AuCNCN- + OH-.

Use the feature to determine the coefficients for the reactants and products.

Click in the upper-right corner of the section.

The effective rate expression does not follow the law of mass action, instead use the rate expression derived in the reference publication.

Locate the section. From the list, choose .

In the rj text field, type flakes_R_Au/4.

While not strictly needed, set the rate parameters to descriptive values.

Locate the section. Find the subsection. In the text field, type 4.

Locate the section. In the kf text field, type 0.

Initial Values 1

Enter initial values for a slightly alkaline (pH: 9.4) air saturated aqueous solution.

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Species	Concentration (mol/m^3)
Au(s)	liquid_c0_Au
AuCNCN-	0[mol/dm^3]
CN-	cyanide_c0
H2O	55[mol/dm^3]
O2(aq)	p0_O2g * H_O2
OH-	4e-4[mol/dm^3]

Dissolution of gold flakes

Enter a descriptive label for the first component, which treats the case of thin foil or flakes of gold.

In the window, click .

In the window for , type Dissolution of gold flakes in the text field.

Add Physics

In the toolbar, click

to open the window.

Go to the window.

Add a second interface corresponding to the gas phase.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Gas Phase

In the window for , type Gas Phase in the text field.

The gas phase is compressible, hence its volume is not guaranteed to remain constant, change the reactor type to batch to reflect this fact.

Locate the section. From the list, choose .

The volume of the gas phase is defined as a variable depending on the total volume and the volume of the (assumed incompressible) liquid and solid phases.

Find the subsection. In the Vr text field, type V_gas.

Locate the section. In the T text field, type T.

Oxygen will be present in both gas and liquid phase, next add it as a gas phase species.

Species 1

In the toolbar, click

In the window for , locate the section.

In the text field, type O2(g).

For completeness, also add nitrogen, even though it will not participate in any chemical reactions.

In the toolbar, click

In the window for , locate the section.

In the text field, type N2(g).

The concentration of oxygen in the gas phase and in the liquid phase, is assumed to equilibrate on a much shorter time scale than the chemical reaction consuming oxygen (for example, a well stirred system). Hence, at any given time, Henry’s law is assumed to be fulfilled. We can impose this by introducing a

Click the

button in the toolbar.

In the dialog, in the tree, select the checkbox for the node > .

Click .

Henry’s Law for Dioxygen

In the toolbar, click

In the window for , type Henry's Law for Dioxygen in the text field.

Locate the section. In the text field, type re.c_O2_aq - H_O2*R_const*T*re2.c_O2_gas.

Since Henry’s law only dictates that the ratio of concentrations needs to remain constant, the solver would be free to, for example, increase both concentrations, but with different amounts. Clearly this would violate mass conservation. Therefore, add a second constraint on the total amount of oxygen atoms in our system.

Mass Conservation of Oxygen

In the toolbar, click

In the window for , type Mass Conservation of Oxygen in the text field.

Locate the section. In the text field, type V0_gas*(2*re2.c_O2_gas - 2*re2.c0_O2_gas) + V_liquid*(2*re.c_O2_aq + re.c_H2O + re.c_OH_1m - 2*re.c0_O2_aq - re.c0_H2O - re.c0_OH_1m).

Initial Values 1

The model starts with air.

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Species	Concentration (mol/m^3)
N2(g)	p0_N2g/R_const/T
O2(g)	gas_c0_O2g

Currently the rate of reaction is assumed independent of the amount of gold in our system. This corresponds to a constant area of gold interface during the dissolution, which is a good assumption for flakes or foil. However, once the gold is consumed, the reaction will need to stop, or else we would obtain negative concentrations of gold. Therefore we will modulate our rate of reaction with a step function, essentially a smoothed version of Heaviside’s step function.

Global Definitions

Step 1 (step1)

In the toolbar, click

and choose > .

In the window for , click

Locate the section. In the text field, type -1.

Click

This function, step1 is already being referred to in the section.

Dissolution of gold flakes (comp1)

Copy the first component for modeling flakes of gold, and create a second component for a (spherical) particulate suspension.

In the window, right-click and choose .

Dissolution of gold flakes 1 (comp2)

In the window, right-click the root node and choose .

Dissolution of spherical gold

In the dialog, click to accept the new tags.

Give the component a descriptive label.

In the window, click .

In the window for , type Dissolution of spherical gold in the text field.

Definitions (comp2)

Variables 1

In the interest of minimizing the amount of manual input, load variable expressions from a file.

In the window, under > click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file gold_recycling_variables_spheres.txt.

Note how the rate of gold dissolution depends on remaining surface area, because of that, this formulation does not need a step function.

Liquid phase (re3)

1: 4 Au(s) + 8 CN- + O2(aq) + 2 H2O => 4 AuCNCN- + 4 OH-

Update the rate expression to refer to this spherical case.

In the window, expand the > node, then click .

In the window for , locate the section.

In the rj text field, type spherical_R_Au/4.

Gas Phase (re4)

Henry’s Law for Dioxygen

Update the qualified names so that they refer to the interfaces in our new component.

In the window, expand the > node, then click .

In the window for , locate the section.

In the text field, type re3.c_O2_aq - H_O2*R_const*T*re4.c_O2_gas.

Mass Conservation of Oxygen

In the window, click .

In the window for , locate the section.

In the text field, type V0_gas*(2*re4.c_O2_gas - 2*re4.c0_O2_gas) + V_liquid*(2*re3.c_O2_aq + re3.c_H2O + re3.c_OH_1m - 2*re3.c0_O2_aq - re3.c0_H2O - re3.c0_OH_1m).

At this point the model is ready for solving, solve for 15 h.

Study 1

In the window, click .

In the window for , locate the section.

Clear the checkbox.

Step 1: Time Dependent

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the text field, type range(0,1,600).

In the toolbar, click