Dmitri H. Rubisov

Sulphuric acid pressure leaching of laterites — universal kinetics of nickel dissolution for limonites and limonitic/saprolitic blends

Abstract The high-temperature acid pressure leaching of nickeliferous laterites has attracted considerable attention from the nickel industry during the recent years. The process is especially advantageous for low-grade limonitic laterites. It is also applicable to mixtures of limonites and high-grade saprolites, although at higher acid consumption due to magnesium. It is advantageous, therefore, to derive a universal kinetic equation of Ni dissolution that is equally applicable to both types of feed. In the present work, a kinetic equation was derived using the concentration of hydrogen ion “at temperature” calculated from a solution speciation approach, and the assumption that nickel associated with magnesium dissolves instantaneously. This universal kinetic equation was successfully tested against various feeds that contained from 1.2% to 1.9% of Ni and up to 3.85% of Mg at temperatures from 230°C to 270°C, acid/ore ratios from 0.15 to 0.5, and concentrations of solids in the feed (pulp density) of up to 30%. The use of acidity “at temperature” made it possible to explain an apparent dependence of the ultimate Ni extraction on the acid/ore ratio, and on the terminal stoichiometric acid concentration during leaching.

Sulphuric acid pressure leaching of laterites - speciation and prediction of metal solubilities at temperature

Abstract Sulphuric acid pressure leaching of nickeliferous laterites has attracted considerable attention from the nickel industry during the past 5 years. The process is especially advantageous for limonitic laterites that mostly contain goethite, because iron precipitates releasing acid and thus rendering low acid consumption. It is also applicable to mixtures of limonites and saprolites, although at a higher acid consumption due to magnesium. Effective process design requires the solubility of metals that precipitate during the process to be known. In the present work, determination of metal solubilities is based on a simple speciation program that assumes the presence of only one dominant complex for each metal. The thermodynamic data for the precipitation reactions are extracted from high-temperature experiments with monometallic systems published previously. The validity of the approach is then tested against mixed bimetallic systems, and finally applied to calculate the solubility of aluminium, iron and magnesium in laterite leaching effluents “at temperature”. In both cases of limonitic feed and limonitic/saprolitic blends, the prediction closely follows metal solubilities measured experimentally at temperatures from 230 to 270°C and at terminal-free acidities ranging from 10 to 75 g/l.

Sulphuric acid pressure leaching of laterites — a comprehensive model of a continuous autoclave

Abstract The high-temperature acid pressure leaching of nickeliferous laterites employs multi-compartment continuous autoclaves treating a variety of lateritic feeds. Previous work has correlated the kinetics of nickel dissolution, as well as the solubility of important metals in this process, with acid concentration levels calculated at the temperature of leaching. This was achieved by a speciation analysis resulting in a universal kinetic equation for Ni dissolution from limonitic feeds and from limonitic/saprolitic blends. In the present work, these findings were combined to develop a comprehensive model for a continuous multi-compartment autoclave. To this end, the kinetics of Co, Fe, Al, and Mn was also estimated and included in the reactor model. The resulting model is capable of predicting Ni extraction and concentrations of major impurities during autoclave operation for a wide variety of process conditions and feed compositions. It was implemented in a computer simulator that can be used to investigate diverse process scenarios and to select acidity levels for different types of feed. Finally, the model is compared with continuous mini-plant pressure acid leaching data as provided by INCO Technical Services (ITSL) during process development campaigns.

Fundamental Kinetic Models for Gold Ore Cyanide Leaching

AbstractExisting studies of gold ore cyanidation kinetics demonstrate significant diversity in estimated kinetic parameters. By taking into account the size distribution of gold grains in the ore it was made possible to explain this diversity and the apparent “homogeneous” behaviour ofthe heterogeneous particles. A variable order kinetic equation successfully fitted data on different types of gold ores previously published by other investigators. Furthermore, two previously established fundamental kinetic equations, both based on the electrochemistry of pure gold cyanidation, were adopted for gold ores and incorporated into the variable order kinetic equation. The first equation was derived from the theory of mixed potentials, while the second was based on Habashis cyanidation model. Both kinetic equations demonstrated good accuracy in predicting the dependence of the gold extraction rate on the concentrations of free cyanide and dissolved oxygen. The Habashi equation employs fewer parameters than the ot...

Valuing guaranteed withdrawal benefits with stochastic interest rates and volatility

Guaranteed withdrawal benefits are long term contracts which provide investors with equity participation while guaranteeing them a secured income stream. Due to the long investment horizons involved, stochastic volatility and stochastic interest rates are important factors to include in their valuation. Moreover, investors are typically allowed to participate in a mixed fund composed of both equity and fixed-income securities. Here, we develop an efficient method for valuing these path-dependent products through re-writing the problem in the form of an Asian styled claim and a dimensionally reduced partial differential equation (PDE). The PDE is then solved using an Alternating Direction Implicit method. Furthermore, we derive an analytical closed form approximation and compare this approximation with the PDE results and find excellent agreement. We illustrate the various effects of the parameters on the valuation through numerical experiments and discuss their financial implications.

Solution techniques for population balance equations as applied to heterogeneous aqueous processes in stirred tank reactors

In this paper, a combination of analytical and numerical methods for solving the dynamic population balance equations associated with simultaneous leaching-precipitation reactions with size-independent rates is developed. An analytical solution suitable for both dissolving and precipitating phases in either continuous or batch reactors is derived assuming that concentrations of aqueous reactant are known a priori. When these concentrations are unknown, the population balance equations are combined with molar balances for aqueous reactants. The resulting system of equations is solved by converting the population balance equations into systems of ordinary differential equations. This is achieved by applying the moment transformation for the precipitation phases, whereas an original application of the numerical method of lines is developed for the leaching phases. The use of the proposed techniques is demonstrated by solving equations that arise in modelling batch and continuous transient reactors. The application of the numerical method of lines is also generalized for the case of size-dependent rates for either leaching or precipitating phases.

Model-based analysis of pressure oxidation autoclave behaviour during process upsets

Prediction of a hydrometallurgical reactor performance, process optimization and control apparently require reliable process models. Mathematical modelling of hydrometallurgical reactors is a rather complicated task. This is mainly caused by the particulate nature of processed materials, the simultaneous occurrence of several multi-phase heterogeneous reactions and the dependence of process parameters on working temperature. The most suitable technique for describing a process that involves particulate materials, is a special particle-counting procedure termed Population Balance Modelling (PBM). This procedure facilitates the investigation of both steady-state and dynamic behaviours of particulate processes. In this paper the pressure oxidation process serves as a case study to analyse the behaviour of a reactor (autoclave) when various process upsets occur. In practice, such upsets are triggered by sudden changes in oxygen mass transfer, oxygen feed rate, solids feed rate, cooling water injection, etc.

Optimal accelerated share repurchases

An accelerated share repurchase (ASR) allows a firm to repurchase a significant portion of its shares immediately, while shifting the burden of reducing the impact and uncertainty in the trade to an intermediary. The intermediary must then purchase the shares from the market over several days, weeks, or as much as several months. Some contracts allow the intermediary to specify when the repurchase ends, at which point the corporation and the intermediary exchange the difference between the arrival price and the TWAP over the trading period plus a spread. Hence, the intermediary effectively has an American option embedded within an optimal execution problem. As a result, the firm receives a discounted spread relative to the no early exercise case. In this work, we address the intermediarys optimal execution and exit strategy taking into account the impact that trading has on the market. We demonstrate that it is optimal to exercise when the TWAP exceeds Ζ(t) St where St is the fundamental price of the asset and Ζ(t) is deterministic. Moreover, we develop a dimensional reduction of the stochastic control and stopping problem and implement an efficient numerical scheme to compute the optimal trading and exit strategies.

Valuing GWBs with Stochastic Interest Rates and Volatility

Guaranteed withdrawal benefits (GWBs) are long term contracts which provide investors with equity participation while guaranteeing them a secured income stream. Due to the long investment horizons involved, stochastic volatility and stochastic interest rates are important factors to include in their valuation. Moreover, investors are typically allowed to participate in a mixed fund composed of both equity and fixed-income securities. Here, we develop an efficient method for valuing these path-dependent products through re-writing the problem in the form of an Asian styled claim and a dimensionally reduced PDE. The PDE is then solved using an Alternating Direction Implicit (ADI) method. Furthermore, we derive an analytical closed form approximation and compare this approximation with the PDE results and find excellent agreement. We illustrate the various effects of the parameters on the valuation through numerical experiments and discuss their financial implications.