Charles D. Immanuel

A feasible solution technique for higher-dimensional population balance models

Abstract This paper presents a numerical technique for the solution of (multi-dimensional) population balance models. The technique is based on an extension of a so-called hierarchical two-tier technique presented previously in the context of single-dimensional population balances [Immanuel, C. D., & Doyle III, F. J., (2003a). Computationally efficient solution of population balance models incorporating nucleation, growth, and coagulation: Application to emulsion polymerization. Chemical Engineering Science, 58, 3681–3698], and later extended to a three-dimensional problem [Immanuel, C. D., & Doyle III, F. J., (2005). Solution technique for a multi-dimensional population balance model describing granulation processes. Powder Technology, 156, 213–225]. The specific contributions of this article are two-fold: 1. Development of the technique to handle breakage/division phenomena in population balance. 2. Demonstration of the feasibility of the technique to handle modestly multi-dimensional population balance models. The technique is applied to one-dimensional, three-dimensional, and six-dimensional population balance models. In each case, the results are found to be qualitatively consistent with theory. The computational times are also found to be conducive for the intended applications (process analysis, optimisation, and control).

Efficient solution of population balance models employing a hierarchical solution strategy based on a multi-level discretization

This paper addresses the efficient solution of population balance models. Population balance equations are hyperbolic partial differential equations that lead to stiff problems with sharp moving fronts. Thus, a standard discretization algorithm such as the Method of Weighted Residuals is inadequate. The present paper is based on a hierarchical two-tier solution strategy that exploits the physics of the process. The paper examines a multi-level discretization strategy within the framework of the hierarchical algorithm with an aim to ensure efficient computation subject to acceptable accuracy levels.

An integrated framework for model-based flow assurance in deep-water oil and gas production

Flow assurance in deep-water developments has been identified as one of the main technological problems that the oil and gas industry faces today. Extreme conditions such as high pressures and low temperatures promote the formation of gas hydrates that can potentially reduce or completely block the flow path, causing severe financial losses. An integrated framework for model-based flow assurance management is presented. A two-phase flow model describing the thermal-hydraulic dynamics of subsea pipelines is coupled with a hydrate thermodynamic equilibrium calculation module. The model-based flow assurance framework determines whether hydrate formation can occur at every time instant and at every point along the pipe by comparing the hydrate formation equilibrium temperature and the actual pipeline temperature. The injection of hydrate thermodynamic inhibitors (e.g. methanol) is also included in the model. The framework is implemented in a state-of-the-art modelling tool (gPROMS®). In order to demonstrate its capabilities, shut-in and re-start transient production scenarios are evaluated. Our studies illustrate the benefits of a model-based approach in dealing with the complex and multi-faceted problem of flow assurance.

Population Balance Model for Cellular Processes in Biological Systems: Biochemical and Biomedical Applications

Abstract In this paper, the generic problem of the development of a population balance model for those biological systems involving cellular processes is discussed. Such models are of interest for bioreactor optimisation and control, as well as for different biomedical problems including the study of cancer. The generic model and its features are presented, serving partly to consolidate the studies that have been reported in the literature already. The major challenges and issues with this problem are highlighted. One of the challenges is with respect to the solution technique for these complex models, which issue is addressed here. The algorithm proposed for solving these complex models is based on a hierarchical two-tier solution strategy that has been proposed previously (Immanuel and Doyle, III, Chem. Eng. Sci., 2003). The two-tier strategy involves the calculation of the rates of sub-processes that contribute to the population dynamics in the first tier, with the population itself being updated in the second tier. This in turn enables performing a major portion of the calculations off-line (once at the start of the simulation), thereby achieving a major reduction in the computational load. The algorithm is implemented on a six-dimensional population balance bioreactor model.

Dynamic Process Optimisation in Free-Radical Multicomponent Polymerisation: butyl methacrylate and butyl acrylate case study

Abstract In the present work, an effective mathematical model for the calculation of entire molecular weight distribution (MWD) in free-radical copolymerisation is presented. The distribution is obtained by discretising the infinite chain length domain into a finite number of intervals. The model makes use of a pseudo-homopolymerisation approximation, thus allowing for a significant model simplification. An optimisation formulation is developed and tested for the butyl methacrylate-butyl acrylate (BMA-BA) copolymerisation system with the purpose of identifying optimal reactor conditions using the above model, revealing the ability to attain target MWD and copolymer composition, by manipulating process variables such as monomer and initiator feed rate profiles.

A comprehensive population balance model of emulsion polymerisation for PSD & MWD: Comparison to experimental data

Abstract A population balance model for emulsion polymerisation has been developed. This model captures PSD and MWD, both of which are key performance indicators for the end latex product. The model employs purely mechanistic kernels and is aimed at maximising predictive capacity. The model is validated against a multi-objective experimental target. The aim is to predict data for PSD, solids, particle number as well as global molecular weight. The experimental system investigated is a vinyl acetate/butyl acrylate copolymerisation with ionic emulsifier and thermal initiator. The predictive capacity is tested by tuning the model to one set of experimental data, then trying to predict results from a further perturbed experiment, with no further tuning. The results of this study indicate that the model is able to capture the main process trends as well as providing an accurate representation of quantitative data.

Iterative batch-to-batch control of particle size distribution in semi-batch emulsion polymerisation

Abstract In this article, the control of particle size distribution (PSD) is discussed as a means for the inferential control of the rheology of emulsion polymers. A controllability assessment is presented through a consideration of the process mechanisms to illustrate the attainability or otherwise of bimodal PSD. The suitability of a batch-to-batch iterative feedback PSD control is demonstrated, which could act in addition to any in-batch feedback control, the latter being less feasible in certain cases, as argued in this article.

Mechanistic modelling of aggregation phenomena in population balances of granulation

Abstract This paper addresses the development of population balance models for granulation processes. The novelty in the present approach is two fold: firstly, the employment of a multi-dimensional population balance; and secondly, the exploitation of advancements in the underlying science to develop mechanistic models for the various rate processes.

State estimation for dynamic prediction of hydrate formation in oil and gas production systems

Abstract Since oil and gas production is moving to deeper waters, subsen pipelines are being subjected to higher pressures and lower temperatures. Under such conditions, the formation of hydrates is promoted. Hydrates are solid, non-flowing compounds of gas and water whose formation can cause line blockages, with the consequent economical losses and safety risks. The increasing hydrate formation propensity suggests the necessity to predict the possibility of hydrate formation in on-line operation so as to take preventive control actions and thereby provide flow assurance. Although a detailed dynamic model will enable the prediction of the possibility of hydrate formation, model inaccuracies and process disturbances will make this prediction less accurate. The usage of key available measurements will enable to address these disadvantages. The aim of this paper is to develop a combined state and parameter estimator for this process, by combining a dynamic model with available measurements.

SENSITIVITY OF BIFURCATION TRAITS TO MODEL PARAMETERS IN POLY-ß-HYDROXYBUTRYRATE PRODUCTION

Abstract There is growing interest in the chemical engineering community in the development of environmentally friendly products such as biopolymers. Poly-s-hydroxybutyrate (PHB) is an important biopolymer whose commercial application is still limited due to the high costs associated with its production. This paper examines a continuous bioreactor proposed for the production of PHB. The ***in.uence of minor variations in the kinetic parameters of a simple cybernetic model formulated is examined. It is shown that minor variations in these parameters can have ***signi.cant impacts on the bifurcation analyses obtained.