C.C. Pantelides

A general framework for the integration of computational fluid dynamics and process simulation

Abstract Computational fluid dynamics (CFD) and process simulation are widely used in the process industry. The two technologies are largely complementary, each being able to capture and analyse some of the important process characteristics. Their combined application can, therefore, lead to significant industrial benefits. This is especially true for systems, such as chemical reactors, in which steady-state performance, dynamics and control strategy depend on mixing and fluid flow behaviour. This paper presents a new approach for the integration of the capabilities of CFD technology and process simulation via a general interface that allows the automatic exchange of critical variables between the two packages, leading to a simultaneous solution of the overall problem. The approach applies to both steady-state and dynamic problems. The feasibility of the approach and its first practical implementation are demonstrated by integrating a widely used CFD package (Fluent 4.5, by Fluent Inc.) within a general-purpose advanced process simulator (gPROMS 1.7, by Process Systems Enterprise Ltd. (1999)). One case study involving a batch reactor is used to illustrate the ability of the combined tool to provide information on the detailed interactions between fluid mechanics, heat transfer, reaction and control strategy, and to provide insights on important design and operational decisions.

An Interior Point Algorithm for Computing Saddle Points of Constrained Continuous Minimax

The aim of this paper is to present an algorithm for finding a saddle point to the constrained minimax problem. The initial problem is transformed into an equivalent equality constrained problem, and then the interior point approach is used. To satisfy the original inequality constraints a logarithmic barrier function is used and special care is given to step size parameter to keep the variables within permitted boundaries. Numerical results illustrating the method are given.

Optimal experimental design based on global sensitivity analysis

Abstract The starting values considered for the model parameters strongly affect standard techniques for experimental design. When these values are far from the optimal ones, poor quality experiments are achieved or several steps are required resulting in a large experimental burden. Here, a novel criterion based on global sensitivity analysis, and therefore independent of the parameters values, is presented. In order to illustrate the performance of this methodology, a semicontinuous bioreactor is considered as a case study.

Optimal design of hybrid controllers for hybrid process systems

The design of controllers for processing systems has mostly concentrated on the purely continuous and purely discrete cases. However, most chemical processes exhibit hybrid characteristics. This work presents a model-based approach to the controller synthesis problem for hybrid processing systems. A parameterised representation for hybrid controllers is presented that generalises the purely discrete and purely continuous cases. A discrete/continuous mathematical model of the process and the control system is constructed. Then, the mathematical formulations of the control system design and performance verification problems are introduced. The former can be used to design a controller that behaves optimally with respect to a given finite set of disturbance scenarios. The latter, given a controller, determines worst-case disturbance inputs that render the system infeasible or suboptimal. The two problems are finally combined into a two-stage, iterative design algorithm. A simple example is used to illustrate the potential of the proposed approach.

Dynamic Oil and Gas Production Optimization via Explicit Reservoir Simulation

Dynamic oil and gas production systems simulation and optimization is a research trend with a potential to meet the challenges faced by the international oil and gas industry, as has been already demonstrated in a wide variety of publications in the open literature. The complex two-phase flow in reservoirs and production wells governs fuel transport, but is mostly handled by algebraic approximations in modern optimization applications; the true reservoir state variable profiles (initial/boundary conditions) are not known. Integrated modeling and optimization of oil and gas production systems treats oil reservoirs, wells and surface facilities as a single (yet multiscale) system, focusing on computing accurate reservoir and well state variable profiles, useful for optimization. This paper discusses a strategy for interfacing reservoir simulation (ECLIPSE®) with equation-oriented process optimization (gPROMS®) and presents a relevant application.

Risk analysis and robust design under technological uncertainty

Technological innovation in process design often leads to increased technological risk arising from incomplete knowledge. We propose a systematic approach to manage this risk using mathematical models that are sufficiently detailed to quantify risk. Global sensitivity analysis is used to determine the complete probability distributions for the key performance indicators of the process, thereby allowing informed decisions to be taken regarding the acceptability of the risk inherent in a given design. It also produces global sensitivity indices which allow the identification of the critical uncertain parameters on which additional R&D needs to be foused if the risk is deemed to be unacceptably high. If the risk is acceptable, then scenario-based approximation is used to handle the residual uncertainty in the critical parameters. Issues regarding the robust and efficient solution of problems involving large numbers of scenarios based on nonlinear models with thousands of variables are considered. The methodology is demonstrated via a case study concerning the design of a catalytic tubular reactor.

An object-oriented approach to hybrid CFD/multizonal modelling

Abstract Process simulation and Computational Fluid Dynamics (CFD) are well-established tools in the process industry. The two technology are largely complementary and their combined application can lead to significant industrial benefits. In view of the advantages and limitations of process simulation and CFD modelling, it is natural to consider hybrid approaches that attempt to combine the two. This may bring great advantages in the process and product design, in the equipment scaling up and down, in the capability of optimising the process and delivering solid technical criteria for business decision making. A few works have recently appeared demonstrating the feasibility of a combined approach where critical parameters are exchanged between a CFD and a process simulation model. In this paper a novel design for hybrid CFD/multizonal modelling is considered in terms of an object oriented approach. This generic modelling approach allows an easy-to-use and effective representation of the process by a synergic use of available technologies.

Hybrid Systems Applications: An Oxymoron?

Hybrid systems are richly expressive models for a large variety of potential ap- plications. However, being so rich as to include continuous nonlinear dynamical systems, discrete-event systems and other models of computation (unite-state machines and data ow come to mind here), they are not amenable to com- putationally attractive techniques for synthesis and analysis and present hard numerical problems to simulation. Hence, applying the methods typical of this technology requires non trivial amount of approximation and abstraction. And approximation and abstraction are effective only if the domain of application is deeply understood. Thus, significant applications of hybrid systems require a great deal of work both to select the right abstraction level and to derive algo- rithms that exploit the particularities of the domain of application. In addition, one needs to motivate and document convincingly why using hybrid systems can yield better results than other techniques. In this respect, there has been an on- going debate as to what constitutes a meaningful result in applications: on one hand, novel languages for describing hybrid systems and capturing their prop- erties may be considered sophomoric exercises by experts in languages, on the other, formal verification tools that in general can handle small systems may be seen as toys for who is trying to tame entire chemical plants. On the simulation front, how to deal with discontinuities of trajectories is a major issue. Numerical analysts have been looking at these problems only recently and with a great deal of skepticism as to what can be proven rigorously. Hybrid system researchers are now getting seriously in the simulation arena exploiting what has been done in the numerical analysis arena.

Optimisation of Hybrid Processes and Hybrid Controllers

Most processes of practical interest are hybrid in nature, exhibiting both continuous and discrete characteristics. In many cases, the hybrid behaviour is a result of intrinsic physical phenomena that lead to (practically) instantaneous events such as the appearance and disappearance of thermodynamic phases, changes in flow regimes, equipment failures etc. All such events effect qualitative changes in the underlying continuous dynamics, thereby leading to hybrid macroscopic behaviour. In other cases, the hybrid nature arises from external discrete actions imposed on the process by its control system. For example, the latter may apply quantisation to convert continuous process measurements into discrete ones and/or continuous control outputs into discrete actions. Hybrid processes and hybrid controllers, and their combination, can be modelled in terms of State-Transition Networks (STNs). The system behaviour in each state is described by a different set of continuous equations (typically a mixed system of partial and/or ordinary differential and algebraic equations). At any particular time during its operation, the system is in exactly one such state. An instantaneous transition to a different state may take place if a certain logical condition becomes true. Each transition is also characterised by a set of continuous relations that determine unique values for the system variables immediately following the transition in terms of their values immediately preceding it. In this presentation, we consider mathematical formulations and techniques for the optimisation of hybrid systems described by STNs. This generally seeks to determine the time variation of a set of controls and/or the values of a set of time-invariant parameters that optimise some aspect of the dynamic behaviour of the system. The time horizon of interest may be fixed or variable, subject to specified lower and upper bounds. The equations that determine the system behaviour in each state may be augmented with additional inequality constraints imposing certain restrictions (related to safety or operability) on the acceptable system trajectories. The objective function to be minimised or maximised is usually a combination of fixed contributions (depending on the values of the time-invariant parameters) and variable contributions (depending on the system trajectory, including the variation of the controls). As an illustration, we start with simple linear systems operating in the discrete time domain, possibly involving uncertain parameters. We then proceed to consider the more complex problem of the optimisation of nonlinear hybrid systems operating in the continuous time domain.

Novel methods for the efficient evaluation of stored mathematical expressions on vector computers

Publisher Summary This chapter briefly explains some methods for the efficient evaluation of stored mathematical expressions on vector computers. It presents an approach to improving the speed of evaluation of expressions stored as binary trees. In addition, it briefly reviews the binary tree representation of algebraic expressions. Going further, the chapter describes an entirely different representation mechanism suitable for vector computers. Finally, it presents results that demonstrate the substantial efficiency gains, using two dynamic simulation examples. The chapter demonstrates that alternative approaches to evaluation of expressions represented as binary trees are worth considering. These methods can reduce the CPU demands of such evaluation to the point that they are relatively small compared with other costs involved in process simulation (for example, linear algebra computations). The method presented for the vectorization of equation residuals is of particular interest. It has been generally accepted until now that the equations arising from general process engineering models are too diverse to offer significant scope for vectorization—as opposed, for instance, to those arising from the discretization of partial differential equations in computational fluid dynamics applications. Therefore, efforts for the exploitation of novel computer architectures in process simulation have mostly focused on the use of multiple-instruction multiple-data (MIMD) type machines.