Determination of optimal reactor type

Optimization of complex reactor networks—I. Isothermal operation

Abstract: In this paper, the synthesis problem of complex nonisothermal reactor networks is addressed. The focus is on developing a superstructure of alternatives for the nonisothermal reactor system, and subsequently formulate and solve the synthesis problem according to the proposed general structure. The nonisothermal case features alternatives related to the type of temperature control for the reactors and includes options for directly or indirectly intercooled or interheated reactors. The approach is applicable to any homogeneous exothermic or endothermic complex reaction and the synthesis problem, formulated as a mixed integer nonlinear programming (MINLP) problem, can handle both thermodynamic and economic objective functions. The solution of the resulting MINLP problem provides information about the optimal type of temperature control, the optimal temperature profile, the feeding, recycling and bypassing strategy as well as the optimal type and size of the reactor units (CSTR, PFR) to be used. The efficiency of the method is illustrated with three different examples considering complex nonisothermal reaction mechanisms.

A superstructure based approach to chemical reactor network synthesis

Abstract: Frequently the product mix in a reacting system is influenced by both heat and mixing effects in the reactor. This paper presents a nonlinear programming (NLP) formulation for optimally generating reactor networks that would produce the desired effects, given a kinetic mechanism and expressions for the reaction rate. Using a generalized configuration of recycle reactors and heat exchangers (superstructure) as a basis, the NLP is able to extract the optimal subnetwork of units that would maximize an arbitrary objective function defined over a given kinetic scheme. Thus mixing and heat effects that affect reactions occurring in the homogeneous phase are taken into account. The resulting model and adjoint equations of this formulation form a two-point boundary value problem that interfaces with an efficient optimization strategy. Decisions representing network structure, reactor type and the amount of heat addition are made through continuous parameters in the model. The superstructure allows for serial and parallel connections involving reactor units, and is therefore fairly general. Since the method is equation based and since there are numerous ODE solvers it can be applied to large kinetic mechanisms with almost any objective function. Literature examples are presented and solved in order to demonstrate the effectiveness of this approach.

Optimization Framework for the Synthesis of Chemical Reactor Networks

Abstract: The reactor network synthesis problem involves determining the type, size, and interconnections of the reactor units, optimal concentration and temperature profiles, and the heat load requirements ...

Scoping and screening complex reaction networks using stochastic optimization

Abstract: A systematic methodology to target the performance of chemical reactors with the use of stochastic optimization is presented. The approach employs a two-level strategy where targets are followed by the proposition of reactor configurations that match or are near the desired performance. The targets can be used for synthesis and retrofit problems, as they can provide the incentives to modify the operation, and ideas in developing the reactor design. The application of stochastic optimization enables confidence in the optimization results, can afford particularly nonlinear reactor models, and is not restricted by the dimensionality or the size of the problem.

The application of the attainable region analysis to comminution

Abstract: The aim of any comminution circuit is to produce material of a desired particle size distribution (PSD) at a minimum operational cost. Currently, the comminution process is energy intensive and operates at very low efficiency when the input energy is compared to the breakage achieved. The attainable region (AR) technique has been successfully used to solve optimization problems simultaneously with the process synthesis formulation of reactor systems. The AR looks at the fundamental processes of a given system and determines all the possible outputs to which the objective function can be applied and an optimal process solution selected. Particle breakage, separation (classification) and mixing are identified as the three fundamental processes of interest taking place during comminution. Breakage and mixing processes are used in this paper to illustrate the applicability of the AR theory in comminution. We develop a fundamentally based model which is equipment independent to describe breakage. Specific energy is the independent variable and the production of particles with a certain PSD is the objective function. We use geometric construction to represent this PSD as a point in an n -dimensional space in relation to an input specific energy. Output PSDs are dependent on the input PSDs, allowing connectivity of the batch grinding stages to form a pseudo-continuous process. Specific energy is used as the control variable to obtain sharper product PSDs. It is shown that the same net energy consumed in the system can produce different product PSDs. Therefore, this implies that the design of comminution circuits should achieve better control of the specific energy. Once the candidate AR is constructed, operational process targets can be defined more accurately. This establishment of targets permits a measure of the actual process efficiency against a theoretical target. The advantage of the AR method lies in its ability to develop not only the performance of the optimal circuit but also the operational conditions to be used in the optimal process circuit. This also answers the process synthesis question of the type of equipment to be used which is a function of the specific energy.

Quasi-linearization, non-linear boundary value problems and optimization

Abstract: A quasi-linearization technique which was developed by B ellman and K alaba is used to solve non-linear differential equations of the two-point boundary value type encountered in chemical engineering. The non-linear equation is represented by a sequence of linear equations which converges quadratically to the solution of the non-linear equation in the sense that the error of any iteration is approximately the square of the error of the preceding iteration. This technique can be used to solve a variety of engineering problems of the multi-point boundary value type; in particular, it can be used to overcome the boundary value difficulties in the calculus of variation. The advantage of this technique is its rapid covergence to the solution of the non-linear equation. With very poor starting values of the unknown initial conditions the optimum pressure profile in a tubular reactor has been obtained in four iterations.