Comments on “Optimal Use of Mixed Catalysts for Two Successive Chemical Reactions”

Abstract

The paper "Optimal use of mixed catalysts for two successive chemical reactions" by Jackson was first presenting an analytical solution for the plug flow reactor catalyst blend problem. However, the exact optimal value of the problem was not given, which has caused confusion and inaccuracies in the subsequent literatures. As a supplement and correction, this study gives the optimal solutions and optimal objective values analytically for the cases when the reactor length equals 1 and 12. These results are also verified numerically using the time-scaling method.

An effective pseudospectral optimization approach with sparse variable time nodes for maximum production of chemical engineering problems

“…Using the method of dynamic programming, Dadebo et al obtained a performance index of 0.048 05 . Recently, Li et al derived the theoretical solution of this problem and the corresponding optimal value was 0.048 055 68 …”

“…Figure displays the optimal control trajectories of the two methods under different subintervals. The dotted line, which is the analytical solution obtained by Li and Liu, is also plotted to make a comparison. It can be seen that the variable time nodes and obtained by SVTN‐GPM are the jumps of the control.…”

“…With the growing appreciation for dynamic simulation in computer aided chemical process engineering, accurate dynamic optimization methods have become more and more important . Many chemical dynamic problems focus on maximizing the yield of a product by finding the corresponding control and state trajectories under some constraints arising from the physical bounds on the control as well as state and safety limitations and environmental regulations . Simple dynamic optimization problems (DOPs) can be solved through the so‐called indirect method based on the first order optimality conditions of variation.…”

An iterative multi-objective particle swarm optimization-based control vector parameterization for state constrained chemical and biochemical engineering problems

“…(9) Compute the new position of each particle with Eqs. (10) If i x goes beyond its search boundaries, set the decision variable the value of its corresponding lower or upper boundary and change to the opposite direction of the particle Perform an mutation in the population Evaluate all the particles in the population Update pBest for each particle. If the current solution is dominated by the current pBest , the pBest is retained; otherwise, the particle position is updated.…”

“…Since the theoretical solutions are not prone to be obtained, many researchers devoted themselves to seeking numerical solutions using control vector parameterization (CVP) or complete (control and states) parameterization, a technique that converts dynamic problem into a finite dimensional nonlinear programming (NLP) problem by discretizing control variables or both control and state variables [6,7]. Though gradient-based algorithms [8][9][10][11] are accurate and effective, the gradient is not always available for complex NLP problem, and additionally, the algorithms are easy to be trapped into a local optimum for multimodal problem. Furthermore, the resulting NLP problem is often more difficult to be solved when the system contains the state constraints or other forms of constraints.…”