Khalid Alhumaizi

Comparison of finite difference methods for the numerical simulation of reacting flow

Abstract The scope of this paper is to give a comparative evaluation of several competitive finite difference schemes developed to solve a one-dimensional convection-reaction problem. Numerical results show that compared with traditional first- or second-order difference schemes, the high-resolution techniques such as flux-corrected transport (FCT), the monotone upstream scheme for conservation laws (MUSCL) and weighted essentially non-oscillatory (WENO) schemes are efficient to track steep moving fronts and are essential for cases which use small numbers of grid points. The Superbee flux corrector is found to be the most appropriate for simulating the sharp fronts of the reactor model.

Numerical analysis of a reaction-diffusion-convection system

Abstract This paper is concerned with the numerical analysis of the behavior of a homogeneous tubular reactor in which a cubic autocatalytic reaction is coupled to diffusion and convection transport. The set of one-dimensional partial differential equations describing the reaction–diffusion–convection system is analyzed using different standard reduction techniques (finite difference, orthogonal collocation, and finite element methods) within the framework of the method of lines. Both steady state and dynamic behaviors of the system are considered. Special high-resolution finite difference methods such as essentially non oscillatory (ENO) and total variation diminishing (TVD) are applied to the convectively dominant case. The calculation results that special high-resolution schemes such as ENO are essential to track efficiently steep moving fronts exhibited by the strongly convective problems. The strengths and limitations of the different numerical schemes considered are examined and discussed.

Model reduction and robust control of multi-stage flash (MSF) desalination plants

An orthogonal collocation method is used for the reduction of a large nonlinear model of a multi-stage flash (MSF) desalination plant. The real plant located in Saudi Arabia consists of 19 stages in the heat recovery section and three in the heat rejection section. It is shown that three collocation points, i.e., two for the heat recovery section and one for the heat rejection section, are sufficient for a good representation of the full-order model for both steady-state and dynamic behavior. The reduced model is then used for a robust controller design of the plant using a constrained nonlinear model predictive control (NLMPC) strategy. Numerical simulations show that the controlled system obtained when the reduced model is used for output prediction yields the same performances as with the full-order model but with a considerable reduction in the computational time and a much easier tuning of the controller.

Effect of control loop configuration on the bifurcation behavior and gasoline yield of industrial fluid catalytic cracking (FCC) units

This paper addresses the main problem associated with controlling the industrial fluid catalytic cracking units (FCC); the stabilization of the unstable high gasoline yield operating points. Six simple feedback control strategies are proposed using combinations of two manipulated and two controlled variables. The static and dynamic bifurcation behavior of the controlled FCC unit are examined in order to define the region of the controller gain values at which the desired operating point is globally stable. The results show that the performance of these units depends strongly on the structure of the control loop configuration. The analysis leads to quite useful insights on how to achieve stable operation of the process with high gasoline yield.

Biodegradation of substitutable substrates in a continuous bioreactor with cell recycle: A study of static bifurcation

The static bifurcation of an unstructured model of a continuous bioreactor with cell recycle involving the biodegradation of mixed wastes is analyzed using the singularity theory. The biodegradation of the dissimilar substrates follows Andrews inhibitory kinetic models. It is shown that the steady state locus of the model can be described by a polynomial of seven order. The stability analysis shows that the model exhibits a number of singularities, including hysteresis and pitchfork that occurs at clean feed conditions. It is also shown that the model cannot predict isola, mushroom, or winged cusp singularities. The effect of the model kinetic and operating parameters on its stability characteristics are also discussed.

Competition of plasmid-bearing and plasmid-free organisms in a chemostat: A study of bifurcation phenomena

The stability of the classical Levin-Stewart model that describes the competition between plasmid-bearing and plasmid-free populations in a chemostat is revisited using a combination of bifurcation theory and continuation techniques. Simple analytical conditions are derived that describe the conditions for the coexistence of the competing cells and for the safe operation of the chemostat. The ability of the model to predict the coexistence of the competing cells in an oscillatory mode is also studied. Analytical results with respect to arbitrary growth kinetics are derived that set the necessary conditions for the existence of Hopf points in the model as well as for the occurrence of a number of Hopf degeneracies. These general conditions are applied to Monod/Haldane substrate inhibition growth models. Practical branch sets in terms of model parameters are readily constructed for Monod-Monod, Monod-inhibition, inhibition-Monod and inhibition-inhibition cases. The dynamic analysis, on the other hand, allows the identification of regions of one and two Hopf points predicted by the model. The combination of results of both static and dynamic bifurcation allows the delineation of a total of 45 qualitatively different regions and helps to construct a useful picture, in the multidimensional parameter space, of the different behaviors predicted by the model. Practical criteria are also set for the comparison between these regions, and for the study of the effects that various limiting substrates can have on recombinant culture stability and as regards the desired rate properties to be looked for in screening media formulations.

Optimization-based periodic forcing of RO desalination process for improved performance

AbstractThe performance of a tubular reverse osmosis (RO) process for water desalination is investigated using periodically forced feed parameters. The study was performed using a dynamic model that was developed and validated in a previous work. Simultaneous forcing of feed pressure and flow rate were studied. Fully symmetric rectangular pulses were used for input forcing because of their applicability for digital control implementation. It was found that the simultaneous periodic operation of the RO inputs improves its performance in the sense of higher permeate flow rate and reduced salt concentration. Increasing the pressure forcing amplitude will further enhance the performance; however, the attainable performance is limited by the constraints on the operating pressure. Depending on the RO unit constraints and characteristics, a maximum increase in permeate flow rate up to 42% and reduction in salt concentration of about 20% could be obtained.

Robust control of industrial multi-stage flash desalination plants

The paper investigates the use of non-linear model predictive control (NLMPC) as an advanced control strategy for the control of multi-stage flash (MSF) desalination plants. For this purpose, a comprehensive non-linear dynamic model was developed for the MSF plant and was validated with actual plant data. A control structure for the plant was then developed from which two control objectives were selected. One control objective is to maximize the distillate product and the other is to maximize the performance ratio while maintaining the manipulated variables in both cases under tight hard constraints. The NLMPC algorithm was then tested with these two objectives for both nominal and non-nominal model cases. In the non-nominal case the effects of parametric modeling error on the NLMPC performance were examined. Closed-loop simulations show that the advanced control strategy allows good control performance and substantial energy savings even when the plant is under the influence of unavoidable model uncertainties. The performances of the NLMPC algorithm were compared with a conventional proportional-integral (PI) controller.

Spatiotemporal patterns in a two-dimensional reaction-diffusion-convection system: Effect of transport parameters

We report on spatiotemporal patterns emerging in a system consisting of an autocatalytic reaction in a continuous flow tubular reactor. The autocatalyst undergoes a mutation and the resulting mutant is assumed to compete with the original autocatalyst. The system is modeled by a set of three partial differential equations with eight design parameters. We examine and discuss the effect of transport parameters, reactor inlet boundary condition, and reactor aspect ratio on the dynamics of the system. The results show a variety of regimes going from steady propagation of a reaction front to the development of chemical waves in the form of pulsating, more or less regularly, reaction front.

MODEL-BASED ENERGY ANALYSIS OF AN INTEGRATED MIDREX-BASED IRON/STEEL PLANT

This article presents modeling and simulations of an integrated plant for the production of steel using the direct reduced iron (DRI)/electric arc furnace (EAF) route. In a previous work (Alhumaizi et al., 2012), a comprehensive mathematical model of an iron plant based on MIDREX technology was developed, validated, and simulated. In this article, the model is extended to account for an empirical model of an EAF plant. Numerical simulations were carried out for the effect of different operating parameters of the integrated plant. Useful profiles as well as a summary table were compiled to illustrate the results of the sensitivity analysis. Key performance indicators of the plant include metallization degree and operating costs of the DRI and of the EAF as well as the total operating cost of the plant. The analysis allows the identification of operating parameters that can lead to a more profitable operation of the plant.