M.A. Soliman

A tridiagonal matrix model for multistage flash desalination plants

Abstract An efficient and reliable technique has been developed to solve the large system of non-linear equations which describe the behaviour of multistage flash (MSF) desalination plants. The new method depends on decomposition of the equations, after linearization, into subsets which are grouped by type rather than by stage, followed by formulation of the enthalpy balance equations into a tridiagonal matrix (TDM) form which is solved by the Thomas algorithm. The computer program developed in this work converged rapidly over a wide range of conditions, showing significant reduction in run times relative to those required by previous stage-by-stage approaches. Both recirculatory and once-through type plants have been simulated for different practical operating situations. The development of the linearized equations is discussed in detail, all physical property correlation are documented and full details of a numerical example given.

On the non-monotonic behaviour of methane—steam reforming kinetics

Abstract A parameteric study on the rate expression recently developed by Xu and Froment (1989a, A.I.Ch.E.J. 35 , 88-96) is carried out over a wide range of parameters. The analysis of this rate expression has shown a non-monotonic dependence of the reaction rate upon steam partial pressure which explains the contradictions between the rate expressions a available in the literature, that is the prediction of positive, as well as negative effective reaction order with respect to steam. A simplified pseudo-homogeneous model with a constant effectiveness factor, with Xu and Froments rate expression was used to investigate the implications of the non-monotonic kinetics on the performance of steam reformers. The main implication was also checked using a heterogeneous model that represents very closely industrial steam reformers.

Optimal feedback control for linear-quadratic systems having time delays†

The optimal feedback control law for linear-quadratic problems with time delays in both the state and the control is derived. Results are given for both multiple and time-varying delays. Computational schemes for pre-computing the Riccati partial differential equations are discussed and two examples worked out to illustrate the results.

Simulation of steam reformers for methane

A model is developed for industrial steam reformers for both top fired and side fired furnaces. The catalyst tube model is a one-dimensional heterogeneous model with intra-particle diffusional resistances. The two point boundary value differential equations of the catalyst pellets are solved using a modified novel orthogonal collocation technique to obtain the effectiveness factor variation along the length of the reactor. The side fired furnace equations are algebraic equations, the top fired furnace equations are two-point boundary value differential equations which are solved using the orthogonal collocation technique. A recently developed more general rate expression is used. The model performance is checked against industrial steam reformers. The model is used to investigate the effect of various parameters on the behaviour of the catalyst tubes and the furnace. The effectiveness factor variation along the length of the catalyst tube is also analysed.

Avoidance of flammability and temperature runaway during oxidative dehydrogenation using a distributed feed

Abstract A relatively simple model has been used to simulate the oxidative dehydrogenation of ethane to ethylene in a fixed-bed reactor. Full account of the kinetics of the main oxygenconsuming reaction have been incorporated in the model using previously published kinetics for the reaction over a Mo–V–Nb catalyst. Use of a distributed oxygen feed enables the problem of the feed flammability to be avoided and in addition, shows a significant improvement on reactor performance in terms of ethylene yield and selectivity. A distributed oxygen feed also overcomes the problem of reaction runaway and enables operation to be achieved over a wider range of reactor parameters.

The optimal control of processes containing pure time delays—I necessary conditions for an optimum

Abstract The optimal control problem for processes modelled by ordinary differential equations containing pure time delays is treated. A survey of previous work is given, and the necessary conditions for optimality are extended to a more general class of processes than previously covered. Various computational techniques are discussed, and a conjugate gradient control vector iteration algorithm is proposed and tested on a CSTR example. “Optimal” start-up policies are found for both constant and variable time delays.

Process sensitivity studies of the Westinghouse sulfur cycle for hydrogen generation

Abstract The effect of variations of acid concentration, pressure and temperature on the thermal process efficiency of the Westinghouse Sulfur Cycle was examined using the University of Kentuckys HYDRGN program. Modifications to the original program were made to duplicate the process flowsheet and take into account combined-cycle heat-to-work efficiencies for electrochemical work requirements, aqueous solutions, and heat-of-mixing effects. A total of 125 process variations were considered (acid concentration: 50–90 w/o; pressure: 15–750 psia; temperature: 922 K (1200°F)-1366 K (2000°F)). The methods of analysis, results, and conclusions are presented.

A spline collocation method for the solution of diffusion—convection problems with chemical reactions

A spline collocation method which can be considered as an extension of the dead-zone concept of Paterson and Cresswell (1971 is developed. The method is applied to a system of consecutive first-order reactions in a catalyst particle, to an isothermal tubular reactor and to a tubular reactor with axial dispersion for an exothermic chemical reaction

Mathematical modelling of diffusion and reaction for gas-solid catalytic systems with complex reaction networks. Negative effectiveness factors

The concept of effectiveness factor (@h) as a measure of diffusional limitations for gas-solid catalytic reactions has gone a long way since the time of Thiele. Multiple steady states giving rise to multiple values of (@h) for the same bulk conditions, and @h values greater than unity have been widely reported in the literature in the last three decades. In this paper an interesting phenomenon associated with the effectiveness factors (@h) for industrial gas-solid catalytic reactions is reported, that is the possible occurrence of negative values of @h for certain intermediate components. This physically means that diffusional resistance can also reverse the direction of the net production or consumption of intermediate components in consecutive and/or reversible reaction networks. It is shown both numerically and analytically that the results represent real physical phenomenon and not artefacts resulting from numerical problems or model simplifications. Two industrially important reactions are considered, namely, the steam reforming of natural gas which is a highly endothermic reaction and the partial oxidation of O-xylene to phthalic anhydride which is a highly exothermic reaction.

Hydrogen production via thermochemical cycles based on sulfur chemistry

Abstract A class of closed thermochemical cycles for hydrogen production based on sulfur chemistry is presented. This class is described by the following set of chemical reactions: M + H 2 O ⇄ MO + H 2 (low temperature) MO +0.5 S ⇄ M +0.5 SO 2 (high temperature) M′O +1.5 SO 2 ⇄ M′SO 4 +.5 S (low temperature) M′SO 4 rlarr2; M′O + SO 2 +0.5 O 2 (high temperature) Experimental investigation of some of the reactions is presented. Thermodynamic analysis indicates efficiencies of the range of 40–50% and sometimes higher. Not all of the reactions in the proposed cycles have been verified in the literature or through experimentation.