Chemical processing numerical computations

Before the advent of modem computer-aided mathematics, most mathematical models of real chemical processes were so idealized that they had severely limited utility— being reduced to one dimerrsion and a few variables, or Unearized, or limited to simplified variability of parameters. The increased availability of supercomputers along with progress in computational mathematics and numerical functional analysis is revolutionizing the way in which chemical engineers approach the theory and engineering of chemical processes. The means are at hand to model process physics and chenustry from the... 

Any numerical experiment is not a one-time calculation by standard formulas. First and foremost, it is the computation of a number of possibilities for various mathematical models. For instance, it is required to find the optimal conditions for a chemical process, that is, the conditions under which the reaction is completed most rapidly. A solution of this problem depends on a number of parameters (for instance, temperature, pressure, composition of the reacting mixture, etc.). In order to find the optimal workable conditions, it is necessary to carry out computations for different values of those parameters, thereby exhausting all possibilities. Of course, some situations exist in which an algorithm is to be used only several times or even once. 

Specifically, in Chapter 3 we create a surface for a transcendental function /(a, y) as an elevation matrix whose zero contour, expressed numerically as a two row matrix table of values, solves the nonlinear CSTR bifurcation problem. In Chapter 6 we investigate multi-tray processes via matrix realizations in Chapter 5 we benefit from the least squares matrix solution to find search directions for the collocation method that helps us solve BVPs and so on. Matrices and vectors are everywhere when we compute numerically. That is, after the laws of physics and chemistry and differential equations have helped us find valid models for the physico-chemical processes. 

If there is a question of losing a product such as an amine chemical, say diethanolamine, in an amine gas absorber overhead KO vessel, use this recommended 150-pm liquid particle sizing in the gas phase. I have personally witnessed hundreds of thousands of dollars of annual amine chemical losses in numerous amine gas-treating plants due to poor overhead KO drum design. Spend a few more very well justified dollars at design time and realize a payout of only a few weeks for this added expense I have witnessed 1.5 lb amine loss per million scf gas processed in an amine absorber overhead KO drum. For a 150-mmscfd gas plant absorber, 355 days per year production, at 1.20 per pound amine chemical cost, this computes to a 95,750 yearly loss. This is not a new discovery, as many an amine absorber installed in the 1950s had several trays in the tower top section dedicated to a water-wash section. I am confident that equal losses can be computed for other chemicals or petroleum products in similar fractionation overheads. 

Thus, the main problems concern firstly, the input of the reaction mechanism into the computer (problem of chemical notation) and secondly, the processing of the reaction mechanism itself (problem of chemical compiler). Let us point out that the knowledge of tile matrix of stoichiometric coefficients allows us to compute the partial derivatives of the reaction rates with respect to the concentrations, i.e. a Jacobian matrix which has been shown to play a central role in the numerical computations. 

To analyze the transport and retention of chemical contaminants in groundwater flowing through soils, experimental and theoretical studies generated several reliable models. Diverse numerical methods have been applied to solve the governing equations efficiently. Some computer models include the simulation of physical and chemical processes. 

Carnahan, B., and J. O. Wilkes. Numerical Solution of Differential Equations—An Overview in Foundations of Computer-Aided Chemical Process Design, AIChE, New York (1981). 

Unsteady-state or dynamic simulation accounts for process transients, from an initial state to a final state. Dynamic models for complex chemical processes typically consist of large systems of ordinary differential equations and algebraic equations. Therefore, dynamic process simulation is computationally intensive. Dynamic simulators typically contain three units (i) thermodynamic and physical properties packages, (ii) unit operation models, (hi) numerical solvers. Dynamic simulation is used for batch process design and development, control strategy development, control system check-out, the optimization of plant operations, process reliability/availability/safety studies, process improvement, process start-up and shutdown. There are countless dynamic process simulators available on the market. One of them has the commercial name Hysis [2.3]. 

For ease of fabrication and modular construction, tubular reactors are widely used in continuous processes in the chemical processing industry. Therefore, shell-and-tube membrane reactors will be adopted as the basic model geometry in this chapter. In real production situations, however, more complex geometries and flow configurations are encountered which may require three-dimensional numerical simulation of the complicated physicochemical hydrodynamics. With the advent of more powerful computers and more efficient computational fluid dynamics (CFD) codes, the solution to these complicated problems starts to become feasible. This is particularly true in view of the ongoing intensified interest in parallel computing as applied to CFD. 

Throughout this book, we have seen that when more than one species is involved in a process or when energy balances are required, several balance equations must be derived and solved simultaneously. For steady-state systems the equations are algebraic, but when the systems are transient, simultaneous differential equations must be solved. For the simplest systems, analytical solutions may be obtained by hand, but more commonly numerical solutions are required. Software packages that solve general systems of ordinary differential equations— such as Mathematica , Maple , Matlab , TK-Solver , Polymath , and EZ-Solve —are readily obtained for most computers. Other software packages have been designed specifically to simulate transient chemical processes. Some of these dynamic process simulators run in conjunction with the steady-state flowsheet simulators mentioned in Chapter 10 (e.g.. SPEEDUP, which runs with Aspen Plus, and a dynamic component of HYSYS ) and so have access to physical property databases and thermodynamic correlations. 

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