We now address some simulation and convergence issues in the design of reactive distillation as the process configuration changes. The relaxation approach5 is taken here. For a given reactive distillation design (e.g., number of reactive, rectifying, and stripping trays feed flowrates and feed tray locations), a control system is set up to drive the process toward the design specifications. Given the initial guesses for tray compositions, the set of ordinary differential equations is integrated from the initial conditions until a steady state is reached. Note that the control structure for relaxation is very different from the one in control practice. The reason is that perfect flow control can be achieved in a computer simulation so the problem of stoichiometric imbalance does not occur. For example, for the type Ip system shown in Figure 17.2a with the product as the lightest component, all four external flows (inlet and outlet streams) are under flow control. The composition of one...
For the ideal chemical cases, a dynamic model is simulated in Matlab. This model consists of ordinary differential equations for tray compositions and algebraic equations for vapor-liquid equilibrium, reaction kinetics, tray hydraulics, and tray energy balances. The dynamic model is used for steady-state design calculations by running the simulation out in time until a steady state is achieved. This dynamic relaxation method is quite effective in providing steady-state solutions, and convergence is seldom an issue.
Simultaneous solution of the very large set of nonlinear and algebraic equations that describe a reactive distillation column is difficult, especially with the high degree of non-linearity attributable to reaction kinetics. The relaxation method is efficient and robust in solving this large set of equations. This method is used to calculate steady-state mole fractions and temperature profiles throughout the column. In general, relaxation methods use the equilibrium stage model equations in unsteady-state form and integrate them numerically until the steady-state solution is found (all time derivatives 0). Liquid holdups on trays are assumed constant, that is, instantaneous hydraulics. The net reaction rate for component j on tray n in the reactive zone is given by
Regime analysis is based on the consideration that, generally, biochemical processes involve a series of steps, some being mass or heat transfer by convection, some being diffusive mechanisms (activated or not), and others being chemical reaction steps. In the latter case, a mass-transfer mechanism is superimposed, since molecules must encounter one another in order to react, and usually a heat effect will accompany the reaction. Depending on whether these steps take place in parallel or in series and on the relaxation time for each step (185), the rate of the total process is often given as the rate of one single step. But the equilibrium between all the individual rates can be (and usually is) upset by a change in scale. This is to be expected, because a change in scale will not bring a change in the physicochemical or kinetic parameters (scale-insensitive variables), but will affect the overall convective mass and
First, the Wang-Henke method is used to converge the flowsheet (MESH equations) to a certain degree (actually to the point at which the objective function fluctuates). Second, the temperature and composition profiles are fed to a dynamic program that is integrated until temperatures and compositions converge (relaxation approach).
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