Sequential solutions energy balance

The essential differences between sequential-modular and equation-oriented simulators are ia the stmcture of the computer programs (5) and ia the computer time that is required ia getting the solution to a problem. In sequential-modular simulators, at the top level, the executive program accepts iaput data, determines the dow-sheet topology, and derives and controls the calculation sequence for the unit operations ia the dow sheet. The executive then passes control to the unit operations level for the execution of each module. Here, specialized procedures for the unit operations Hbrary calculate mass and energy balances for a particular unit. FiaaHy, the executive and the unit operations level make frequent calls to the physical properties Hbrary level for the routine tasks, enthalpy calculations, and calculations of phase equiHbria and other stream properties. The bottom layer is usually transparent to the user, although it may take 60 to 80% of the calculation efforts. 

One feasible network would correspond to the cold streams Cl, C8, and C9 diverted to suitable jacketed reactor compartments, as the simple network in Fig. 14 shows. The hot streams not shown in this network are matched directly with cooling water (CW), and the amount of steam used here is very small. Note that this network would require the same minimum utility consumption predicted by the solution of (PIO). It can be inferred that the network in Fig. 14 is equally suitable for both the simultaneous and sequential solutions. In fact, Balakrishna and Biegler (1993) showed that, for exothermic systems in which the reactor temperature is the highest process temperature, the pinch point is known a priori as the highest reactor temperature (in this case, the feed temperature) and the inequality constraints in (PIO), Qh 2h () ). F G P. can be replaced by a simple energy balance constraint. This greatly reduces the computational effort to solve (PIO). 

To obtain a solution for the material and energy balances in a flowsheet by the sequential modular method, you must partition the flowsheet, select tear streams, nest the computations, and thus determine the computation sequence. 

EXAMPLE 5.8 Solution of Material and Energy Balances Using a Sequential Modular-Based Flowsheeting Code... 

Prepare a block diagram of the modules involved in solving the material and energy balances for the extraction process used in a refinery for the production of normal paraffins shown in Fig. P5.18. Which additional modules not in Fig. 5.9a would you need Also indicate what streams might be cut for a sequential modular solution of the material and energy balances. 

One very simple example is the solution of the steady-state model of distillation columns. Avoid sequentially solving the liquid-vapor equilibria and the material and energy balances, stage by stage from top to bottom, while iterating toward convergence through an overall material balance in order to achieve consistency in input/output flow rates. 

As is true in the design of many separation techniques, the choice of specified design variables controls the choice of the design method. For the flash chamber, we can use either a sequential solution method or a simultaneous solution method. In the sequential procedure, we solve the mass balances and equilibrium relationships first and then solve the energy balances and enthalpy equations. In the simultaneous solution method, all equations must be solved at the same time. In both cases, we solve for flow rates, compositions, and temperatures before we size the flash drum. 

In the sequential solution procedure, we first solve the mass balance and equilibrium relationships, and then we solve the energy balance and enthalpy equations. In other words, the two sets of equations are uncoupled. The sequential solution procedure is applicable when the last degree of freedom is used to specify a variable that relates to the conditions in the flash drum Possible choices are ... 

If the temperature of the feed to the drum, Tp, is the specified variable, the mass and energy balances and the equilibrium equations must be solved simultaneously. You can see from the energy balance, Eq. (2-7 why this is true. The feed enthalpy, hp, can be calculated, but the vapor and liquid enthalpies, and depend upon x, which are unknown. Thus a sequential solution is not possible. 

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