Energy balance optimization

Specify separation. If product composition or product flow requirements are not defined, determine them by material and energy balance optimization. 

Mass and energy balance (optimized process flow sheet) research, development, engineering dept. 

Optimizing Product Recovery (Material Balartce Optimization) 90 Optimizing Separation (Energy Balance Optimization) S3... 

Those based on strictly empirical descriptions Mathematical models based on physical and chemical laws (e.g., mass and energy balances, thermodynamics, chemical reaction kinefics) are frequently employed in optimization apphcations. These models are conceptually attractive because a gener model for any system size can be developed before the system is constructed. On the other hand, an empirical model can be devised that simply correlates input-output data without any physiochemical analysis of the process. For... 

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as T, and the temperature of the outer surface of the steam coil as U then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

Accordingly, serious commercially oriented attempts are currently being made to develop special gas-phase micro and mini reactors for reformer technology [91, 247-259], This is a complex task since the reaction step itself, hydrogen formation, covers several individual processes. Additionally, heat exchangers are required to optimize the energy balance and the use of liquid reactants demands micro evaporators [254, 260, 261], Moreover, further systems are required to reduce the CO content to a level that is no longer poisonous for a fuel cell. Overall, three to six micro-reactor components are typically needed to construct a complete, ready-to-use micro-reformer system. 

Edgar, T. E. and Himmelblau, D. M., 2nd edn (2001) Optimization of Chemical Processes (McGraw-Hill). Henley, E. J. and Rosen, E. M. (1969) Material and Energy Balance Computations (Wiley). 

In this chapter, we first consider uses of batch reactors, and their advantages and disadvantages compared with continuous-flow reactors. After considering what the essential features of process design are, we then develop design or performance equations for both isothermal and nonisothermal operation. The latter requires the energy balance, in addition to the material balance. We continue with an example of optimal performance of a batch reactor, and conclude with a discussion of semibatch and semi-continuous operation. We restrict attention to simple systems, deferring treatment of complex systems to Chapter 18. 

Two valuable sources of data for identifying opportunities for optimization include (1) profit and loss statements for the plant or the unit and (2) the periodic operating records for the plant. The profit and loss statement contains much valuable information on sales, prices, manufacturing costs, and profits, and the operating records present information on material and energy balances, unit efficiencies, production levels, and feedstock usage. 

Steady-state mathematical models of single- and multiple-effect evaporators involving material and energy balances can be found in McCabe et al. (1993), Yannio-tis and Pilavachi (1996), and Esplugas and Mata (1983). The classical simplified optimization problem for evaporators (Schweyer, 1955) is to determine the most suitable number of effects given (1) an analytical expression for the fixed costs in terms of the number of effects n, and (2) the steam (variable) costs also in terms of n. Analytic differentiation yields an analytical solution for the optimal n, as shown here. 

Process simulators contain the model of the process and thus contain the bulk of the constraints in an optimization problem. The equality constraints ( hard constraints ) include all the mathematical relations that constitute the material and energy balances, the rate equations, the phase relations, the controls, connecting variables, and methods of computing the physical properties used in any of the relations in the model. The inequality constraints ( soft constraints ) include material flow limits maximum heat exchanger areas pressure, temperature, and concentration upper and lower bounds environmental stipulations vessel hold-ups safety constraints and so on. A module is a model of an individual element in a flowsheet (e.g., a reactor) that can be coded, analyzed, debugged, and interpreted by itself. Examine Figure 15.3a and b. 

Wolbert et al. in 1991 proposed a method of obtaining accurate analytical first-order partial derivatives for use in modular-based optimization. Wolbert (1994) showed how to implement the method. They represented a module by a set of algebraic equations comprising the mass balances, energy balance, and phase relations ... 

For this type of problem, the specific rate of operation is designed to increase with the optimized screw. When the specific rate increases, the torque required to turn the screw at the same rate will increase. If the new screw is huilt and torque is not available to turn it, then the design process will fail and the rate increase will not he achieved. The designer must perform an overall energy balance to make sure that torque is available for example, see Section 9.2. 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

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