Energy balance control

Figure 12.84 Impact of lower temperature control (energy balance scheme)...

Stea.dy-Sta.teFeedforwa.rd, The simplest form of feedforward (FF) control utilizes a steady-state energy or mass balance to determine the appropriate manipulated variable adjustment. This form of feedforward control does not account for the process dynamics of the disturbance or manipulated variables on the controlled variable. Consider the steam heater shown ia Figure 15. If a steady-state feedforward control is designed to compensate for feed rate disturbances, then a steady-state energy balance around the heater yields ... 

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. 

In the equation-oriented approach, the executive organizes the equations and controls a general-purpose equation solver. The equations for material and energy balances may be grouped separately from those for the calculation of physical properties or phase equiHbria, or as ia the design of some simulators, the distinction between these groups of equations may disappear completely. 

Material and energy balances are based on the conservation law, Eq. (7-69). In the operation of liquid phase reactions at steady state, the input and output flow rates are constant so the holdup is fixed. The usual control of the discharge is on the liquid level in the tank. When the mixing is adequate, concentration and temperature are uniform, and the effluent has these same properties. The steady state material balance on a reacdant A is... 

Parameter Estimation Relational and physical models require adjustable parameters to match the predicted output (e.g., distillate composition, tower profiles, and reactor conversions) to the operating specifications (e.g., distillation material and energy balance) and the unit input, feed compositions, conditions, and flows. The physical-model adjustable parameters bear a loose tie to theory with the limitations discussed in previous sections. The relational models have no tie to theory or the internal equipment processes. The purpose of this interpretation procedure is to develop estimates for these parameters. It is these parameters hnked with the model that provide a mathematical representation of the unit that can be used in fault detection, control, and design. 

Matias I, Di Marzo V (2007) Endocannabinoids and the control of energy balance. Trends Endocrinol Metab 18 27-37... 

Neurotransmitter and biogenic amine derived from the amino acid histidine synthesized in hypothalamic tuber-omamillary neurons (TMN) to maintain wakefulness, feeding rhythms, energy balance, neuroendocrine autonomic control, and memory functions prominent immu-nomodulator and proinflammatory signal released from mast cells in response to allergic reactions or tissue damage. 

This chapter has presented time-domain solutions of unsteady material and energy balances. The more usual undergraduate treatment of dynamic systems is given in a course on control and relies heavily on Laplace transform techniques. One suitable reference is... 

Energy balances are needed whenever temperature changes are important, as caused by reaction heating effects or by cooling and heating for temperature control. For example, such a balance is needed when the heat of reaction causes a change in reactor temperature. This is seen in the information flow diagram for a non-isothermal continuous reactor as shown in Fig. 1.19. 

CFD may be loosely thought of as computational methods applied to the study of quantities that flow. This would include both methods that solve differential equations and finite automata methods that simulate the motion of fluid particles. We shall include both of these in our discussions of the applications of CFD to packed-tube simulation in Sections III and IV. For our purposes in the present section, we consider CFD to imply the numerical solution of the Navier-Stokes momentum equations and the energy and species balances. The differential forms of these balances are solved over a large number of control volumes. These small control volumes when properly combined form the entire flow geometry. The size and number of control volumes (mesh density) are user determined and together with the chosen discretization will influence the accuracy of the solutions. After boundary conditions have been implemented, the flow and energy balances are solved numerically an iteration process decreases the error in the solution until a satisfactory result has been reached. 

The input and output terms of equation 1.5-1 may each have more than one contribution. The input of a species may be by convective (bulk) flow, by diffusion of some kind across the entry point(s), and by formation by chemical reaction(s) within the control volume. The output of a species may include consumption by reaction(s) within the control volume. There are also corresponding terms in the energy balance (e.g., generation or consumption of enthalpy by reaction), and in addition there is heat transfer (2), which does not involve material flow. The accumulation term on the right side of equation 1.5-1 is the net result of the inputs and outputs for steady-state operation, it is zero, and for unsteady-state operation, it is nonzero. 

The result for ATp>max contained in equation 8.5-40 can be obtained from the following energy balance for a control surface or a core of radius r ... 

In order to assess the design of both the reactor and the heat exchanger required to control T, it is necessary to use the material balance and the energy balance, together with information on rate of reaction and rate of heat transfer, since there is an interaction between T and /A. In this section, we consider two cases of nonisothermal operation adiabatic (Q = 0) and nonadiabatic (Q = 0). 

For a continuous-flow reactor, such as a CSTR, the energy balance is an enthalpy (H) balance, if we neglect any differences in kinetic and potential energy of the flowing stream, and any shaft work between inlet and outlet. However, in comparison with a BR, the balance must include the input and output of H by the flowing stream, in addition to any heat transfer to or from the control volume, and generation or loss of enthalpy by reaction within the control volume. Then the energy (enthalpy) equation in words is... 

The energy balance for a PFR, as an enthalpy balance, may be developed in a manner similar to that for a CSTR in Section 14.3.1.2, except that the control volume is a differential volume. This is illustrated in Figure 15.3, together with the symbols used. 

Figure 153 Control volume and symbols used for energy balance for PFR...

The energy balance for the flame control volume is given as... 

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