Balance and enthalpy

The material balances and enthalpy balance in the dilute phase are given by the following equations in dimensionless form ... 

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 ... 

The model of the regenerator consists of the coke balance, oxygen balance and enthalpy balance... 

The column section may be solved by simultaneous solution of the component mass balance and enthalpy balance equations and the vapor-liquid equilibrium relations. Additional equations include the temperature, pressure, and composition dependence of the equilibrium coefficients and enthalpies. The equations for stage j are as follows ... 

Check the consistency of the data by ensuring mass balance and enthalpy... 

The analysis of the heat exchanger network first identifies sources of heat (termed hot streams) and sinks (termed cold streams) from the material and energy balance. Consider first a very simple problem with just one hot stream (heat source) and one cold stream (heat sink). The initial temperature (termed supply temperature), final temperature (termed target temperature), and enthalpy change of both streams are given in Table 6.1. 

In unsteady states the situation is less satisfactory, since stoichiometric constraints need no longer be satisfied by the flux vectors. Consequently differential equations representing material balances can be constructed only for binary mixtures, where the flux relations can be solved explicitly for the flux vectors. This severely limits the scope of work on the dynamical equations and their principal field of applicacion--Che theory of stability of steady states. The formulation of unsteady material and enthalpy balances is discussed in Chapter 12, which also includes a brief digression on stability problems. 

Chapter 11. STEADY STATE MATERIAL AND ENTHALPY BALANCES IN POROUS catalyst PELLETS... 

As In the case of the material balance equations, the enthalpy balance can be written in dimensionless form, and this introduces new dimensionless parameters in addition to those listed in Table 11.1. We shall defer consideration of these until Chapter 12, where we shall construct the unsteady state enthalpy and material balances, and reduce them to dimensionless form. 

Chapter 12. MATERIAL AND ENTHALPY BALANCES IN UNSTEADY STATES... 

This fundamental relationship points out that the temperature at which crystal and liquid are in equilibrium is determined by the balancing of entropy and enthalpy effects. Remember, it is the difference between the crystal and... 

Condition of Feed (q Fine). The q line, which marks the transition from rectifying to stripping operating lines, is determined by mass and enthalpy balances around the feed plate. These balances are detailed in distillation texts (15). 

Computer solutions entail setting up component equiUbrium and component mass and enthalpy balances around each theoretical stage and specifying the required design variables as well as solving the large number of simultaneous equations required. The expHcit solution to these equations remains too complex for present methods. Studies to solve the mathematical problem by algorithm or iterational methods have been successflil and, with a few exceptions, the most complex distillation problems can be solved. 

Distillation columns are controlled by hand or automatically. The parameters that must be controlled are (/) the overall mass balance, (2) the overall enthalpy balance, and (J) the column operating pressure. Modem control systems are designed to control both the static and dynamic column and system variables. For an in-depth discussion, see References 101—104. 

Most of the analytical treatments of center-fed columns describe the purification mechanism in an adiabatic oscillating spiral column (Fig. 22-9). However, the analyses by Moyers (op. cit.) and Griffin (op. cit.) are for a nonadiabatic dense-bed column. Differential treatment of the horizontal-purifier (Fig. 22-8) performance has not been reported however, overall material and enthalpy balances have been described by Brodie (op. cit.) and apply equally well to other designs. 

Equation 1 is normally integrated by graphical or numerical means utilizing the overall material balance and the saturated air enthalpy curve. 

If an evaporation temperature (Pc) is pre-selected as a parametric independent variable, then the temperatures and enthalpies at c and e are found from (b) above the temperature T(, is also determined. If there is no heat loss, the heat balance in the HRSG between gas states 4 and 6 is... 

Tlic heat duty is best calculated with a process simulation program hi will account for phase changes as the fluid passes throiigli ilic ctioke. It will balance the enthalpies and accurately predict the change m tcnipcrature across the choke. Heat duty should be checked for vanoits combinations of inlet temperature, pressure, flow rate, and outlet temper ature and pressure, so as to determine the most critical combination. 

The height of a water-cooling tower can be determined l2) by setting up a material balance on the water, an enthalpy balance, and rate equations for the transfer of heat in the liquid and gas and for mass transfer in the gas phase. There is no concentration gradient in the liquid and therefore there is no resistance to mass transfer in the liquid phase. 

Section 6.11, when we calculated the enthalpy change for an overall physical process as the sum of the enthalpy changes for a series of two individual steps. The same rule applied to chemical reactions is known as Hess s law the overall reaction enthalpy is the sum of the reaction enthalpies of the steps into which the reaction can be divided. Hess s law applies even if the intermediate reactions or the overall reaction cannot actually be carried out. Provided that the equation for each step balances and the individual equations add up to the equation for the reaction of interest, a reaction enthalpy can be calculated from any convenient sequence of reactions (Fig. 6.30). 

The solubilities of the ionic halides are determined by a variety of factors, especially the lattice enthalpy and enthalpy of hydration. There is a delicate balance between the two factors, with the lattice enthalpy usually being the determining one. Lattice enthalpies decrease from chloride to iodide, so water molecules can more readily separate the ions in the latter. Less ionic halides, such as the silver halides, generally have a much lower solubility, and the trend in solubility is the reverse of the more ionic halides. For the less ionic halides, the covalent character of the bond allows the ion pairs to persist in water. The ions are not easily hydrated, making them less soluble. The polarizability of the halide ions and the covalency of their bonding increases down the group. 

The kinetic equilibrium constant is estimated from the thermodynamic equilibrium constant using Equation (7.36). The reaction rate is calculated and compositions are marched ahead by one time step. The energy balance is then used to march enthalpy ahead by one step. The energy balance in Chapter 5 used a mass basis for heat capacities and enthalpies. A molar basis is more suitable for the current problem. The molar counterpart of Equation (5.18) is... 

A dynamic model should be consistent with the steady-state model. Thus, Eqs (1) and (4) should be extended to dynamic form. For the better convergence and computational efficiency, some assumption can be introduced the total amounts of mass and enthalpy at each plate are maintained constant. Then, the internal flow can be determined by total mass balance and total energy balance and the number of differential equations is reduced. Therefore, the dynamic model can be established by replacing component material balance in Eq. (1) with the following equation. 

We use a short version of the seven-step method. The problem asks for the entropy and enthalpy changes accompanying a chemical reaction, so we focus on the balanced chemical equation and the thermodynamic properties of the reactants and products. 

If a material balance is to be solved, then the convergence variables can be taken to be the component molar flowrates. When a material and energy balance is to be solved, the additional convergence variables are usually taken to be pressure and enthalpy. 

Our discussion of multiphase CFD models has thus far focused on describing the mass and momentum balances for each phase. In applications to chemical reactors, we will frequently need to include chemical species and enthalpy balances. As mentioned previously, the multifluid models do not resolve the interfaces between phases and models based on correlations will be needed to close the interphase mass- and heat-transfer terms. To keep the notation simple, we will consider only a two-phase gas-solid system with ag + as = 1. If we denote the mass fractions of Nsp chemical species in each phase by Yga and Ysa, respectively, we can write the species balance equations as... 

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