Energy Balance Basis

For purposes of distillation calculations, a rough diagram of saturated vapor and liquid enthalpy concentration tines can be drawn on the basis of pure component enthalpies. Even with such a rough diagram, the accuracy of distiUation calculation can be much superior to those neglecting enthalpy balances entirely. Example 13.8 deals with preparing such a Merkel diagram. 

The construction for the minimum number of trays is independent of the heat balance. The minimum reflux corresponds to a minimum condenser load Q and hence to a minimum value of Q = hp + Qc/D. It can be found by trial location of pointP until an operating curve is found that touches the equilibrium curve. 

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Binary Distillation 379 Material and Energy Balances 380 Constant Molal Overflow 380 Basic Distillation Problem 382 Unequal Molal Heats of Vaporization 382 Material and Energy Balance Basis 382 Algebraic Method 382... 

Because densification occurs via tire shrinkage of tliennodynamically unstable pores, densification and microstmcture development can be assessed on tire basis of tire dihedral angle, 0, fonned as a result of tire surface energy balance between tire two solid-vapour and one solid-solid interface at tire pore-grain boundary intersection [, 78, 79 and 80],... 

The scientific basis of extractive metallurgy is inorganic physical chemistry, mainly chemical thermodynamics and kinetics (see Thermodynamic properties). Metallurgical engineering reties on basic chemical engineering science, material and energy balances, and heat and mass transport. Metallurgical systems, however, are often complex. Scale-up from the bench to the commercial plant is more difficult than for other chemical processes. 

On an energy-content basis, the system is balanced at all times i.e., there is sufficient energy in the gas (or solids) present in the system at any time to complete the work on all the solids (or gas) present at the same time. This is significant in that there is no lag in response to control changes or in starting up and shutting down the system no partially processed residual solids or gas need be retained between runs. 

The first law of thermodynamics is the basis for material- and energy-balance calculations. Because there is no significant transformation of mass to energy in most manufacturing operations, for a material balance the first law can be reduced to the simplified form ... 

Often in plant operations condensate at high pressures are let down to lower pressures. In such situations some low-pressure flash steam is produced, and the low-pressure condensate is either sent to a power plant or is cascaded to a lower pressure level. The following analysis solves the mass and heat balances that describe such a system, and can be used as an approximate calculation procedure. Refer to Figure 2 for a simplified view of the system and the basis for developing the mass and energy balances. We consider the condensate to be at pressure Pj and temperature tj, from whence it is let down to pressure 2. The saturation temperature at pressure Pj is tj. The vapor flow is defined as V Ibs/hr, and the condensate quality is defined as L Ibs/hr. The mass balance derived from Figure 2 is ... 

Acceptable systems are compared to each other and the most suitable system is selected on the basis of different parameters, such as power and energy consumption and investment and life cycle costs. See Fig. 3.12. Tools for comparison are energy balances and cost analyses. 

The first term on the right-hand side of Eq. (14.113) comes from the inertial forces. Because of the pressure drop the density of gas decreases in the di rection of the flow and therefore, on the basis of mass balance of gas flow, the velocity v increases along the flow. If the pipe is isolated, then the flow can be treated as adiabatic, which on the basis of energy balance implies that along the flow we have... 

Except for very small systems it is impractical to saturate the basis set so that the absolute error in the energy is reduced below chemical accuracy, for example 1 kcal/ mol. The important point in choosing a balanced basis set is to keep the error as constant... 

The basis of the calculation is operation for 1 hour. Necessary data are presented in Table 9.1. The energy balance is based on first law of thermodynamics ... 

A homogeneous flow basis must be used when thermodynamic equilibrium is assumed. For furtl er simplification it is assumed there will be no reaction occurring in the pipeline. The vapor and liquid contents of the reactor are assumed to be a homogeneous mass as they enter the vent line. The model assumes adiabatic conditions in the vent line and maintains constant stagnation enthalpy for the energy balance. 

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... 

If a batch process is being considered, or if the rate of energy generation or removal varies with time, it will be necessary to set up a differential energy balance, similar to the differential material balance considered in Chapter 2. For batch processes the total energy requirements can usually be estimated by taking as the time basis for the calculation 1 batch but the maximum rate of heat generation will also have to be estimated to size any heat-transfer equipment needed. 

It is good practice to show on the flow-sheet the basis used for the flow-sheet calculations. This would include the operating hours per year the reaction and physical yields and the datum temperature used for energy balances. It is also helpful to include a list of the principal assumptions used in the calculations. This alerts the user to any limitations that may have to be placed on the flow-sheet information. 

These four equations are the so-called MESH equations for the stage Material balance, Equilibrium, Summation and Heat (energy) balance, equations. MESH equations can be written for each stage, and for the reboiler and condenser. The solution of this set of equations forms the basis of the rigorous methods that have been developed for the analysis for staged separation processes. 

P IDs (3) electrical classification (4) relief system design and design basis (5) ventilation system design (6) design codes and standards (7) material and energy balances for processes built after May 26, 1992 and (8) safety systems. 

Equation 12.3-16 is valid whether heat is transferred to or from the system, and whether the reaction is exothermic or endothermic. Note that each term on the left side of equation 12.3-16 may be an input or an output. Furthermore, CP is the molar heat capacity of the system, and is given by equation 12.3-13 as such, it may depend on both T and composition (through /A). The right side of equation 12.3-16 may also be expressed on a specific-mass basis (12.3-11). This does not affect the consistency of the units of the terms in the energy balance, which are usually J s-1. 

Data reconciliation of the pyrolysis reactor was performed on the basis of the following mass and energy balance equations (Weiss et al., 1996). 

Component enthalpies are readily available on a per mass basis from data such as JANAF (4). Product enthalpy usually includes the heat of formation in published tables. A typical energy balance calculation is the determination of the cell exit temperature knowing the reactant composition, the temperatures, H2 and O2 utilization, the expected power produced, and a percent heat loss. The exit constituents are calculated from the fuel cell reactions as illustrated in Example 10-3, Section 10. 

The energy equation, with temperature varying as a function of radial, circumferential, and axial position and time, is the basis of the thermochemical submodel. The energy absorbed or released during the cure or crystallization of the matrix is included in the energy balance. The appropriate multidimensional energy equation is Equation 13.1,... 

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