Energy Balance Inputs

Energy inputs include (i) thermodynamic data such as specific heats, heats of combustion, enthalpies of phase change, densities, and so on, (ii) kinetic rate data, and (iii) their state, that is, input and output temperatures. 

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The report around each unit includes material and energy balance, input and output streams, as well as some information about unit performance. Here we may include the sizing report. Some simulation systems may export the results of sizing in the form of specification sheets, which are basic documents in engineering. Here we may mention standardised documents for heat exchangers, distillation columns, vessels, pumps, filters, etc. Some simulators offer automatic interface of simulation data to engineering... 

An equation representing an energy balance on a combustion chamber of two surface zones, a heat sink Ai at temperature T, and a refractory surface A assumed radiatively adiabatic at Tr, inmost simply solved if the total enthalpy input H is expressed as rhCJYTv rh is the mass rate of fuel plus air and Tp is a pseudoadiabatic flame temperature based on a mean specific heat from base temperature up to the gas exit temperature Te rather than up to Tp/The heat transfer rate out of the gas is then H— — T ) or rhCp(T f — Te). The... 

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... 

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... 

Develop via mathematical expressions a valid process or equipment model that relates the input-output variables of the process and associated coefficients. Include both equality and inequality constraints. Use well-known physical principles (mass balances, energy balances), empirical relations, implicit concepts, and external restrictions. Identify the independent and dependent variables (number of degrees of freedom). 

A great variety of factors are in use, depending on the time available and the accuracy expected. Normally the input information required is the base cost. Determination of this cost usually requires a knowledge of equipment sizes, probably using mass and energy balances for the proposed process. 

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. 

The numerical solution of the energy balance and momentum balance equations can be combined with flow equations to describe heat transfer and chemical reactions in flow situations. The simulation results can be in various forms numerical, graphical, or pictorial. CFD codes are structured around the numerical algorithms and, to provide easy assess to their solving power, CFD commercial packages incorporate user interfaces to input parameters and observe the results. CFD... 

Quality-assurance procedures have to be established for the checking of both input and results checks of energy balances, plausibility tests, and comparison with steady-state calculations and with results from similar cases. These checks are demanding and time consuming and thus prone to be omitted but are mandatory for reliable simulations. 

Energy balance The arithmetic relationship between the energy input and output of a system. 

For the Linde process, a material and energy balance has been produced. If the input is some 3 toimes PVC per hour, some 3,500-4,000 m combustible gas and 700 m /h HCl (STP) is produced. No dioxins or furans are expected to be generated given the reducing atmosphere. 

A model based on energy balance was developed by Garcia-calvo et al. [5]. Energy input during gas expansion is dissipated in the flow field and in the phase interfaces, therefore ... 

Figure 5.3 Diagram showing boundaries for Mass Balance (encompassed by black dashed lines) and LCA with processes and flows included. Black arrows and flow names show inputs and outputs of the methods, grey arrows and boxes represent processes analysed to set up mass and energy balances. The process networks for the supply of energy, resources and so on are greatly simplified.

Life Cycle Inventory (LCI). During LCI, mass and energy balances are performed to quantify the material and energy inputs into the system as well as wastes and emissions from the system. 

If specific heat capacities can be assumed constant and the mechanical energy input by the stirrer, Wagit, is significant, the energy balance equation simplifies... 

It is often possible to make a material balance round a unit independently of the heat balance. The process temperatures may be set by other process considerations, and the energy balance can then be made separately to determine the energy requirements to maintain the specified temperatures. For other processes the energy input will determine the process stream flows and compositions, and the two balances must be made simultaneously for instance, in flash distillation or partial condensation see also Example 4.1. 

Equation 10.3.6, the reaction rate expression, and the design equation are sufficient to determine the temperature and composition of the fluid leaving the reactor if the heat transfer characteristics of the system are known. If it is necessary to know the reactor volume needed to obtain a specified conversion at a fixed input flow rate and specified heat transfer conditions, the energy balance equation can be solved to determine the temperature of the reactor contents. When this temperature is substituted into the rate expression, one can readily solve the design equation for the reactor volume. On the other hand, if a reactor of known volume is to be used, a determination of the exit conversion and temperature will require a simultaneous trial and error solution of the energy balance, the rate expression, and the design equation. 

The enthalpy change, AH, can be calculated for a steady-state process, using H°f, which is the enthalpy of formation of the various output and input components. Under the assumption that the inputs and outputs are at ambient conditions, the enthalpy of the components corresponds to the standard enthalpy of formation of each component. The kinetic and potential energy terms are neglected from the energy balance. It is also assumed that water enters the process as a liquid and hydrocarbon products leave the process as a liquid. All other components are in the gas phase. 

Two-phase fire relief equations are available for conservative design. Leung19 presented an equation for the maximum temperature based on an energy balance around the heated vessel. This assumes a constant heat input rate Q ... 

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. 

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. 

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... 

Inputs + Sources = Outputs + Sinks + Accumulations where each of these terms may be a quantity or a rate. Inputs and Outputs are accomplished by crossing the boundary of the reference volume. In case of mass transfer this occurs by bulk flow and diffusion. Sources and Sinks are accretions and depletions of a species without crossing the boundaries. In a mass and energy balance, sinks are the rate of reaction, rdVr, or a rate of enthalpy change, AHrpdC. Accumulation is the time derivative of the content of the species within the reference volume, for example, (<9C/3t)dVr or... 

A set of steady-state input-output material and energy balances (equality constraints). 

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