Energy Balance Module

12 Energy Balance Module Table 9.15 covers the formulas for use to determine the sensible energy for input streams, as well as the sensible heat for the coal conveying air, the inlet air, and the limestone. Table 9.15 Sensible Energy for Input Streams  

---

Equations-Oriented Simulators. In contrast to the sequential-modular simulators that handle the calculations of each unit operation as an iaput—output module, the equations-oriented simulators treat all the material and energy balance equations that arise ia all the unit operations of the process dow sheet as one set of simultaneous equations. In some cases, the physical properties estimation equations also are iacluded as additional equations ia this set of simultaneous equations. 

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. 

There are now constraints for each of the modules within the unit. For example, the material and energy balances must close for each module. Tne overall material and energy balances must also close, but they are not independent. There are three approaches to close these constraints. 

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 ... 

Module INPUT takes user-specified input and constructs proper initial conditions for the detailed mass and energy balance equations. 

In pathologic conditions, such as FAO disorders or organic acidemias due to acyl-CoA dehydrogenase deficiencies, the functions of carnitine as a regulator of substrate flux and energy balance across cell membranes and as a modulator of intracellular concentrations of free CoA become crucial. In such conditions, acyl-CoAs accumulate within the mitochondrial matrix and carnitine is utilized to shuttle these compounds out of the mitochondria as acylcarnitines, providing for free CoA at the same time. 

In real SOFC systems with the associated components like fans, heat exchangers, etc., it is necessary to consider the whole system, see Figure 2.11. The system is defined as a module consisting of SOFCs, which are connected electrically in parallel into stacks supplying a common burner with the depleted fuel. The energy balance of the stacks provides the necessary requirements for the excess air [2],... 

Two different descriptions are possible. The simplest approach is the balance border around the complete module including all stacks and the joint burner from the inlet I of the fuel F and the air A to the outlet aB of the flue gas G after the burner. The more detailed approach is a balance border which surrounds all stacks from the inlet I to the outlets O of the anode side AnO and of the cathode side CaO. The calculation of this power generating burner is similar to the calculation of a combustor of a gas turbine or of a furnace of a boiler. The calculation of the mass flows of the module does not differ from any calculation of a conventional oxidation. The energy balance of this simpler approach (from / to aB) gives... 

S //Asa mediator between CFD calculations and macro-scale process simulations, the reactor geometry is represented by a relatively small number of cells which are assumed to be ideally mixed. The basic equations for mass, impulse and energy balance are calculated for these cells. Mass transport between the cells is considered in a network-of-cells model by coupling equations which account for convection and dispersion. The software is capable of optimizing a process in iterative simulation cycles in a short time on a standard PC, but it also requires experimentally-based data to calibrate the software modules to a specific micro reactor. 

Several steps in implementation of specific urban dynamics and energetics have already been achieved by the HIRLAM/HARMONIE community. Enviro-HIRLAM considers a surface improved description for urban areas roughness, albedo, urban heat sources (Eaklanov et al. 2008). Properties of urban aerosol used to modify the albedo characteristics and the effective radius of cloud droplets for the SW radiation (in the HIRLAM radiation scheme). In FUMAPEX two other more sophisticated urban schemes EEP (Martilli et al. 2002) and SM2-U modules (Dupont and Mestayer 2006) were tested. They are more expensive computationally. Town energy balance (TEE) module (Masson 2000) is a part of SURFEX, available in the HARMONIE framework. Handling of the finest-scale details of momentum fluxes in town (forest) canopy could be developed. 

An animated version of what follows for the derivation of the energy balance can be found in the reaction engineering modules Heat Effects 1 and Heat Effects 2 on the CD-ROM. 

An important aspect of combined material and energy balance problems is how to ensure that the process equations or sets of modules are determinate, that is, have at least one solution, and hopefully no more than one solution. The question is How many variables are unknown, and how many must have their values specified in any problem The number of degrees of freedom is the number of variables in a set of independent equations to which values must be assigned to make the number of unknown variables plus the variables assigned values equal to the number of equations. We will first discuss the number of degrees of freedom associated with a process... 

The interconnections between the unit modules may represent information flow as well as material and energy flow. In the mathematical representation of the plant, the interconnection equations are the material and energy balance flows between model subsystems. Equations for models such as mixing, reaction, heat exchange, and so on, must also be listed so that they can be entered into the computer code used to solve the equation. Table 5.1 lists the common type of equations that might be used for a single subsystem. In general, similar process units repeatedly occur in a plant and can be represented by the same set of equations, which differ only in the names of variables, the number of terms in the summations, and the values of any coefficients in the equations. 

The sequential modular method of flowsheeting, as mentioned previously, is the one most commonly encountered in computer packages. A module exists for each process unit in the information flowsheet. Given the values of each input stream composition, flow rate, temperature, pressure, enthalpy, and the equipment parameters, the module calculates the properties of its outlet streams. The output stream for a module can become the input stream for another module for which the calculations proceed until the material and energy balances are resolved for the entire process. 

Once the tear streams are identified and the sequence of calculations specified, everything is in order for the solution of material and energy balances. All that has to be done is to calculate the correct values for the stream flow rates and their properties. To execute the calculations, many computer codes use the method of successive substitution, which is described in Appendix L. The output(s) of each module on interation k is expressed as an explicit function of the input(s) calculated fi om the previous iteration, A - 1. For example, in Fig. 5.16 for module 1,... 

Prepare a block diagram of the modules involved in solving the material and energy balances for the extraction process used in a refinery for the production of normal paraffins shown in Fig. P5.18. Which additional modules not in Fig. 5.9a would you need Also indicate what streams might be cut for a sequential modular solution of the material and energy balances. 

There are also other modules, for instance one of the most detailed parameterisa-tions of urban effects within current numerical models with explicit consideration of the effects of buildings, roads, and other anthropogenic building materials on the urban surface energy budget, was suggested by Masson 2000 [398] in the Town Energy Balance (TEB) scheme. 

Step 1 Open FEMLAB for 2D/Chemical Engineering Module/Energy Balance/ Conduction/Steady-state analysis. 

---