Heat and material balance

The use of the computer in the design of chemical processes requires a framework for depiction and computation completely different from that of traditional CAD/CAM appHcations. Eor this reason, most practitioners use computer-aided process design to designate those approaches that are used to model the performance of individual unit operations, to compute heat and material balances, and to perform thermodynamic and transport analyses. Typical process simulators have, at their core, techniques for the management of massive arrays of data, computational engines to solve sparse matrices, and unit-operation-specific computational subroutines. 

Mathematically, multiplicities become evident when heat and material balances are combined. Both are functions of temperature, the latter through the rate equation which depends on temperature by way of the Arrhenius law. The curves representing these b ances may intersect in several points. For first order in a CSTR, the material balance in terms of the fraction converted can be written... 

Flash Evaporators The calculation of a heat and material balance on a flash evaporator is relatively easy once it is understood that the temperature rise in each heater and temperature drop in each flasher must all be substantially equal. The steam economy E, kg evap-oration/kg of I055-kJ steam (Ib/lb of lOOO-Btu steam) may be approximated from... 

Multiple-Effect Evaporators A number of approximate methods have been published for estimating performance and heating-surface requirements of a multiple-effect evaporator [Coates and Pressburg, Chem. Eng., 67(6), 157 (1960) Coates, Chem. Eng. Prog., 45, 25 (1949) and Ray and Carnahan, Trans. Am. Inst. Chem. Eng., 41, 253 (1945)]. However, because of the wide variety of methods of feeding and the added complication of feed heaters and condensate flash systems, the only certain way of determining performance is by detailed heat and material balances. Algebraic soluflons may be used, but if more than a few effects are involved, trial-and-error methods are usually quicker. These frequently involve trial-and-error within trial-and-error solutions. Usually, if condensate flash systems or feed heaters are involved, it is best to start at the first effect. The basic steps in the calculation are then as follows ... 

Tests on plant-scale dryers are usually carried out to obtain design data for a specific material, to select a suitable diyer type, or to check present performance of an existing diyer with the objective of determining its capacity potential. In these tests overall performance data are obtained and the results used to make heat and material balances and to estimate overall drying rates or heat-transfer coefficients. 

A model of a reaction process is a set of data and equations that is believed to represent the performance of a specific vessel configuration (mixed, plug flow, laminar, dispersed, and so on). The equations include the stoichiometric relations, rate equations, heat and material balances, and auxihaiy relations such as those of mass transfer, pressure variation, contac ting efficiency, residence time distribution, and so on. The data describe physical and thermodynamic properties and, in the ultimate analysis, economic factors. 

Conditions at steady state are determined by heat and material balances. Such balances for a CSTR can be put in the form. 

The simultaneous equations of heat and material balance and rate equations for these three cases are stated in several tables of Sec. 7. 

The Smith-Brinkley Method can therefore be used to generate a hand base case beginning with either a heat and material balanced plant case, a rigorous computer solution of a plant case, or computer solution of a design case. Once the hand base case is established, alternate cases can be done by hand (or small computer having limited core) using the Smith-Brinkley Method. 

To determine cooling water system flows, use a heat and material balance and a chloride balance (concentration ratio is usually calculated from chloride concentrations). 

The operating company must underwrite the emissions associated with the plant through environmental impact reporting. Such accounting has become an important part of the design. Rather than pass over the need for a closed heat and material balance at the study stage of a project, it is better to get this job done as early as possible. Persistence is sometimes required. 

Solution After thorough analysis, including heat and material balances and hydraulic calculations, the initial design flaws were corrected including ... 

Chapter 1 provides a summary of important equations for estimating the terminal temperatures in a heat exchanger. Here we formalize a short estimating procedure for a countercurrent flow situation. Assume that a specifier of a heat exchanger has defined a preliminary sizing of the unit. The system requires heat and material balances. 

Prepare heat and material balance studies for a proposed process, both by hand and by use of computer programs. 

Prepare final detailed heat and material balances. 

Used to present the heat and material balance of a process. This may be in broad block form with specific key points delineated, or in more detailed form identifying essentially every flow, temperature and pressure for each basic piece of process equipment or processing step. This may and usually does include auxiliary services to the process, such as steam, water, air, fuel gas, refrigeration, circulating oil, etc. This type of sheet is not necessarily distributed to the same groups as would receive and need the piping flowsheet described next, because it may contain detailed confidential process data. 

Figure 1-7. Heat and material balance establishes material and thermal requirements. By permission, J. P. O Donnell [9].

Multicomponent distillation is by far the common requirement for process plants and refineries, rather than the simpler binary systems. There are many computer programs which have been developed to aid in accurately handling the many iterative calculations required when the system involves three to possibly ten individual components. In order to properly solve a multicomponent design, there should be both heat and material balance at every theoretical tray throughout the calculation. 

Davison Div., W.R. Grace Co., Cat Cracker Heat and Material Balance Calculations, Grace Davison Catalagram, No. 59, 1980. 

Application of the Balzhinimaev model requires assumptions about the reactor and its operation so that the necessary heat and material balances can be constructed and the initial and boundary conditions formulated. Intraparticle dynamics are usually neglected by introducing a mean effectiveness factor however, transport between the particle and the gas phase is considered. This means that two heat balances are required. A material balance is needed for each reactive species (S02, 02) and the product (SO3), but only in the gas phase. Kinetic expressions for the Balzhinimaev model are given in Table IV. 

Mean heat capacities for the combustion gases are readily available in handbooks and texts on heat and material balances. The following values are taken from K. A. Kobe, Thermochemistry of Petrochemicals, reprint No. 44, Pet. Ref. 1958 converted to SI units, J/mol°C, reference temperature 0°C. 

An example illustrating the calculation of stream composition from reaction equilibria, and also an example of a combined heat and material balance. 

Heat and material balances of a batch reactor are derived in Section 2.6.2. In the present instance, the differential heat balance is Heat of reaction + Heat tranfer = Sensible heat gain or... 

A phenomenon that arises particularly with continuous stirred reactors is the occurrence of more than one steady state. This becomes apparent from the heat and material balances. "Heat generation" is made up of the heat of reaction plus any heat transfer, and the "heat removal" is the sensible and latent heat change of the reaction products. In problem P4.10.13, for instance, both the heat generation and the heat removal are plotted against the temperature. The two lines intersect at three points which represent the steady states. A point at which the slope of the heat generation line is... 

Given the conditions on the sketch and the following data, find the temperature and composition out of each stage. pCp = 900/1iter-°K AHr = 9000 cal/gmol Ca0 = 5 gmol/liter T0 = 400 K V0 = 1000 liters/hr = 500 liters/hr Vri = Vr2 = 250 liters Heat and material balances ... 

For a first order adiabatic reaction in a CSTR, the variation of concentration and temperature with time and in the steady state will be analyzed. Heat and material balances are based on the relation,... 

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