Mass heat balances

Next, we integrate the differential mass (heat) balance equation by multiplying the LHS and RHS of Eq. 12.1a with x dx and integrate over the whole domain of interest (i.e., [0,1]), to find... 

For example a process flow scheme for crude oil stabilisation might contain details of equipment, lines, valves, controls and mass and heat balance information where appropriate. This would be the typical level of detail used in the project definition and preliminary design phase described in Section 12.0. 

Mass and energy balances are used to evaluate blast furnace performance. Many companies now use sophisticated computeri2ed data acquisition and analysis systems to automatically gather the required data for daily calculation of the mass and heat balances. Typical mass and heat balances are shown in Figure 4 and Table 5, respectively. 

Wet-bulb temperature is the dynamic equilibrium temperature attained by a water surface when the rate of heat transfer to the surface by convection equals the rate of mass transfer away from the surface. At equilibrium, if neghgible change in the dry-bulb temperature is assumed, a heat balance on the surface is... 

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 ... 

The rate constant k is expressed as k = exp(15.32 - 7,550/T), sec Determine the operating points for both the mass and heat balance equations. 

The first order reaction is represented by (-r ) = kC, and applying the mass balance Equation 6-120 and the heat balance Equation 6-121, respectively, gives the fractional conversion in terms of the mass balance equation ... 

The fractional conversions in terms of both the mass balance and heat balance equations were calculated at effluent temperatures of 300, 325, 350, 375, 400, 425, 450, and 475 K, respectively. A Microsoft Excel Spreadsheet (Example6-ll.xls) was used to calculate the fractional conversions at varying temperature. Table 6-7 gives the results of the spreadsheet calculation and Eigure 6-24 shows profiles of the conversions at varying effluent temperature. The figure shows that die steady state values are (X, T) = (0.02,300), (0.5,362), and (0.95,410). The middle point is unstable and die last point is die most desirable because of die high conversion. 

A second order reaction is performed adiabatically in a CESTR. Use die data in Example 6-11 to plot bodi conversions for die mass and heat balance equations. The second order rate constant k is... 

Fractional conversions (mass and heat balances) at effluent temperatures... 

When a damp cloth is laid in an air flow, it settles after a certain time ic an equilibrium temperature, the so-called wet bulb temperature (0 ), which is determined through heat and mass transfer. Negotiating the heat flow obtained by radiation and conduction, the heat balance of the wet cloth in a stationary situation can be expressed as... 

Parallel dispersions can be introduced by the mass and heat balance equations... 

This is derived by substituting from the heat-balance expression, Eq. (20). Now, the skewed-cosine heat-flux profile being considered gives a known functional relationship between the flux and the quality at any position along the channel. By equating this relationship with Eq. (35), a solution can be obtained giving the local values of (j> and k at the predicted burn-out position. The corresponding peak flux can then be evaluated, and in this way the predicted burn-out lines for the three mass velocities in Fig. 40 can be drawn. 

Making a heat balance over the column, it is seen that the heat of vaporisation of the liquid must come from the sensible heat in the gas. The temperature of the gas falls from 6 to the adiabatic saturation temperature 6S, and its humidity increases from to Jfv (the saturation value at 9S). Then working on the basis of unit mass of dry gas ... 

Available data sets for flow boiling critical heat flux (CHF) of water in small-diameter tubes are shown in Table 6.9. There are 13 collected data sets in all. Only taking data for tube diameters less than 6.22 mm, and then eliminating duplicate data and those not meeting the heat balance calculation, the collected database included a total of 3,837 data points (2,539 points for saturated CHF, and 1,298 points for subcooled CHF), covering a wide range of parameters, such as outlet pressures from 0.101 to 19.0 MPa, mass fluxes from 5.33 to 1.34 x lO kg/m s, critical heat fluxes from 0.094 to 276 MW/m, hydraulic diameters of channels from 0.330 to 6.22 mm, length-to-diameter ratios from 1.00 to 975, inlet qualities from —2.35 to 0, and outlet thermal equilibrium qualities from -1.75 to 1.00. 

This result is perfectly general for a constant-volume reactor. It continues to apply when p, Cp, and H are expressed in mass units, as is normally the case for liquid systems. The current example has a high level of inerts so that the molar density shows little variation. The approximate heat balance... 

This heat balance contains two terms not seen before mgCR represents the mass times specific heat of the agitator and vessel walls and q represents the energy input by the agitator. Although the model is nominally for constant physical properties, Vermeulen and Fortuin found a better fit to the experimental data when they used a slightly different specific heat for the inlet stream (Cp), . 

Mass and heat balance equations for typical gas-liquid reactors in heterogeneous systems at steady state... 

Regions of stable and unstable operation determined by numerical simulation of mass and heat balances equations first- and second-order, autocatalytic, and product-inhibited kinetics graphically presented boundaries in co-ordinates in practice. safe operation if l/5e>2. Equality of heat generation and heat removal rates Semenov approach modified for first-order kinetics. 

The starting point of the approximate sizing procedure is to compose blank flow-sheets for all products (processes) specifying types of all equipment units of yet unknown capacity for each process no matter whether units are common for a majority of stages or unique for one process only. Preliminary mass and heat balances for all items and processes must be made. The size factors Sij are evaluated based on these balances. The balances can be corrected after equipment has been selected. Evaluation of size factors thus is an iterative procedure. 

Liquid flows continuously into an initially empty tank, containing a full-depth heating coil. As the tank fills, an increasing proportion of the coil is covered by liquid. Once the tank is full, the liquid starts to overflow, but heating is maintained. A total mass balance is required to model the changing liquid volume and this is combined with a dynamic heat balance equation. 

The component mass balance, when coupled with the heat balance equation and temperature dependence of the kinetic rate coefficient, via the Arrhenius relation, provide the dynamic model for the system. Batch reactor simulation examples are provided by BATCHD, COMPREAC, BATCOM, CASTOR, HYDROL and RELUY. 

Solution of the required column height is achieved by integrating the two component balance equations and the heat balance equation, down the column from the known conditions Xi , yout and TLin, until the condition that either Y is greater than or X is greater than Xqui is achieved. In this solution approach, variations in the overall mass transfer capacity coefficient both with respect to temperature and to concentration, if known, can also be included in the model as required. The solution procedure is illustrated by the simulation example AMMON AB. 

Levy, Healzer, and Abdollahian (1980) predicted the dryout flux in vertical pipes by a semiempirical adiabatic model (Levy and Healzer, 1980) for liquid film flow and entrainment. It starts with a heat balance along the flow direction and a mass balance perpendicular to the flow direction ... 

The mass and heat balances of the process are satisfactory when coal is gasified to a 53% carbon conversion in the gasifier and the remaining 47% of carbon is sent to the regenerator. From the heat values of the produced fuel gas and the input coal, the cold-gas efficiency (91 vol% H2 with 9 vol% CH4 298 K, 0.1 MPa) was calculated to be higher than 0.77. 

Three different principles govern the design of bench-scale calorimetric units heat flow, heat balance, and power consumption. The RC1 [184], for example, is based on the heat-flow principle, by measuring the temperature difference between the reaction mixture and the heat transfer fluid in the reactor jacket. In order to determine the heat release rate, the heat transfer coefficient and area must be known. The Contalab [185], as originally marketed by Contraves, is based on the heat balance principle, by measuring the difference between the temperature of the heat transfer fluid at the jacket inlet and the outlet. Knowledge of the characteristics of the heat transfer fluid, such as mass flow rates and the specific heat, is required. ThermoMetric instruments, such as the CPA [188], are designed on the power compensation principle (i.e., the supply or removal of heat to or from the reactor vessel to maintain reactor contents at a prescribed temperature is measured). 

The polymerization reactor is of the heat-balance type because of the change in the heat transfer characteristics of the reaction mass during the polymerization. As the viscosity increases, the rate of heat dissipation by mixing will generally decline, which must be taken into consideration in setting up the equipment and in taking the appropriate measurements. 

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