Condenser energy balance

Then, since the terms on the right-hand side of Eq. (3-91 are known, we can calculate The condenser energy balance is... 

Total material, condensable component, and energy balances can be written for the entire column ... 

Application of these equations gives the results in Table 13-12. A set of T is calculated from the normahzed by bubble-point calculations. Corresponding values of are obtained from y = K x. Once newA. andT are available, new values of Vn are calculated from energy balances by using data from Maxwell (Data Book on Hydiocaihons, Van Nostrand, Princeton, N.J., 1950). First, an estimate of condenser duty is computed from an energy balance around the condenser. 

Energy balances around condenser and reboiler respectively ... 

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 of heat accumulation is balanced by the heat of condensation and the heat losses. An energy balance therefore gives... 

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. 

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. 

Prepare an energy balance diagram for the reactor-stripper high-pressure condenser complex. 

Thus, in this example, assumption of the deaeration steam allows the steam balance to be closed. However, this is based on an assumed deaerator flow. The actual flow to the deaerator can be calculated from a heat balance around the deaerator. Figure 23.23 shows the flows into and out of the deaerator. If the boiler feedwater flow and condensate flows are known, together with an assumed value of the vent steam, then the flowrate of deaeration steam can be calculated from an energy balance. 

Here, it is assumed that all the steam condenses in the distillation vessel. In this period, the organic phase component masses remain constant The rate of heat accumulation is balanced by the heat of condensation and the heat losses. An energy balance therefore gives... 

In most jacketed reactors or steam-heated reboilers the volume occupied by the steam is quite small compared to the volumetric flow rate of the steam vapor. Therefore the dymamic response of the jacket is usually very fast, and simple algebraic mass and energy balances can often be used. Steam flow rate is set equal to condensate flow rate, which is calculated by iteratively solving the heat-transfer relationship (Q = UA AT) and the valve flow equation for the pressure in the jacket and the condensate flow rate. 

Figure 3. Except for the latent heat of condensation released at the transparent surface, they all are forms of energy loss. Of primary significance in design and in evaluation of performance is the energy balance drawn around the distiller basin. This input is seen to be the incident solar energy minus reflection from the cover and the very small absorption in the cover. The feed water might also be considered a sensible heat supply, but it would usually be cooler than the product streams, and hence at a convenient base temperature, having zero energy input.

Formulation of the mathematical model here adopts the usual assumptions of equimolar overflow, constant relative volatility, total condenser, and partial reboiler. Binary variables denote the existence of trays in the column, and their sum is the number of trays N. Continuous variables represent the liquid flow rates Li and compositions xj, vapor flow rates Vi and compositions yi, the reflux Ri and vapor boilup VBi, and the column diameter Di. The equations governing the model include material and component balances around each tray, thermodynamic relations between vapor and liquid phase compositions, and the column diameter calculation based on vapor flow rate. Additional logical constraints ensure that reflux and vapor boilup enter only on one tray and that the trays are arranged sequentially (so trays cannot be skipped). Also included are the product specifications. Under the assumptions made in this example, neither the temperature nor the pressure is an explicit variable, although they could easily be included if energy balances are required. A minimum and maximum number of trays can also be imposed on the problem. 

The mass and energy balances constitute a linear set of constraints. The energy balances for the condensers state that all cooling required by a condenser of a particular column must be transferred either to a reboiler of another column in the same sequence or to a cold utility. Similarly, the energy balances for the reboilers state that all heating required by a condenser must be provided by either the condenser of another column in the same sequence or by the two available hot utilities. 

The theoretical approach to modelling frontal polymerization is based on the well developed theory of the combustion of condensed materials.255 "6 The main assumptions made in this approach are the following the temperature distribution is one-dimensional die development of the reaction front is described by the energy balance equation, including inherent heat sources, with appropriate boundary and initial conditions. Wave processes in stationary and cyclical phenomena which can be treated by this method, have been investigated in great detail. These include flame spreading, diffusion processes, and other physical systems with various inherent sources. 

The flowrate of the vapor to the condenser V (and the liquid returned to the reactor) is calculated by first using an overall energy balance around the entire system to find the condenser heat removal Qc... 

The holdup in the condenser is assumed to be negligible, so the thermal and composition dynamics are neglected. This means that xcj is equal to y, at each point in time. The condenser process temperature Tc is determined from a bubblepoint calculation from the known pressure Pc and liquid composition xCj. Instantaneous thermal effects mean that the energy balance can be used to calculate the rate of condensation ... 

Now we can make an energy balance on feedwater heater I to find the mass of steam condensed ... 

This chapter has introduced the concepts of mass and energy balances. These are essential steps in the analysis of any process. Simple examples have been used to illustrate the different steps, including not only formulating mass and energy balances but also simultaneously solving mass and energy balances together (the analysis of the condenser in the distillation unit). 

The calculation begins with the energy balance of the condenser to get its duty and continues stage to stage down through the column. 

The SR method can be applied to distillation columns, but the equations of the algorithm do not allow the solution of the condenser and the reboiler with the other stages in the column. Because only the energy balances are used as independent functions, reboiler and condenser duties, reflux ratio, and the boilup ratio have to be specified. This overspecifies the column and the solution cannot be found. The condenser and the reboiler can be solved as separate unit operations in a flowsheet as demonstrated by Fonyo et al. (39). The SR method is used in the ABSBR step of FLOWTRAN of Monsanto, St. Louis, Missouri, and also in both the public release version of ASPEN and in ASPENPlus of AspenTech, Cambridge, Massachusetts. 

More refined analyses of film condensation are presented in detail by Rohsenow [37], The most significant refinements take into account a nonlinear temperature profile in the film and modifications to the energy balance to include additional energy to cool the film below the saturation temperature. Both effects can be handled by replacing htx with h fg, defined by... 

Starting with a basic energy balance, derive an expression for the effectiveness of a heat exchanger in which a condensing vapor is used to heat a cooler fluid. Assume that the hot fluid (condensing vapor) remains at a constant temperature throughout the process. 

---