Material balance vaporization

The performance of a given column or the equipment requirements for a given separation are established by solution of certain mathematical relations. These relations comprise, at every tray, heat and material balances, vapor-liquid equilibrium relations, and mol fraction constraints. In a later section, these equations will be stated in detail. For now, it can be said that for a separation of C components in a column of n trays, there still remain a number, C + 6, of variables besides those involved in the dted equations. These must be fixed in order to define the separation problem completely. Several different combinations of these C + 6 variables may be feasible, but the ones commonly fixed in column operation are the following ... 

The basic equations describing a single stage in a fractionator in which chemical reaction may occur include component material balances, vapor-liquid equilibrium relationships, and energy balance, and restrictions on the liquid vapor phase mol fractions. The model equations for stage j may be expressed as follows ... 

Fig. 18. Separation of ethanol from an ethanol—water—benzene mixture using benzene as the entrainer. (a) Schematic representation of the azeo-column (b) material balance lines where I denotes the homogeneous and the heterogeneous azeotropes D, the end points of the Hquid tie-line and A, the overhead vapor leaving the top of the column. The distillate regions, I, II, and III, and the boundaries are marked. Other terms are defined in text.

Fig. 19. Separation of ethanol and water from an ethanol—water—benzene mixture. Bottoms and are water, B is ethanol, (a) Kubierschky three-column sequence where columns 1, 2, and 3 represent the preconcentration, azeotropic, and entrainer recovery columns, respectively, (b) Material balance lines from the azeotropic and the entrainer recovery columns, A and E, respectively, where represents the overall vapor composition from the azeo-column, 2 1SP Hquid in equiUbrium with overhead vapor composition from the azeo-column, Xj, distillate composition from entrainer...

Example This equation is obtained in distillation problems, among others, in which the number of theoretical plates is required. If the relative volatility is assumed to be constant, the plates are theoretically perfect, and the molal liquid and vapor rates are constant, then a material balance around the nth plate of the enriching section yields a Riccati difference equation. 

Operating Lines The McCabe-Thiele method is based upon representation of the material-balance equations as operating lines on the y-x diagram. The lines are made straight (and the need for the energy balance obviated) by the assumption of constant molar overflow. The liqmd-phase flow rate is assumed to be constant from tray to tray in each sec tiou of the column between addition (feed) and withdrawal (produc t) points. If the liquid rate is constant, the vapor rate must also be constant. 

The constant-molar-overflow assumption represents several prior assumptions. The most important one is equal molar heats of vaporization for the two components. The other assumptions are adiabatic operation (no heat leaks) and no heat of mixing or sensible heat effects. These assumptions are most closely approximated for close-boiling isomers. The result of these assumptions on the calculation method can be illustrated with Fig. 13-28, vdiich shows two material-balance envelopes cutting through the top section (above the top feed stream or sidestream) of the column. If L + i is assumed to be identical to L 1 in rate, then 9 and the component material balance... 

Material Balances (2C + 2 Equations) Component for the vapor phase ... 

If we represent the moles of vapor by moles of liquid in the pot by M, the mole fraction of the more volatile component in this hquid by X, and the mole fraction of the same component in the vapor by y, 2l material balance yields... 

Only parts needed above but for the vapor-phase reactor are listed here. Most of the description for the installation for methanol synthesis experiments (Figure 4.2.1) holds for this installation, too. In the mentioned unit, product was blown down while still hot, thus keeping all product in a single vapor phase. This simplifies material balance calculations. When avoiding condensation is difficult, cooling and separation becomes necessary. This method was used in the cited AIChEJ publication. 

Determine top tray temperature for use in relative volatility calculations by running a dew point on the overhead rapor. For total condenser its composition is same as distillate product. For a partial condenser, run a dew point on the column overhead vapor composition as determined by a material balance around the partial condenser, reflux, and product. 

Whether for a distillation, absorption, or stripping system the material balance should be established around the top, bottom, and feed sections of the column. Then, using these liquid and vapor rates at actual flowing conditions, determine the flooding and maximum operating points or conditions. Then, using Figures 9-21B, -21E, or -21F, establish pressure drop, or assume a pressure drop and back-calculate a vapor flow rate, and from this a column diam-... 

By material balance, the composition of the vapor entering the condenser is the same composition as the liquid leaving the condenser (with no bleed olf). 

Material balances, Gas (vapor) phase Equation for variation of liquid phase bulk content ... 

Consider a simple process in which a multicomponent feed is allowed to separate into a vapor and a liquid phase with the phases coming to equilibrium, as shown in Figure 4.2. An overall material balance and component material balances can be written as ... 

These equations can be solved simultaneously with the material balance equations to obtain x[, x, xf and x1,1. For a multicomponent system, the liquid-liquid equilibrium is illustrated in Figure 4.7. The mass balance is basically the same as that for vapor-liquid equilibrium, but is written for two-liquid phases. Liquid I in the liquid-liquid equilibrium corresponds with the vapor in vapor-liquid equilibrium and Liquid II corresponds with the liquid in vapor-liquid equilibrium. The corresponding mass balance is given by the equivalent to Equation 4.55 ... 

Figure 4.2 shows a feed being separated into a vapor and liquid phase and being allowed to come to equilibrium. If the feed to the separator and the vapor and liquid products are continuous, then the material balance is described by Equations 4.57, 4.58 and 4.61x. If Kl is large relative to V/F (typically Kl > 10) in Equation 4.57, then2 ... 

Start by considering the material balance for the part of the column above the feed, the rectifying section. Figure 9.6 shows the rectifying section of a column and the flows and compositions of the liquid and vapor in the rectifying section. First, an overall balance is written for the rectifying section (assuming L and V are constant, i.e. constant molar overflow) ... 

However, to fully understand the design of the column, the material balance must be followed through the column. To simplify the analysis, it can be assumed that the molar vapor and liquid flowrates are constant in each column section, which is termed constant molar overflow. This is strictly only true if the component molar latent heats of vaporization are the same, there is no heat of mixing... 

Let B be the total number of moles and xiB the liquid mole fraction of Component i of liquid in the batch pot at time t. If a small amount of liquid dB with a vapor mole fraction x,o is vaporized, a material balance on Component i gives ... 

The effectiveness of a ventilation system is determined using material balance equations, described in chapter 3 in the section Estimating Worker Exposures to Toxic Vapors, and as illustrated in the following example. 

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