Condensation material balance relations

Related Calculations. It is also possible to calculate the recycle rate in the preceding example by making a material balance around the reactor-condenser system. 

We first do the degree-of-freedom analysis. There are six unknowns on the chart—h through h(,. We are allowed up to three material balances—one for each species. We must therefore find three additional relations to solve for all unknowns. One is the relationship between the volumetric and molar flow rates of the condensate we can determine from the given volumetric flow rate and the... 

To accomplish this analysis, an overall material balance is written for the condenser as V = L + D, which relates the vapor (V) leaving the top stage, the liquid reflux returning (L) to the column from the condenser (reflux), and the distillate (D) collected. A material balance for component A is written as... 

A material balance around the condenser relates the L/V ratio to the reflux ratio... 

For the case where a total condenser is employed and Lx and LN are specified, the problem is formulated as follows. Specification of LN fixes D, since by total material balance, D = F - LN. Since and lu have the same composition, they are related by... 

The term e/(ee — 1), which appears in equations 1 and 2, was first developed to account for the sensible heat transferred by the diffusing vapor (1). The quantity 8 represents the group M4-C 4 / hg, the ratio of total transported energy to convective heat transfer. Thus it may be thought of as the fractional influence of mass transfer on the heat-transfer process. The last term of equation 3 is the latent heat contributed to the gas phase by the fog formation. The vapor loss from the gas phase through both surface and gas-phase condensation can be related to the partial pressure of the condensing vapor by using Dalton s law and a differential material balance. 

From material balances, it is generally concluded that solvent plays a keyrole in the solvolysis step it avoids intermediate components to recondense, preventing production of highly condensed molecules giving char. Besides, water is produced whilst the production of gases is negligible. Analysis of the material balance allows only an overall description of the solvolysis process and the mechanism of the solvolysis step is not well established, in relation to specific characteristics of wood polymers. 

In addition to the basic continuous column model assumptions of equilibrium stages and adiabatic operation, dynamics related assumptions are made for the batch model. Distefano (1968) assumed constant volnme of liquid holdup, negligible vapor holdup, and negligible fluid dynamic lag. Although different solntion strategies may be employed, the fundamental model equations are the same. Condenser total material balance ... 

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 nature of the Chapman-Jouget and other special thermodynamic states important to energetic materials is strongly influenced by the equation of state of stable detonation products. Cheetah can predict the properties of this state. From these properties and elementary detonation theory the detonation velocity and other performance indicators are computed. Thermodynamic equilibrium is found by balancing chemical potentials, where the chemical potentials of condensed species are just functions of pressure and temperature, while the potentials of gaseous species also depend on concentrations. In order to solve for the chemical potentials, it is necessary to know the pressure-volume relations for species that are important products in detonation... 

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