Material balances compositions

Material balance compositions are related on lines through the... 

Point P is at the intersection of lines E F and SR,. Equilibrium compositions are related on lines through the origin, point A. Material balance compositions are related on lines through the operating point P. 

Number of independent equality constraints Material balances Composition of inlet and outlet streams the same Energy balance Total no. d.f. 

When only the total system composition, pressure, and temperature (or enthalpy) are specified, the problem becomes a flash calculation. This type of problem requires simultaneous solution of the material balance as well as the phase-equilibrium relations. 

The amounts of each phase and their compositions are calculated by resolving the equations of phase equilibrium and material balance for each component. For this, the partial fugacities of each constituent are determined ... 

To reduce the material balance conditions (11,1) to differential equations for the composition and pressure, flux relations must be used to relate the vectors to the gradients of the composition and pressure... 

The differential material balances contain a large number of physical parameters describing the structure of the porous medium, the physical properties of the gaseous mixture diffusing through it, the kinetics of the chemical reaction and the composition and pressure of the reactant mixture outside the pellet. In such circumstances it Is always valuable to assemble the physical parameters into a smaller number of Independent dimensionless groups, and this Is best done by writing the balance equations themselves in dimensionless form. The relevant equations are (11.20), (11.21), (11.22), (11.23), (11.16) and the expression (11.27) for the effectiveness factor. 

Current Efficiency. Current efficiency for caustic production in diaphragm and membrane cells can be estimated from collection of a known amount of caustic over a period of time and from a knowledge of the number of coulombs of electricity passed during that time period. An alternative method involves analysis of the gases evolved during electrolysis and determining the anolyte composition. Material balance considerations (7) show the expression for the caustic efficiency for membrane cells to be... 

An important use of the triangular equiHbrium diagram is the graphical solution of material balance problems, such as the calculation of the relative amounts of equiHbrium phases obtained from a given overall mixture composition. As an example, consider a mixture where the overall composition is represented by point M on Figure 2a. If the A-rich phase is denoted by point R (raffinate) and the B-rich phase is denoted by point E (extract), it can be shown that points R, M, and E are coUinear, and also... 

A typical material balance as well as chemical compositions are given in Table 5. The raw materials are metered into the makeup tanks in the proper ratios. Crysta11i2ation takes place in a separate crysta11i2er. An intermediate aging step at ambient temperature may be requited for the synthesis of certain high purity 2eobtes. 

Zone Melting. A similar material balance may be made for a zone of mass moving a short distance in such a manner that the mass dm of sohd is frozen out and an identical mass melts into the zone (Fig. 4). For the first zone pass, it is assumed that the rod is initially at uniform composition i to obtain the following (1,4,8) ... 

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...

Fig. 20. Three sets of material balance lines for the Kubierschky three-column sequence where design 1 corresponds to the upper tie-line having Tmin = 8.78 design 2, to the subcooled upper tie-line having = 12.23 and design 3, to the lower tie-line having = 17.31 represents overall decanter composition , the overall feed composition to the azeo-column , the distillate composition from the entrainer recovery column and O, the...

Exploitation of Boundary Curvature A second approach to boundaiy crossing exploits boundaiy curvature in order to produce compositions in different distillation regions. When distillation boundaries exhibit extreme curvature, it may be possible to design a column such that the distillate and bottoms are on the same residue curve in one distillation region, while the feed (which is not required to lie on the column-composition profile) is in another distillation region. In order for such a column to meet material-balance constraints (i.e., bottom, distillate, feed on a straight hne), the feed must be located in a region where the boundary is concave. 

For the reaction system under consideration, experiments are made at a series of bulk-liqiiid and bulk-gas compositions representing the compositions to be expected at different levels in the commercial absorber (on the basis of a material balance). 

Algebraic Comptttation This method starts with calculation of the quantities and compositions of all the terminal streams, using a convenient quantity of one of the streams as the basis of calculation. Material balance and stream compositions are then computed for a terminal ideal stage at either end of an extraction battery (i.e., at Point A or Point B in Fig. 18-81), using equilibrium and solution-retention data. Calculations are repeated for each successive ideal stage from one end of the system to the other until an ideal stage which corresponds to the desired conditions is obtained. Any solid-hquid extraction problem can be solved by this method. 

For more precise values, computer programs can be used to calculate soluble recoveiy as weh as solution compositions for conditions that are typical of a CCD circuit, with varying underflow concentrations, stage efficiencies, and solution densities in each of the stages. The calculation sequence is easily performed by utihzing material-balance equations around each thickener. 

During this preparation stage, analysts will frequently find that there is insufficient quantity or quality of measurements to close the material balance. Analysts should make eveiy effort to measure aU stream flows and compositions for the actual test. They should not rely upon closing material balances by back-calculating missing streams. Tne material balance closure will provide a check on the vahdity of the measurements. This preparatoiy material balance will help to identify additional measurements and schedule the installation of the additional instruments. 

Spreadsheet Structure There are three principal sections to the spreadsheet. The first has tables of as-reported and normalized composition measurements. The second section has tables for overall and component flows. These are used to check the overall and component material balance constraints. The third has adjusted stream and component flows. Space is provided for recording the basis of the adjustments. The structure changes as the breadth and depth of the analysis increases. 

The second section of the spreadsheet contains the overall flows, the calculated component flows, and the material balance closure of each. The weighted nonclosure can be calculated using the random error calculated above, and a constraint test can be done with each component constraint if desired. Whether the measurement test is done or not, the nonclosure of the material balance for each component gives an indication of the validity of the overall flows and the compositions. If particiilar components are found to have significant constraint error, discussions with laboratory personnel about sampling and analysis and with instrument personnel about flow-measurement errors can take place before any extensive computations begin. 

This program helps calculate the rate of methanol formation in mol/m s at any specified temperature, and at different hydrogen, carbon monoxide and methanol concentrations. This simulates the working of a perfectly mixed CSTR specified at discharge condition, which is the same as these conditions are inside the reactor at steady-state operation. Corresponding feed compositions and volumetric rates can be calculated from simple material balances. 

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