Unit ratio material balance

Since the total gas and Hquid flow rates per unit cross-sectional area vary throughout the tower (Fig. 5) rigorous material balances should be based on the constant iaert gas and solvent flow rates and respectively, and expressed ia terms of mole ratios and X. A balance around the upper... 

The unit ratio material balance is often included in the scope. For discussion of this, see Chapter 4. Any information that might be useful for designing equipment of optimizing operating conditons should also be included. 

The unit ratio material balance is based on the production of one pound of salable product. This basis is used because it is independent of the plant size and because the use of numbers near one minimizes the possibility of future calculation errors. 

The material balance is presented on a block flow sheet so that the reader can graphically visualize what is happening. An example is given in Figure 4E- 1. Each major operation appears as a block. No attempt is made to identify the specific pieces of equipment or to size them. The blocks are interconnected with flow lines, which indicate for each substance where it enters the process, what path it follows, and where it is eventually discharged. These flow lines are keyed to a chart that gives the composition and amount of each stream in the form of a unit ratio material balance. A material balance should be given for each product made by a multipurpose plant. 

The unit ratio material balances and the flow diagram are shown in Figures 4E-1, 4E-2, 4E-3 and 4E4. Much of what appears is a direct result of assumptions presented in the scope. Some of the reasoning that was used follows. 

Unit Ratio Material Balance for General Purpose Polystyrene (GPPS)... 

Unit Ratio Material Balance for High Impact Polystyrene (HIPS) 0.912 if Styrene... 

Size a methanol storage tank for a plant producing 10,000,000 lb of product. From the scope and unit ratio material balance, the following information is obtained 0.3 lb of methanol is required for each pound of product a 15-day storage capacity is specified for methanol and the plant will operate 8,300 hours per year. 

The amounts of each stream can be related to the rate of polystyrene produced by multiplying by the numbers in the unit ratio material balance (Figs. 4E-l,4E-2, and 4E-3). 

The flow rate, pressure, and temperature of each stream must be specified. This has already been done in part by constructing the unit ratio material balance. It must be extended to all energy transfer systems by using material and energy balances. 

Raw materials Conversion costs Unit ratio material balance chemical prices... 

The utilities are those provided by facilities outside the specific plant boundaries. These costs may be obtained from publications issued by the Federal Power Commission4 or Chemical Week s plant site issue. The amounts of each needed can be obtained from the energy balance and/or the unit ratio material balance. 

The investment cost for a 120,000,000 lb/yr plant is estimated at 15,000,000. The working capital is 3,000,000. From the unit ratio material balance, the energy balance, and an estimation of the labor, the following costs per pound of product were determined ... 

The stoichiometric data is included in order to perform material balances in each unit operation. The second column of the stoichiometric data shows the amount of raw material required (tons) per unit mass (tons) of the overall output, i.e. s6 + si + s8. The third column shows the ratio of each byproduct (si and. S 8 ) to product (s6) in ton/ton product. The objective function is the maximisation of product (56) output. A 20% variation in processing times was assumed. 

Subsequently, the condition of complete separation has to be coupled with the material balances derived for the nodes of the SMB unit and implemented in the Equilibrium Theory Model for Langmuir-type systems. That leads to the set of mathematical conditions given below, which the flow rate ratios have to fulfil in order to achieve complete separation, in particular ... 

Taking a material balance on the solute from the bottom of the column to any plane where the mole ratios are Y and X gives for unit area of cross-section ... 

Referring to Fig. 4.4, let flowrate of the carrier gas (air) per unit cross-sectional area be G kmol/m2 s, and the mole fraction of CO2 be y (because the gas is very dilute, the mole fraction is virtually the same as the mole ratio which should appear in the following material balance). Taking a balance across the element shown in Fig. 4.4 ... 

If ion exchange regenerant recovery as a 13% ammonium bicarbonate solution involves too much distillation for the process to be attractive, might not some other distillation conditions appear more favorable To answer this question the second material balance was made which assumed a still overhead product of a 1 1 1 mole ratio of NH3 C02 H20, the same ratio in which these compounds unite to form anhydrous ammonium bicarbonate. This is the composition of the distillate which gives a minimum amount of distillate product, and still a process which might be feasible. 

The ratio (1 /v) is the volume of mixture in the reactor divided by the volume of mixture fed to the reactor per unit time and is called the space time, t. The inverse of the space time is called the space velocity. In each case, the conditions for the volume of the feed must be specified temperature, pressure (in the case of a gas), and state of aggregation (liquid or gas). Space velocity and space time should be used in preference to contact time or holding time since there is no unique residence time in the CSTR (see below). Why develop this terminology Consider a batch reactor. The material balance on a batch reactor can be written [from Equation (3.2.1)] ... 

For the transfer unit determination with the given ratio of mass transfer coefficients, corresponding values of (y, y ) are found by intersections of the material balance and equilibrium lines with lines whose slopes are -kjk = -1 as indicated on Figure (a) and in detail with Example 13.12. These values are tabulated together with the couesponding integrands. The number of transfer units is found by trapezoidal rule integration of... 

Scheme 2 (Figure 3.16) indirectly adjusts the material balance through the two level control loops. If the reflux flow is increased, then the reflux accumulator level controller decreases the distillate flow. As the additional liquid proceeds to flow down to the sump, the sump level controller increases the bottoms flow a like amount. The separation is held constant by manually setting the reboiler steam flow to maintain a constant energy per unit feed. This scheme is recommended for columns with a small reflux ratio (R/D < 1). This scheme also offers improved dynamics, which may be required, particularly if the column has a large horizontal reflux accumulator. 

Table VI shows a hydrocarbon material balance for operation of a neohexane unit. This operation is typical in that pentane and hexane are isomerized together and the recycle ratio is set by the amount of feedstock available and the capacity of the equipment.

So far we have examined single units without a reaction occurring in the unit. How is the count for Nd affected by the presence of a reaction in the unit The way Nv is calculated does not change. As to Nr, all restrictions and constraints are deducted from N that represent independent restrictions on the unit. Thus the number of material balances is not necessarily equal to the number of species (H2O, O2, CO2, etc.) but instead is the number of independent material balances that exist determined in the same way as we did in Secs. 2.2 to 2.4, usually (but not always) equal to the number of elemental balances (H, O, C, etc.). Fixed ratios of materials such as the O2/N2 ratio in air or the CO/CO2 ratio in a product gas would be a restriction, as would be a specified conversion fraction or a known molar flow rate of a material. If some degrees of freedom exist still to be specified, improper specification of a variable may disrupt the independence of equations and/or specifications previously enumerated in the unit of Nr, so be carefiil. 

Side Heaters/Coolers The effect of a side heater or cooler on the L/V ratio is determined from an energy balance at stage j, the stage where heat duty per unit time, Qj, is transferred. If the side heater/cooler is placed at stagethe streams directly affected by the heat transfer are Lj and Vj (compositions Xj and Yp. The role of the side heater/cooler in modifying the vapor and liquid profiles above it and below it is analyzed based on energy and material balances. The energy balance is written as... 

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