Carrying out a mass balance

Although it is common practice to calibrate the Coulter Counter using a standard powder, it is possible to calibrate the instrument with the powder being examined. This is the preferred British Standard method [17]. It is reiterated that this procedure cannot be carried out with some instruments due to count loss. Essentially one balances the volume of particles passing through the measuring aperture with the known volume in the measurement sample. This serves a multiple purpose in that  

This procedure should be used as routine since it indicates whether all the powder is accounted for and allows for correction for powder outside the measuring range of the aperture used. In an extreme case, it has been found that less than 5% of the total distribution was being measured and decisions were made based on these incorrect distributions. Alternatively, if the whole size range cannot be covered using a single aperture tube, a two-tube technique is required. 

This is not possible if the fraction unaccounted for is below the limit of the technique and the alternative mass balance procedure, as used with BCR 66 standard quartz powder, is as follows. 

Disperse w gram of powder in Vj cm of liquid. Pipette out V2 cm of suspension and add it to electrolyte to make up cm. Determine the corrected Coulter count on a metered volume of v cm.  

10 Oversize counts on a mass basis using the Coulter Counter 

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Moving the mixing junction to the inlet of the operation, as shown in Figure 26.20, and carrying out a mass balance... 

Ans. Carry out a mass balance for ammonia. Ammonia entering the column with the gas-ammonia leaving the column with the gas = ammonia leaving the column with the liquid-ammonia entering the column with the liquid. V(y, — y2) = L(x, — x2). 1362.86 kg/h. 

The normal procedure for determining the number oversize is to carry out a mass balance and present the derived Coulter data graphically as counts/gram against particle size. The problem with using this procedure is that, in some cases, there are only one or two oversize particles in the presence of millions of smaller ones. It is therefore necessary to filter out many of the smaller particles and carry out a count on the oversize residue. This poses problems in that some oversize particles may be lost in the process and, even more likely, large contaminant particles may be introduced in the filtration process. 

Following the approach detailed in Chapter 3, Section 3.4, we begin by carrying out a mass balance on... 

Similarly, we may carry out a mass balance on the vapour space ... 

Note that the solute concentration changes with time because the reservoir is finite (i.e., the solute capacity is finite). To learn how this solute concentration changes with time, we must also carry out a mass balance for the fluid contained in the reservoir (i.e., excluding the particles which carry their own pore fluid). 

Similarly carrying out a mass balance in the adsorbed phase, we derive the following mass balance equation ... 

In order to develop such an equation, we carry out a mass balance on a space element (see Figure 10-2). Note that the principal terms will include accumulation, the balance of the mass fluxes, and chemical reaction. If we consider this in a differential element that we shrink to an infinitesimal basis, we obtain (in rectangular coordinates)... 

Carrying out the mass balance over a thin shell at the position r with a thickness of Ar, we have... 

We are now in a position to derive the mass balance equation inside the particle. Carrying out the mass balance equation over a small element of thickness Ar at the position r (Fig. 11.8), we obtain for an element of spherical particle... 

Having obtained the dimensions of the system, we now turn to setting up the mass balance equation describing the concentration distribution along the capillary. We consider a thin shell of thickness dz at the position z as shown in Figure 7.4-2a, and carry out the mass balance around that shell to obtain ... 

By carrying out the mass balance for the component 1 over a thin shell in the capillary we have ... 

Consider a steady flow through the control volume in Figure 7.18 with uniform velocities over each plane at positions 1 and 2. We shall first carry out a momentum balance in the x direction. Let v denote the x component of the velocity at plane 1, etc. The mass flowrate into the control volume is ViP A and hence the rate at which x momentum enters is The rate at... 

Mass units. Before formulating and carrying out a material balance analysis and calculations (especially for nonreactive systems), it is strongly advised that all streams be expressed in mass units. As we will see in the next chapter, for reactive systems, it might be better to express streams in molar units. 

Thus, the K-value is Kt = Hi/P, and a straight line would be expected on a plot of v, against x,. A mass balance can be carried out around a part of the absorber to obtain the operating line as shown in Figure 10.1 ... 

The optimization can be carried out using nonlinear optimization techniques such as SQP (see Chapter 3). The nonlinear optimization has the problems of local optima if techniques such as SQP are used for the optimization. Constraints need to be added to the optimization in order that a mass balance can be maintained and the product specifications achieved. The optimization of the side-rectifier and side-stripper in a capital-energy trade-off determines the distribution of plates, the reflux ratios in the main and sidestream columns and condition of the feed. If a partitioned side-rectifier (Figure ll.lOd) or partitioned side-stripper (Figure 11.lid) is to be used, then the ratio of the vapor flowrates on each side of the partition can be used to fix the location of the partition across the column. The partition is located such that the ratio of areas on each side of the partition is the same as the optimized ratio of vapor flowrates on each side of the partition. However, the vapor split for the side-rectifier will only follow this ratio if the pressure drop on each side of the partition is the... 

The corresponding mass balance can also be carried out around the stripping section of a column, as illustrated in Figure 12.16. A mass balance around the bottom of the column for Component i gives ... 

For multicomponent systems, components A and B refer to the light and heavy keys respectively. In this problem, o-cresol is the light key and m-cresol is the heavy key. A mass balance may be carried out in order to determine the bottom composition. Taking as a basis, 100 kmol of feed, then ... 

The effort to carry out all these balances is high, but it significantly increases the reliability of the results, that should be based not only on single measurements (analyses). Usually, incorrect data are only detectable on the basis of at least two independent values or balances. If various balances are found, often an error can be identified as a false measurement or analysis mistake and not a real failure. As far as possible, several samples should be taken during each experiment for improved reliability. For continuous operation under stationary conditions, the average of some measurements and analyses will be used (any tendency in the individual values shows that the stationary state is not yet achieved). In case of batch operation a consistent change with time confirms reasonable results (here, in the mass balance the decrease of the cell liquid by the sampling has to be considered). 

The system consists of the conversion and combustion system, according to the three-step model. A system boundary is put around the combustion system. In other words, a mass-balance is carried out over the combustion system. 

A new mesurement method, based on the three-step model, has been verified. It is based on a mass-balance approach similar to the work carried out by Rogers (see Appendix A) [18]. Besides information about the mass flow and the stoichiometry of the conversion gas, this method also determines the air factors of the conversion system and the combustion system, which Rogers method did not. 

For example, suppose that you need 2.3 mol of potassium chloride to carry out a reaction. You need to convert the molar amount to mass so that you can measure the correct amount with a balance. 

We carried out one experiment to discover the mass balance of acetone. In this experiment we achieved a yield of 0.030 moles of TAA and recovered, by distillation, 0.207 mole of acetone, from a reaction in which we started with 0.30 moles of acetone, for a mass balance of 99%. 

Adiabatic gas-liquid contact is usually carried out in some sort of packed tower, frequently with countercurrent flow of gas and liquid. Figure 8.5 is a schematic diagram of such a tower of cross-sectional area S. A mass balance for substance A over the lower part of the tower is... 

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