CALCULATION PROCEDURES

Two methods of balancing reactions are of interest. We can balance reactions in terms of the stoichiometries of the species considered. In this case, the existing basis B is a list of elements and, if charged species are involved, the electron e. Alternatively, we may use a dataset of balanced reactions, such as the llnl database. Basis B, in this case, is the one used in the database to write reactions. We will consider each possibility in turn. 

A straightforward way to balance reactions is to use as the initial basis the stoichiometries of the species involved. If the species free energies of formation are 

The process is best shown by example. Suppose that we wish to balance the reaction by which calcium clinoptilolite (CaAl2Siio024 8H2O), a zeolite mineral, reacts to form muscovite [KAl3Si30io(OH)2] and quartz (Si02). We choose to write the reaction in terms of the aqueous species Ca++, K+, and OH-. 

Reserving clinoptilolite for the reaction s left side, we write the stoichiometry of each remaining species in matrix form, 

Notice that we have added the electron to B and B in order to account for the electrical charge on the aqueous species. This incorporation provides a convenient check the electron s reaction coefficient must work out to zero in order for the reaction to be charge balanced. 

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As the feed composition approaches a plait point, the rate of convergence of the calculation procedure is markedly reduced. Typically, 10 to 20 iterations are required, as shown in Cases 2 and 6 for ternary type-I systems. Very near a plait point, convergence can be extremely slow, requiring 50 iterations or more. ELIPS checks for these situations, terminates without a solution, and returns an error flag (ERR=7) to avoid unwarranted computational effort. This is not a significant disadvantage since liquid-liquid separations are not intentionally conducted near plait points. 

The calculational procedure employed in BLIPS, when used with the particular initial phase-composition estimated included in the subroutine, has converged satisfactorily for all systems we have encountered (except very near plait points as noted). 

Let us consider the calculation of sensitivity threshold in the case when the cracks are revealing by PT method. Constant distance H between crack s walls along the whole defect s depth is assumed for the simplicity. The calculation procedure depends on the dispersity of dry developer s powder [1]. Simple formula has to be used in the case when developer s effective radius of pores IC, which depends mainly on average particle s size, is smaller than crack s width H. One can use formula (1) when Re is small enough being less than the value corresponding maximum sensitivity (0,25 - 1 pm). For example. Re = 0,25 pm in the case when fine-dispersed magnesia oxide powder is used as the developer. In this case minimum crack s width H that can be detected at prescribed depth lo is calculated as... 

A wide variety of procedures have been developed to evaluate the performance of explosives. These include experimental methods as well as calculations based on available energy of the explosives and the reactions that take place on initiation. Both experimental and calculational procedures utilize electronic instmmentation and computer codes to provide estimates of performance in the laboratory and the field. 

Computer codes are used for the calculational procedures which provide highly detailed data, eg, the Ruby code (70). Rapid, short-form methods yielding very good first approximations, such as the Kamlet equations, are also available (71—74). Both modeling approaches show good agreement with experimental data obtained ia measures of performance. A comparison of calculated and experimental explosive detonation velocities is shown ia Table 5. 

The simplest calculation of radiation damage involves only monatomic materials and has been described by many authors (17—20). For polyatomic materials, a calculation procedure for estimating damage energy from ion implantation has been outlined (8). The extension of this formalism (8) to direct calculations of damage energies in polyatomic materials has been addressed by several authors (11,21—24). 

After breakup, droplets continue to interact with the surrounding environment before reaching thein final destination. In theory (24), each droplet group produced during primary breakup can be traced by using a Lagrangian calculation procedure. Droplet size and velocity can be deterrnined as a function of spatial locations. 

Example 2 Calculation of Kremser Method For the simple absorber specified in Fig. 13-44, a rigorous calculation procedure as described below gives results in Table 13-9. Values of were computed from component-product flow rates, and corresponding effective absorption and stripping factors were obtained by iterative calculations in using Eqs. (13-40) and (13-41) with N = 6. Use the Kremser method to estimate component-product rates if N is doubled to a value of 12. 

The ability of a rigorous calculation procedure to simulate operation of an... 

In concentrated wstems the change in gas aud liquid flow rates within the tower and the heat effects accompanying the absorption of all the components must be considered. A trial-aud-error calculation from one theoretical stage to the next usually is required if accurate results are to be obtained, aud in such cases calculation procedures similar to those described in Sec. 13 normally are employed. A computer procedure for multicomponent adiabatic absorber design has been described by Feiutnch aud Treybal [Jnd. Eng. Chem. Process Des. Dev., 17, 505 (1978)]. Also see Holland, Fundamentals and Modeling of Separation Processes, Prentice Hall, Englewood Cliffs, N.J., 1975. 

Maximum Ground-Level Concentrations The effective height of an emission having been determined, the next step is to study its path downward by using the appropriate atmospheric-dispersion formula. Some of the more popular atmospheric-dispersion calculational procedures have been summarized by Buonicore and Theodore (op. cit.) and include ... 

Figure 1 A stepwise view of the Verlet integration algorithm and its variants, (a) The basic Verlet method, (b) Leap-frog integration, (c) Velocity Verlet integration. At each algorithm dark and light gray cells indicate the initial and calculating variables, respectively. The numbers in the cells represent the orders m the calculation procedures. The arrows point from the data that are used in the calculation of the variable that is being calculated at each step.

Plants, situations, and causes of overpressure tend to be dissimilar enough to discourage preparation of generalized calculation procedures for the rate of discharge. In lieu of a set procedure most of these problems can be solved satisfactorily by conservative simplification and analysis. It should be noted also that, by general assumption, two unrelated emergency conditions will not occur simultaneously. 

The calculation procedure for temperature correction factors won t work for a temperature cross in a single shell pass, but this is an undesirable situation anyway. 

Calculation/Procedure for Ballast Tray Minimum Tower Diameter... 

Once all computations are completed, SCREEN summarizes the maximum concentrations for each of the calculation procedures examined. Before execution terminates, whether it is after complex terrain calculations are completed or at the end of the simple terrain calculations, you are given the option of printing a hardcopy of the results. 

Often in plant operations condensate at high pressures are let down to lower pressures. In such situations some low-pressure flash steam is produced, and the low-pressure condensate is either sent to a power plant or is cascaded to a lower pressure level. The following analysis solves the mass and heat balances that describe such a system, and can be used as an approximate calculation procedure. Refer to Figure 2 for a simplified view of the system and the basis for developing the mass and energy balances. We consider the condensate to be at pressure Pj and temperature tj, from whence it is let down to pressure 2. The saturation temperature at pressure Pj is tj. The vapor flow is defined as V Ibs/hr, and the condensate quality is defined as L Ibs/hr. The mass balance derived from Figure 2 is ... 

Pressure Rehef Valve Specification - Standard calculation procedures are applied to determine the size of the pressure rehef valve required for the maximum reheving rate, together with other information necessary to specify the valve. 

This section describes the various pressure relief devices that are commonly used, with their characteristics and criteria for selection. Basic calculation procedures for sizing PR valves are covered in subsequent discussions. 

Flare elevation and spacing must be such that permissible radiant heat densities for persoimel at grade are not exceeded under conditions of maximum heat release. The appropriate calculation procedures and personnel exposure criteria are described later. In some special cases, flare elevation and spacing may be governed by radiant heat exposure of certain vulnerable items of equipment, rather than personnel. 

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