Value of the objective function [(7-23) or (7-24)] at T + AT used for finite difference approximation of the derivative. [Pg.327]

When the main object of the absorption is to remove impurities these columns are often referred to as scrubbers. [Pg.9]

FIND ENTHALPY OBJECTIVE FUNCTION G lAOIABATICI 255 CALL ENTH(N lOfKEEfOtX TNyPfHLfER) [Pg.325]

Given that the objective is to manufacture a certain product, there are often a number of alternative reaction paths to that product. Reaction paths which use the cheapest raw materials and produce the smallest quantities of byproducts are to be preferred. Reaction paths which produce significant quantities of unwanted byproducts should especially be avoided, since they create significant environmental problems. [Pg.16]

In Chap. 2 the objective set was to maximize selectivity for a given conversion. This also will minimize waste generation in reactors for a given conversion. [Pg.276]

F Rachford-Rice objective function for liquid-liquid separa- [Pg.335]

FIND EQUILIBRIUM OBJECTIVE FUNCTION F AND UNNORMALIZEO COMPOSITIONS [Pg.324]

Example 2.1 Given that the objective is to manufacture vinyl chloride, there are at least three reaction paths which can be readily exploited. [Pg.16]

APPLY STEP-LIMITING PROCEDURE TO DECREASE OBJECTIVE FUNCTION 265 KD=l [Pg.325]

DFA Partial derivative of the Rachford-Rice objective function (7-13) with respect to the vapor-feed ratio. [Pg.321]

Life-cycle analysis, in principle, allows an objective and complete view of the impact of processes and products on the environment. For a manufacturer, life-cycle analysis requires an acceptance of responsibility for the impact of manufacturing in total. This means not just the manufacturers operations and the disposal of waste created by those operations but also those of raw materials suppliers and product users. [Pg.296]

Inertial collectors. In inertial collectors, an object is placed in the path of the gas. An example is shown in Fig. 11.1. While the gas passes around the shutters, particles with sufficiently high inertia impinge on them and are removed from the stream. Only particles in excess of 50/um can reasonably be removed. Like gravity settlers, inertial collectors are widely used as prefilters. [Pg.302]

In batch process optimization, one of the principal objectives is to improve equipment utilization through reduction in dead time. This requires both structural and parameter optimization, with many options available. [Pg.252]

Convergence of the iteration requires the norm of the objective vector 1g to be less than the convergence criterion, e. The initial estimates used, if not provided externally, are, in addition to Equation (7-28) [Pg.122]

In application of the Newton-Raphson iteration to these objective functions [Equations (7-23) through (7-26)], the near linear nature of the functions makes the use of step-limiting unnecessary. [Pg.119]

Centrifugal separators make use of the common principle that an object whirled about an axis at a constant radial distance from the point is acted on by a force. Use of centrifugal forces increases the force acting on the particles. Particles that do not settle readily in gravity settlers often can be separated from fluids by centrifugal force. [Pg.71]

For bubble and dew-point calculations we have, respectively, the objective functions [Pg.118]

For liquid-liquid systems, the separations are isothermal and the objective function is one-dimensional, consisting of Equation (7-17). However, the composition dependence of the [Pg.117]

A step-limited Newton-Raphson iteration, applied to the Rachford-Rice objective function, is used to solve for A, the vapor to feed mole ratio, for an isothermal flash. For an adiabatic flash, an enthalpy balance is included in a two-dimensional Newton-Raphson iteration to yield both A and T. Details are given in Chapter 7. [Pg.319]

More than 7.5 MW could be added from a hot utility to the first interval, but the objective is to find the minimum hot and cold utility. Thus from Fig. 6.186, QHmin = 7.5MW and Qcmm = 10MW. This corresponds with the values obtained from the composite curves in Fig. 6.5a. One further important piece of information can be deduced from the cascade in Fig. 6.186. The point where the heat flow goes to zero at T = 145°C corresponds to the pinch. Thus the actual hot and cold stream pinch temperatures are 150 and 140°C. Again, this agrees with the result from the composite curves in Fig. 6.5a. [Pg.179]

Change in extract-feed ratio from one iteration to the next. Partial derivative of Rachford-Rice objective function with respect to extract-feed ratio. [Pg.335]

For binary vapor-liquid equilibrium measurements, the parameters sought are those that minimize the objective function [Pg.98]

In the case of the adiabatic flash, application of a two-dimensional Newton-Raphson iteration to the objective functions represented by Equations (7-13) and (7-14), with Q/F = 0, is used to provide new estimates of a and T simultaneously. The derivatives with respect to a in the Jacobian matrix are found analytically while those with respect to T are found by finite-difference approximation [Pg.121]

The Newton-Raphson approach, being essentially a point-slope method, converges most rapidly for near linear objective functions. Thus it is helpful to note that tends to vary as 1/P and as exp(l/T). For bubble-point-temperature calculation, we can define an objective function [Pg.118]

The equation systems representing equilibrium separation calculations can be considered multidimensional, nonlinear objective functions [Pg.115]

Subroutine FUNDR. This subroutine calculates the required derivatives for REGRES by central difference, using EVAL to calculate the objective functions. [Pg.218]

Liquid-liquid equilibrium separation calculations are superficially similar to isothermal vapor-liquid flash calculations. They also use the objective function. Equation (7-13), in a step-limited Newton-Raphson iteration for a, which is here E/F. However, because of the very strong dependence of equilibrium ratios on phase compositions, a computation as described for isothermal flash processes can converge very slowly, especially near the plait point. (Sometimes 50 or more iterations are required. ) [Pg.124]

As indicated in Chapter 6, and discussed in detail by Anderson et al. (1978), optimum parameters, based on the maximum-likelihood principle, are those which minimize the objective function [Pg.67]

Equations (7-8) and (7-9) are then used to calculate the compositions, which are normalized and used in the thermodynamic subroutines to find new equilibrium ratios,. These values are then used in the next Newton-Raphson iteration. The iterative process continues until the magnitude of the objective function 1g is less than a convergence criterion, e. If initial estimates of x, y, and a are not provided externally (for instance from previous calculations of the same separation under slightly different conditions), they are taken to be [Pg.121]

Unwanted byproducts usually cannot be converted back to useful products or raw materials. The reaction to unwanted byproducts creates both raw materials costs due to the raw materials which are wasted in their formation and environmental costs for their disposal. Thus maximum selectivity is wanted for the chosen reactor conversion. The objectives at this stage can be summarized as follows [Pg.25]

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