# Adiabatic

The calculation of single-stage equilibrium separations in multicomponent systems is implemented by a series of FORTRAN IV subroutines described in Chapter 7. These treat bubble and dewpoint calculations, isothermal and adiabatic equilibrium flash vaporizations, and liquid-liquid equilibrium "flash" separations. The treatment of multistage separation operations, which involves many additional considerations, is not considered in this monograph. [c.6]

In modern separation design, a significant part of many phase-equilibrium calculations is the mathematical representation of pure-component and mixture enthalpies. Enthalpy estimates are important not only for determination of heat loads, but also for adiabatic flash and distillation computations. Further, mixture enthalpy data, when available, are useful for extending vapor-liquid equilibria to higher (or lower) temperatures, through the Gibbs-Helmholtz equation. [c.82]

The single-stage separations for which we present computational procedures are the incipient separations (one product phase present in very small amount) represented by bubble and dew-point calculations, vapor-liquid equilibrium separations at fixed pressure under isothermal or adiabatic conditions, and liquid-liquid equilibrium separations at fixed pressure and temperature. These calculations are implemented by FORTRAN IV subroutines designed to minimize the number of vapor and liquid-phase fugacity evaluations necessary to achieve satisfactory solutions. This criterion for efficiency of the algorithms is based on the recognition that, with relatively rigorous thermodynamic methods such as those used here, most of the computation effort in any separation calculation is devoted to evaluation of thermodynamic equilibrium functions. It is important to avoid unnecessary calculations of fugacities or fugacity (activity) coefficients in computer programs used in chemical engineering practice. [c.111]

It is important to stress that unnecessary thermodynamic function evaluations must be avoided in equilibrium separation calculations. Thus, for example, in an adiabatic vapor-liquid flash, no attempt should be made iteratively to correct compositions (and K s) at current estimates of T and a before proceeding with the Newton-Raphson iteration. Similarly, in liquid-liquid separations, iterations on phase compositions at the current estimate of phase ratio (a)r or at some estimate of the conjugate phase composition, are almost always counterproductive. Each thermodynamic function evaluation (set of K ) should be used to improve estimates of all variables in the system. [c.118]

The vapor-liquid equilibrium separation calculations considered here are for two cases, isothermal and adiabatic, both at fixed pressure. [c.120]

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 [c.121]

Both vapor-liquid flash calculations are implemented by the FORTRAN IV subroutine FLASH, which is described and listed in Appendix F. This subroutine can accept vapor and liquid feed streams simultaneously. It provides for input of estimates of vaporization, vapor and liquid compositions, and, for the adiabatic calculation, temperature, but makes its own initial estimates as specified above in the absence (0 values) of the external estimates. No cases have been encountered in which convergence is not achieved from internal initial estimates. [c.122]

UNIQUAC interaction parameters were not determined, but were assumed to be zero for this system. Quantities in parentheses refer to adiabatic flash. [c.123]

The temperature and composition of each feed stream and the stream ratios are specified along with a common feed pressure (significant only for the vapor stream) and the flash pressure. For an isothermal flash the flash temperature is also specified. Resulting vapor and liquid compositions, phase ratios, vaporization equilibrium ratios, and, for an adiabatic flash, flash temperature are returned. [c.319]

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. [c.319]

T temperature (K) of isothermal flash for adiabatic flash, estimate of flash temperature if known, otherwise set to 0 to activate default initial estimate. [c.320]

T calculated flash temperature (°K) for adiabatic flash [c.320]

FIND FEED ENTHALPY FOR ADIABATIC FLASH [c.323]

F FIND INITIAL ESTIMATES FOR A AND T (IF NOT GIVEN) FOR ADIABATIC FLASH. lF(EB.LT -2) T9=200. [c.323]

DETERMINE KS AND ENTHALPIES AT 0.2 K T INCREASE FOR T DERIVATIVES (ADIABATIC) [c.324]

UPDATE PHASE COMPOSITIONS (ADIABATIC) [c.324]

FIND TEMPERATURE DERIVATIVES BY FINITE DIFFERENCE (ADIABATIC) OFT=(FP-F) S. [c.324]

LIMIT T TO RANGE TB - TO (ADIABATIC) [c.324]

FIND DERIVATIVE OF G WRT A (ADIABATIC) [c.325]

ON FAILURE TO CONVERGE ITERATION SET A TO 0 (T TO 0 ADIABATIC) AND [c.325]

Creating and optimizing a reducible structure. In this approach, a structure known as a superstructure or hyperstructure is first created that has embedded within it all feasible process operations and all feasible interconnections that are candidates for an optimal design. Initially, redundant features are built into the structure. As an example, consider Fig. 1.7. This shows one possible structure of a process for the manufacture of benzene from the reaction between toluene and hydrogen. In Fig. 1.7, the hydrogen enters the process with a small amount of methane as an impurity. Thus in Fig. 1.7 the option is embedded of either purifying the hydrogen feed with a membrane or passing directly to the process. The hydrogen and toluene are mixed and preheated to reaction temperature. Only a furnace has been considered feasible in this case because of the high temperature required. Then two alternative reactor options, isothermal and adiabatic reactors, are embedded, and so on. Redundant features have been included in an effort to ensure that all features that could be part of an optimal solution haVe been included. [c.9]

Temperature control. Let us now consider temperature control of the reactor. In the first instance, adiabatic operation of the reactor should be considered, since this leads to the simplest and cheapest reactor design. If adiabatic operation produces an unacceptable rise in temperature for exothermic reactions or an unacceptable fall in temperature for endothermic reactions, this can be dealt with in a number of ways [c.42]

Is Adiabatic Operation Acceptable [c.63]

Reactor heat carrier. Also as pointed out in Sec. 2.6, if adiabatic operation is not possible and it is not possible to control temperature by direct heat transfer, then an inert material can be introduced to the reactor to increase its heat capacity flow rate (i.e., product of mass flow rate and specific heat capacity) and to reduce [c.100]

The heat integration characteristics of reactors depend both on the decisions made for the removal or addition of heat and the reactor mixing characteristics. In the first instance, adiabatic operation is considered, since this gives the simplest design. [c.325]

Most gases (except H and He) undergo cooling when they are expanded adiabatically through a throttle. This is called the Joule-Thomson effect. The change in temperature is proportional to the drop in pressure the Joule-Thomson coefficient is the change of temperature per unit change of pressure. The effect, which is used for liquefying air, making solid carbon dioxide, etc. is related to departures from Boyle s law and Joule s law. H and He, which show a warming effect at ordinary temperatures, also show cooling if the experiment is conducted below their inversion temperatures. [c.229]

There can be subtle but important non-adiabatic effects [14, ll], due to the non-exactness of the separability of the nuclei and electrons. These are treated elsewhere in this Encyclopedia.) The potential fiinction V(R) is detennined by repeatedly solving the quantum mechanical electronic problem at different values of R. Physically, the variation of V(R) is due to the fact that the electronic cloud adjusts to different values of the intemuclear separation in a subtle interplay of mutual particle attractions and repulsions electron-electron repulsions, nuclear-nuclear repulsions and electron-nuclear attractions. [c.56]

FLASH determines the equilibrium vapor and liquid compositions resultinq from either an isothermal or adiabatic equilibrium flash vaporization for a mixture of N components (N 20). The subroutine allows for presence of separate vapor and liquid feed streams for adaption to countercurrent staged processes. [c.319]

FLASH CONDUCTS ISOTHERMAL (TVPE=1) OR ADIABATIC

THE SUBROUTINE ACCEPTS BOTH A LIQUID FEED OF COMPOSITION XF AT TEMPERATURE TL(K) AND A VAPOR FEED OF COMPOSITION YF AT TV

SOLVE 2 DIMENSIONAL NEMTON-RAPHSON ITERATION FOR A AND T CORRECTIONS 4 (ADIABATIC) [c.324]

Fixed-bed catalytic reactors. Tubular reactors are also used extensively for catal3dic reactions. Here the reactor is packed with particles of solid catalyst. Most designs approximate to plug-flow behavior. Figure 2.6 shows four possible arrangements for flxed-bed reactors. The first (Fig. 2.6a) is similar to a shell-and-tube exchanger in which the tubes are packed with catalyst. The second (Fig. 2.66) has the tubes constructed inside a furnace for high temperatures. The third (Fig. 2.6c) is a series of adiabatic beds with intermediate cooling or heating to maintain temperature control. The heating or cooling can be effected by internal or external exchangers. The fourth (Fig. 2.6rf) uses direct injection of a fluid to perform heat transfer. The injected fluid might typically be cold fresh feed or cooled recycled product to control the temperature rise in an exothermic reaction. This is known as cold-shot cooling. Many other arrangements are possible. [c.55]

Adiabatic operation. If adiabatic operation leads to an acceptable temperature rise for exothermic reactors or an acceptable fall for endothermic reactors, then this is the option normally chosen. If this is the case, then the feed stream to the reactor requires heating and the efiluent stream requires cooling. The heat integration characteristics are thus a cold stream (the reactor feed) and a hot stream (the reactor efiluent). The heat of reaction appears as elevated temperature of the efiluent stream in the case of exothermic reaction or reduced temperature in the case of endothermic reaction. [c.325]

Heat carriers. If adiabatic operation produces an unacceptable rise or fall in temperature, then the option discussed in Chap. 2 is to introduce a heat carrier. The operation is still adiabatic, but an inert material is introduced with the reactor feed as a heat carrier. The heat integration characteristics are as before. The reactor feed is a cold stream and the reactor efiluent a hot stream. The heat carrier serves to increase the heat capacity fiow rate of both streams. [c.325]

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. [c.409]

One common approximation is to separate the nuclear and electronic degrees of freedom. Since the nuclei are considerably more massive than the electrons, it can be assumed that the electrons will respond mstantaneously to the nuclear coordinates. This approximation is called the Bom-Oppenlieimer or adiabatic approximation. It allows one to treat the nuclear coordinates as classical parameters. For most condensed matter systems, this assumption is highly accurate [11, 12]. [c.88]

A dramatic set of experiments by Zewail involves the use of femtosecond pulse pairs to probe the wavepacket dynamics at the crossing between covalent and ionic states of Nal [25]. A first pulse promotes wavepacket amplitude from the ionic to tire covalent potential curve. The packet begins to move out, but most of the amplitude is reflected back from the crossmg between the covalent and ionic curves, that is, the adiabatic potential changes character to ionic at large distances, and this curve is bound, leading to wavepacket reflection back to the FC region. The result is a long progression of wavepacket revivals, with a slow overall decay coming from amplitude which dissociates on the diabatic curve every period. [c.243]

Consider two distinct closed thermodynamic systems each consisting of n moles of a specific substance in a volnme Vand at a pressure p. These two distinct systems are separated by an idealized wall that may be either adiabatic (lieat-impemieable) or diathermic (lieat-condncting). Flowever, becanse the concept of heat has not yet been introdnced, the definitions of adiabatic and diathemiic need to be considered carefiilly. Both kinds of walls are impemieable to matter a permeable wall will be introdnced later. [c.323]

See pages that mention the term

**Adiabatic**:

**[c.112] [c.115] [c.122] [c.319] [c.42] [c.326] [c.16] [c.426] [c.426] [c.89] [c.278] [c.323]**

Rules of thumb for chemical engineers (0) -- [ c.0 ]

Compressors selections and sizing (1997) -- [ c.30 ]