Adiabatic heat of adsorption

In a completely analogous way, it is possible to obtain an expression corresponding to the adiabatic heat of adsorption. The final result is... 

Equilibrium vapor pressure of bulk liquid Relative pressure, p/p 0 Statistical mechanical partition function Density in molecules/cubic centimeter Gas constant per mole Number of moles of adsorbed gas Number of moles of adsorbent Isosteric heat of adsorption Differential heat of adsorption Isothermal heat of adsorption Adiabatic heat of adsorption... 

A survey of the literature shows that although very different calorimeters or microcalorimeters have been used for measuring heats of adsorption, most of them were of the adiabatic type, only a few were isothermal, and until recently (14, 15), none were typical heat-flow calorimeters. This results probably from the fact that heat-flow calorimetry was developed more recently than isothermal or adiabatic calorimetry (16, 17). We believe, however, from our experience, that heat-flow calorimeters present, for the measurement of heats of adsorption, qualities and advantages which are not met by other calorimeters. Without entering, at this point, upon a discussion of the respective merits of different adsorption calorimeters, let us indicate briefly that heat-flow calorimeters are particularly adapted to the investigation (1) of slow adsorption or reaction processes, (2) at moderate or high temperatures, and (3) on solids which present a poor thermal diffusivity. Heat-flow calorimetry appears thus to allow the study of adsorption or reaction processes which cannot be studied conveniently with the usual adiabatic or pseudoadiabatic, adsorption calorimeters. In this respect, heat-flow calorimetry should be considered, actually, as a new tool in adsorption and heterogeneous catalysis research. 

In addition, there are a number of different calorimetric methods to determine heats of adsorption. For example, we may distinguish between isothermal and adiabatic heats depending on the type of calorimeter involved. Of course, thermodynamic relationships exist among these various quantities. We shall not pursue these topics, but one should be aware of the differences and seek precise definitions if the need arises. 

For a system with n components (including nonad-sorbable inert species) there are n — 1 differential mass balance equations of type (17) and n — 1 rate equations [Eq. (18)]. The solution to this set of equations is a set of n — 1 concentration fronts or mass transfer zones separated by plateau regions and with each mass transfer zone propagating through the column at its characteristic velocity as determined by the equilibrium relationship. In addition, if the system is nonisothermal, there will be the differential column heat balance and the particle heat balance equations, which are coupled to the adsorption rate equation through the temperature dependence of the rate and equilibrium constants. The solution for a nonisothermal system will therefore contain an additional mass transfer zone traveling with the characteristic velocity of the temperature front, which is determined by the heat capacities of adsorbent and fluid and the heat of adsorption. A nonisothermal or adiabatic system with n components will therefore have n transitions or mass transfer zones and as such can be considered formally similar to an (n + 1)-component isothermal system. 

Microcalorimeters are well suited for the determination of differential enthalpies of adsorption, as will be commented on in Sections 3.2.2 and 3.3.3. Nevertheless, one should appreciate that there is a big step between the measurement of a heat of adsorption and the determination of a meaningful energy or enthalpy of adsorption. The measured heat depends on the experimental conditions (e.g. on the extent of reversibility of the process, the dead volume of the calorimetric cell and the isothermal or adiabatic operation of the calorimeter). It is therefore essential to devise the calorimetric experiment in such a way that it is the change of state which is assessed and not the mode of operation of the calorimeter. 

R. B. Anderson The heat of adsorption was the cause of the temperature increase. The adiabatic compression of gas introduced to the evacuated sample should lead to a negligible temperature increase. 

The heat of adsorption is a measure of the energy required for regeneration in gas- or vapor-phase applications, and low values are desirable. It also indicates the temperature rise that can be expected due to adsorption under adiabatic conditions. Again, there are several definitions isosteric, differential, integral, and equilibrium, to name a few. The most relevant (because it applies to flow systems instead of batch systems) is the isosteric heat of adsorption, which is analogous to the heat of vaporization and is a weak function of temperature. The definition is... 

If the heat of adsorption is measured adiabatically and reversibly (including a PdV work term) there is an analogous heat of compression with the result (87)... 

There has been considerable experimental uncertainty for some time about the connections between calorimetric and isosteric heats. Hill (18) showed that in the reversible isothermal process, Eq. (56) must be replaced by Eq. (57). Kington and Aston (87) derived the analogous Eq. 58 for the reversible adiabatic process and then proceeded to show experimentally that their adiabatic calorimeter actually behaves reversibly. Thus for six values of 6 from 1.16 to 1.33, qa is larger than qBt by successive values of 84, 107, 143, 128, 154, and 111 cal./mole. But qa is larger than the right-hand side of Eq. (58), i.e., qst properly corrected, only by the successive values —48, —25, +10, —9, +14 and —34 cal./mole, which is excellent agreement in view of the estimated maximum error of 15 cal./mole in qa and +15 cal./mole in q,t. Hence the work of Kington and Aston completely clarifies for the first time the relations between isosteric and calorimetric heats of adsorption. 

The operation mode of fixed bed adsorbers can be isothermal (very small adsorptive concentration in the fluid and low heats of adsorption), nonisothermal, and adiabatic. The heat loss of large industrial adsorbers is often so small in comparison to the heat production by adsorption that the bed is nearly operated adiabatically. In such a case not only the mass balances but also the ener balances have to be taken into accoimt to get information on the operating mode and the fields of concentration and temperature in a fixed bed. These balances for the adsorbent (Index S = solid) and the fluid (Index G) are... 

Equations (22j-(2dJshow that the unsteady-state mass and energy balances within the adiabatic adsorber can be written using the surface excess of each component of the gas mixture as the primary variables to define the extent of adsorption. The isosteric heat of adsorption of component i (q,) and the heat capacity of the adsorption system (C ), defined using the GSE framework, become the appropriate thermodynamic properties to describe the energy balance. 

With adiabatic operation, 0 = 0, the temperature of the adsorbent bed starts from an initial value at the begiiming of the loading phase and increases to the final value Since the heat of adsorption... 

The simplifying assumption found useful in gas absorption, that the temperature of the fluid remains substantially constant in adiabatic operations, will be satisfactory only in solute collection from dilute liquid solutions and is unsatisfactory for estimating temperatures in the case of gases. Calculation of the temperature effect when heats of adsorption are large is very complex [2, 89]. The present discussion is limited to isothermal operation. 

Energy balances may need to be retained in the rigorous model if the heat of adsorption is significant and is retained in, or lags behind, the MTZ. Real packed bed adsorption systems are likely to encompass the entire spectrum from near-isothermal to near-adiabatic operation. Since the behaviour of each extreme is quite different it is important to know whether either of the extreme cases can be regarded as a reasonable representation or whether a more general model is required. 

The concept provides for adiabatic steam catalytic one-stage conversion with carbon dioxide removal through short-cycle heat-free adsorption, followed by return of a part of product fraction to conversion. This option assumes maximum usage of initial hydrocarbon raw material to produce the HMM. 

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