The modelling and identification of the mechanisms governing adsorption of gases in microporous and biporous sorbent material using the batch frequency response technique is the subject of this thesis. Mathematical models of the batch frequency response apparatus in both full frequency response and single step frequency response modes of operation have been rigorously derived and solved using both analytical and numerical methods, thereby providing a library of solutions directly applicable to the analysis of experimental frequency response data. These analyses cover sorption of a single component or of multiple components under both isothermal and nonisothermal conditions, in microporous or biporous sorbent material, allowing for various microparticle and macroparticle shapes and several typical microparticle size distributions. An indirect approach to systems identification is adopted in which an appropriate model of the sorption dynamics is matched to a series of frequency response data sets and the defining dynamic parameters extracted, terminating when the defining dynamic parameters are physically reasonable and a good match is achieved between the experimental frequency response data and the model prediction.
Simple models of single component adsorption in microporous adsorbents under isothermal conditions incorporating mass diffusion and surface barrier resistance to mass transfer are the initial focus of attention. It is shown that such simplistic models can account for the idealised diffusion and surface barrier forms of characteristic functions. On extending the isothermal analysis to cases of multiple sorbate adspecies with different affinities and mobilities it is shown that an isothermal model can also account for the idealised bimodal out-of-phase and in-phase offset forms of characteristic functions. According to the isothermal paradigm, the bimodal out-of-phase form of characteristic functions occurs with either two mobile adspecies having variant mass transfer dynamic time scales, or one immobile adspecies and one mobile adspecies with interchange between them, where the time scale of the immobilisation step is slower than the mobile mass transfer dynamic time scale. An apparent in-phase offset form of characteristic functions is observed when the respective mass transfer time scales of the two sorbate adspecies are significantly different, and the uptake of the faster adsorbing sorbate adspecies is close to that at saturation.
Adsorption is intrinsically an exothermic process and nonisothermal influences accompanying sorption may impact upon both the adsorption dynamics and equilibria. Indeed, the intrusion of such nonisothermal influences has led to the incorrect assignment of controlling mechanisms in many cases reported in the literature. An interesting feature of these nonisothermal influences is their proportional impact on the characteristic functions. Even in experiments conducted at low pressures where the magnitude of the raw frequency response functions is small, these influences remain significant and apparent after normalisation of the characteristic functions. Accordingly models of single and multiple component absorption in microporous and biporous adsorbents allowing for particle and gas phase heat transfer mechanisms are considered in the second section of the thesis. It is shown that such nonisothermal models can also account for the idealised bimodal out-of-phase and in-phase offset forms of characteristic functions. According to the nonisothermal paradigm, the bimodal out-of-phase form of characteristic functions arises when the governing thermal transfer time scale is larger than that governing the intrinsic mass transfer mechanism. The in-phase offset form of characteristic functions results from the blank correction procedure and is particularly marked when the specific heat capacity of the gas phase is small such as is the case with noble gases.
These frequency response models are successfully applied to analyse experimental frequency response data reported in the literature, including single component adsorption in microporous zeolite sorbents - N2 / 5 A and Xe / Silicalite-1, single component adsorption in biporous zeolite pellets - i-C4H10 /13X and Kr / Na-Mordenite, and binary adsorption of N2 and O2 in biporous 4A zeolite pellets.
The frequent intrusion of nonisothermal effects on batch frequency response measurements suggests that a concurrent measurement of the gas phase temperature response, and where practicable, the sorbent temperature response, together with the pressure transducer response is highly desirable and is an important source of corroborating information for systems identification purposes.
It is shown that in experiments using a support such as glass-wool, the additional thermal capacity of the support can account for a reduction in the heat transfer peak in the normalised corrected out-of-phase characteristic function and an increase in the offset between the normalised corrected in-phase and out-of- phase characteristic functions a high frequency.
In the batch frequency response approach macroscale control of mass transfer is distinguished by variation of the dimensions of the sorbent pellets. Coupled macropore and micropore diffusion confrol of mass transfer results in an intersection between the normalised corrected in-phase and out-of-phase characteristic functions even under isothermal conditions. If the sorbent temperature response is measured concurrently with the pressure transducer response, the possibilities of either a surface barrier at the pore mouth of the micropore or coupled macropore and micropore diffusion control of mass transfer can be distinguished. In the former case, an intersection between the in-phase and out-of-phase sorbent particle temperature response functions is observed, however, in the latter it is not.
In the case of multicomponent systems, both dynamic and equilibrium interactions may be significant. In a binary system, numerical simulation indicates that the cases of dynamic interactions with no equilibrium interactions, and equilibrium interactions with no dynamic interactions, maybe distinguished from the default case of neither type of interaction using the overall characteristic functions. Unfortunately, such simulations indicate that both the component and overall characteristic functions of the default case may sometimes be almost indistinguishable from those in the case of both dynamic and equilibrium interactions.
Alternative time-domain volume perturbations including the single step frequency response, stochastic perturbations and pseudo-random binary perturbations are analysed in the third section of the thesis. Such perturbations can be applied with only slight modification to the square-wave type of batch frequency response apparatus. Time domain simulations of the single step frequency response technique indicate that the impact of short time scale mechanisms of mass and heat transfer may be masked by the finite response time of the pressure transducer. The defects in the blank correction procedures to the single step frequency response data suggested by Micke and co-workers and by Rees and co-workers are also highlighted. In the former case, the blank correction is shown to be inconsistent with any physically realisable pressure transducer, whilst in the latter case, the proposed blank correction leads to an overestimate of the diffusion coefficient when thermal dissipation through the apparatus walls is slow, and an underestimate of the diffusion coefficient when thermal dissipation through the apparatus walls is rapid. A potential benefit of stochastic or pseudo-random binary perturbations, is the possibility of determining the impulse response of the system, or alternatively, the frequency response of the system over a finite bandwidth, from response measurements in a single run after the initial settling sequence, without having to apply successive settling sequences at each frequency of interest.
A simple guide to the interpretation of frequency response spectra is provided in the final section of the thesis, detailing the impact of global variables such as the initial equilibrium pressure and temperature on typical single component sorbate / sorbent systems. These simulation indicate that the batch frequency response technique is capable of determining many of the controlling dynamic mechanisms and respective dynamic time scales required in the design of physical plant and provides a degree of detail greater than that of more conventional techniques.