The Design of Hydrocarbon Recovery Units Using Solid Adsorbents
Authors: Leland Thomas , Holmes Richard E. 
Published: December 2007

Abstract
The solution to the unsteady-state mass- and heat-transfer equations describing the adsorption of a dilute component from a gas stream flowing through a packed bed is readily applicable to the design of hydrocarbon recovery units. The solution to these equations depends on the assumption of a linear equilibrium equation to relate concentrations on the surface to concentrations in the gas. This assumption is shown to be justifiable for components which are very dilute in the gas stream. This approach permits the prediction of the effects of bed shape and size, cycle time, and gas mass velocity on the recovery of each component. It also allows the time and gas flow rate needed for regeneration to be determined. The equations involve a constant for each component and another constant characterized by the type of adsorbent. These constants must be evaluated from operating data. Values of these constants determined for silica gel are presented. This paper points out the type of experimental data needed for a thorough design of hydrocarbon adsorption units.

Introduction
The growing importance of adsorption processes to recover hydrocarbons from natural-gas streams has created an urgent need for better methods to design and predict the performance of these processes. Since the original use of solid adsorbents in natural-gas processing was for dehydration, most of the current design methods for hydrocarbon recovery are extensions of those developed earlier for dehydration. These methods are based on an adsorptivity or bed loading factor defined as the amount of a particular component adsorbed per unit weight or per unit volume of the packed bed. The recovery of a given component is then expressed as an empirical function of its adsorptivity on a given adsorbent. In spite of the similarity and initial utility of these methods, they are not completely satisfactory in that they do not predict the effect of the dimensions of the bed in relation to flow rate and cycle time, and do not predict the distribution of various components along the length of the bed. It is possible, however, to make a considerable improvement in the design of these processes by applying the basic equations of mass and heat transfer applicable to gases containing small concentrations of adsorbing components flowing through granular beds. These equations have been developed and solved by Anzelius, Furnas, and Hougen and Marshall.

MASS TRANSFER IN PACKED BEDS
The material balance on one component in a differential length of a packed bed is
............................(1)
where G = mass velocity of the inert constituents (assumed to be methane), lb/hr-sq ft, y = weight of an adsorbing component in the gas per unit weight ofinert, lb of a given constituent per lb of methane, x = bed length, ft,= packed bed density, lb/cu ft,= gas density, lb/cu ft,= void fraction in the bed, t = time, hours, and w = weight of a given component adsorbed per unit weight of adsorbatefree solid, lb/lb pure adsorbent. The term on the left side of Eq. 1 represents the flow rate per unit bed volume of a component entering less the flow rate per unit bed volume of that component leaving the differential bed length. The terms on the right side represent, respectively, the accumulation rates per unit bed volume on the solid and in the gas phase within the differential bed section. The last term is negligible for this application since is quite small in comparison with and. The partial differential ( ) is determined by the mass-transfer rate between gas and solid in the differential section.
............................(2)
where y* = the concentration which would exist in the gas phase if equilibrium existed between gas and solid at composition w, and H = the height of a transfer unit, ft.
JPT
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