Wheeler-Jonas equation

Abstract To design an adsorption cartridge, it is necessary to be able to predict the service life as a function of several parameters. This prediction needs a model of the breakthrough curve of the toxic from the activated carbon bed. The most popular equation is the Wheeler-Jonas equation. We study the properties of this equation and show that it satisfies the constant pattern behaviour of travelling adsorption fronts. We compare this equation with other models of chemical engineering, mainly the linear driving force (LDF) approximation. It is shown that the different models lead to a different service life. And thus it is very important to choose the proper model. The LDF model has more physical significance and is recommended in combination with Dubinin-Radushkevitch (DR) isotherm even if no analytical solution exists. A numerical solution of the system equation must be used. 

The most popular and almost uniquely used equation for representing breakthrough curves is the Wheeler [5] or Wheeler -Jonas equation (Eq.17.4) ... 

Lodewyckx P, Wood GO, Ryu SK (2004) The Wheeler-Jonas equation a versatile tool for the prediction of carbon bed breakthrough times. Carbon 42 1351-1355... 

Wu J, Claesson O, Eangmark I, Hammarstrom LG (2005) A systematic investigation of the overall rate coefficient in the Wheeler-Jonas equation for adsorption on dry activated carbons. Carbon 43 481 90... 

Wheeler-Jonas model for VOCs adsorption The Wheeler-Jonas equation is used for adsorption of VOCs using carbons. This equation is of the same form of the Thomas model with some modifications ... 

According to the experimental data, the first appearance of toluene in the exit stream is at about 50 min, while after 100 min the exit concentration is 10% of the inlet one. Calculate the time needed for the same breakpoint concentration using the Wheeler-Jonas equation and Wood and Stampfer equation for die evaluation of kv. 

Moreover, examine die Wheeler-Jonas equation for the specified experimental conditions. On the basis of the results, predict the breakpoint time for lower interstitial velocities down to 1 m/s. 

P. Lodewyckx and E. F. Vansant, Estimating the overall mass transfer coefficient kv of the Wheeler-Jonas equation a new simple model, Am. Ind. Hyg. Assoc. J. 501 -505 (2000). 

Fig.20. Adsorption front and breakthrough curve for an activated carbon bed 5.2.2, The Wheeler-Jonas equation...

The Wheeler-Jonas equation has been used extensively in the case of pure physisorption on granular carbons. But recently, it has been demonstrated it can be equally well applied in a number of very divergent cases. The first extension is on the type of adsorbent, especially new types. The validly of the Wheeler-Jonas equation has been demonstrated [117,118] for both activated carbon fibres (ACF) and activated carbon monoliths (ACM). The equation itself and the calculation of the capacity IFe remain unchanged. As for the estimation of the overall mass transfer coefficient, the normal equation stays valid, providing a correct interpretation of the equivalent diameter of the particles . For ACFs, dp has been calculated fiom the total external surface. Given their small diameter, dp is essentially related to the length of the fibres [ 119]. For ACMs, dp seems to be related to the internal diameter of the channels. 

Many factors influence adsorption of chemical warfare agents and toxic industrial chemicals by activated carbon. Some of them have already been mentioned in the previous sections. In this section the nature of this influence will be described and explained, where possible. In most cases this can be illustrated by looking at the effect of changing a particular parameter on breakthrough time predictions. Therefore, where possible, the Wheeler-Jonas equation (Eq.36) vrill be used to explain the effect of changing a given parameter. 

The water adsorbed on the carbon will also influence adsorption kinetics. Various authors [137,138] have demonstrated this. In contradiction to the capacity which can be influenced positively or negatively (see section 6.5.1), mass transfer will always slow down. The overall mass transfer coefficient, of the Wheeler-Jonas equation does not differentiate between the different types of diffusion. Consequently, every impact of water on the adsorption kinetics win be translated into a drop of k, values. 

One of tlte most commonly used models is the one proposed by Wheeler and Jonas in the early 70s [113,114], This equation, also known as the Reaction Kinetic equation, can be expressed in several forms. The most explicit one is given in Eq.36 ... 

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