Bed depth service time

The sinq)]ified ertq)irical model assumes that y = w = 0 and z- I, which leaves fewer constants in Equation (6.5) to be determined e q)erimenta]ly. Under these circumstances there should be a linear relation between the filtration constant and the specific deposh. This is the required assunption behind the bed depth service time (BDST) approach. 

Breakthrough Curve-Bed Depth Service Time (BUST) Model. In the operation of a fixed-bed adsorption column, the service time, t, of the bed can be related to the bed depth, Z, for a given set of conditions by a model and equation called the bed depth service time model (BDST). The BDST offers a rapid method of designing fixed-bed columns. The influent solute concentration, Cq, is fed to the column, and it is desired to reduce the solute concentration in the effluent to a value not exceeding Cj. At the beginning of the operation, when the adsorbent is still fresh, the effluent concentration is actually lower than the allowable concentration, Cj, but, as the operation proceeds and the sorbent reaches saturation, the effluent concentration reaches Cj. This condition is called the break point. 

Figure 6,10 Bed depth service time graph (adapted from Faust and Alyl987).

Adsorption for gas purification comes under the category of dynamic adsorption. Where a high separation efficiency is required, the adsorption would be stopped when the breakthrough point is reached. The relationship between adsorbate concentration in the gas stream and the solid may be determined experimentally and plotted in the form of isotherms. These are usually determined under static equilibrium conditions but dynamic adsorption conditions operating in gas purification bear little relationship to these results. Isotherms indicate the affinity of the adsorbent for the adsorbate but do not relate the contact time or the amount of adsorbent required to reduce the adsorbate from one concentration to another. Factors which influence the service time of an adsorbent bed include the grain size of the adsorbent depth of adsorbent bed gas velocity temperature of gas and adsorbent pressure of the gas stream concentration of the adsorbates concentration of other gas constituents which may be adsorbed at the same time moisture content of the gas and adsorbent concentration of substances which may polymerize or react with the adsorbent adsorptive capacity of the adsorbent for the adsorbate over the concentration range applicable over the filter or carbon bed efficiency of adsorbate removal required. 

Hutchins (1993) proposed a linear relation between the bed depth and service time, which can be written as ... 

Equation (15.32) enables the service time, t, of an adsorption bed to be determined for a specific bed depth, Z, of adsorbent. The service time and bed depth are correlated with the process parameters the initial poUutant concentration, solution flow rate, and adsorption capacity are the factors in the first term on the right-hand side of Eq. (15.31). The second term on the right-hand side of Eq. (15.31) represents the time required for the poUutant to establish its breakthrough curve that is, it represents that part of the bed that is not saturated when the poUutant concentration in the solution leaving the bed is above the breakthrough concentration, Q. 

As for the empty bed contact time method, the BDST method is also used extensively by the water industry and can be applied to other industrial situations. The assumption is that the adsorption rate is proportional to both the residual adsorbent capacity and the remaining adsorbate concentration. The relationship between the service time, /, the linear velocity, u, the depth of adsorbent bed, L, the rate constant, k, the adsorptive capacity. No (mass per unit volume), the influent concentration, co, and the concentration at breakthrough, Cb is given by the following equation in which dimensionally consistent units must be used ... 

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