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## Calculations

The breakthrough charge X_{D.} is derived from the experimentally determined breakthrough time, the mass flow of the adsorptive (calculated from the volume flow V_{R.}) and the mass of the adsorbent is calculated.

The saturation load X_{S.} can be calculated analogously from the saturation time. Here, the proportion of adsorptive that flows out of the adsorber after the breakthrough must be subtracted. Since the determination of the integral term of the concentration of adsorptive after the breakthrough is relatively time-consuming, taking into account the so-called half-life t_{H} (c_{A.}/ c_{E.} = 0.5) the equation for the saturation load can be simplified to a good approximation.

$\begin{array}{l}{X}_{\mathrm{D.}}=\frac{\stackrel{\xb7}{m}}{{m}_{\mathrm{A.}d}}{t}_{\mathrm{D.}}\\ \\ {X}_{\mathrm{S.}}=\frac{\stackrel{\xb7}{m}}{{m}_{\mathrm{A.}d}}\phantom{\rule{0.7999999999999999ex}{0ex}}({t}_{\mathrm{S.}}-\phantom{\rule{0.7999999999999999ex}{0ex}}\underset{0}{\overset{{t}_{\mathrm{S.}}}{\int}}\frac{c}{{c}_{\mathrm{E.}}}\phantom{\rule{0.7999999999999999ex}{0ex}}dt)\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\phantom{\rule{0.7999999999999999ex}{0ex}}\underset{0}{\overset{{t}_{\mathrm{S.}}}{\int}}\frac{c}{{c}_{\mathrm{E.}}}\phantom{\rule{0.7999999999999999ex}{0ex}}dt=\mathrm{outflowing}\phantom{\rule{0.7999999999999999ex}{0ex}}\mathrm{Adsorptive}\phantom{\rule{0.7999999999999999ex}{0ex}}\mathrm{after}\phantom{\rule{0.7999999999999999ex}{0ex}}\mathrm{to\; the}\phantom{\rule{0.7999999999999999ex}{0ex}}\mathrm{breakthrough}\\ \\ {X}_{\mathrm{S.}}=\frac{\stackrel{\xb7}{m}}{{m}_{\mathrm{A.}d}}{t}_{H}\end{array}$

The adsorption zone h_{Z} can now be calculated from the breakthrough and saturation loading as well as the bed height of the adsorbent for the respective adsorber with the following equation.

${H}_{Z}=H(1-\frac{{X}_{\mathrm{D.}}}{{X}_{\mathrm{S.}}})$