Batch leaching is similar to batch extraction, and the equations developed in Section 13.6 can be adapted when the solution is dilute or there is an insoluble solid matrix. We have \(12.5 \mathrm{~L}\) of pure water that we will use to leach \(10.0 \mathrm{~L}\) of wet sugarcane solids. Equilibrium data are in Problem 14.D9.

Problem 14.D9

Experimental data for leaching sugar from sugarcane with water show that a reasonable value for effective equilibrium constant \(y / x=m_{E}\) is 1.18 where \(\mathrm{y}\) and \(\mathrm{x}\) are the solute weight fractions in liquid and solid, respectively. Batch leaching is similar to batch extraction, and if the terms are translated, the same equations can be used. We are doing a single-stage batch leaching of sugarcane with water to recover sugar. The feed to the leaching process is \(1.0 \mathrm{~kg}\) of solids (on a dry basis). In this feed, cane contains \(5.5 \mathrm{wt} \%\) sugar. The inlet solvent is pure water. Assume the overflow and underflow amounts are constant.

a. Find the fractional recovery of sugar in the water if the water and wet sugarcane solids are mixed together and after settling, the water layer is removed.

b. Find the fractional recovery of sugar in the water if a continuous solvent addition batch leaching system analogous to Figure 13-12 is used.

Figure 13-12

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Solvent presaturated with diluent 8 settler Solvent Product dE,y diluent Rank tank, X recycle tank