Chapter 8, Problem 8.74P

The manufacturers of a new oatmeal product want to determine the least expensive way to safeguard and transport their product. They choose lyophilization (freeze drying), which removes most of the water from the product, making it lighter and therefore less costly to transport over long distances, and substantially increases its shelf life. Lyophilization also removes some of the impurities introduced by industrial farming methods.

A solid feed stream containing 70.0 wt% oatmeal, 27% water (ice), and the balance organic impurities enters a heated vacuum chamber at a rate of 1.0 × 10³kg/h at a temperature of -10°C. In the vacuum chamber, 97% of the water and 99% of the organic impurities in the feed sublime (vaporize). The dried product is then packaged and shipped. A vapor stream emerges from the chamber at 15°C. During the process, 7.95 × 10 s kJ/h of heat is transferred to the system.

1. Draw and completely label a flowchart of the process and perform a degree-of-freedom analysis.

Calculate the compositions and flow rates of the product and waste streams.

Find the temperature of the product stream, using the following values for heat capacity and heat of sublimation and neglecting the contribution of the organic impurities to the energy balance.

   $\begin{array}{l}{C}_p\left[H_{2}O\left(s\right)\right]=2.11kJ/\left(kg\cdot °C\right)\\ C_p\left[H_{2}O\left(v\right)\right]=1.86kJ/\left(kg\cdot °C\right)\\ C_p\left(oatmeal\right)=1.5kJ/\left(kg\cdot °C\right)\\ \left(\Delta {\hat{H}}_{subl}\right)H_{2}O=2845kJ/kg\end{array}$

(d) Evaporation is a more conventional way to dry a wet solid—that is, heating the solid at atmospheric pressure to a temperature close to the boiling point of the liquid (in this case, water) and holding it there long enough to drive off essentially all of the liquid. Give at least two reasons why freeze drying is a better alternative for drying the oatmeal.