3. In thermal distillation processes such as MED and MSF, heat energy is supplied to warm up and then vaporize the saline feed water. The specific heat capacity, cp, is the heat energy needed to raise the temperature of a unit mass of solution by 1 ˚C, and the enthalpy of vaporization, hvap, is the heat energy required to evaporate a unit mass of water from the saline feed water. For seawater, cp is ~4.0 kJkg−1K −1 over the range of temperatures considered here, hvap is ~2300 kJ/kg ˚C, and the boiling point is ~105 ˚C at atmospheric pressure. The seawater is initially at 20 ˚C. Assume that the density of seawater is equivalent to the density of pure water and is 1.0 kg/L. Express specific energies in kWh/m3 .
a. Determine the energy needed to raise the temperature of a unit mass of seawater from 20 ˚C to 105 ˚C. Compare this to hvap and comment.
b. Calculate the specific energy needed to distill seawater initially at 20 ˚C. I.e., the energy per unit mass to increase the seawater temperature from 20 ˚C to 105 ˚C and then evaporate it.
c. The net energy requirement of thermal distillation of seawater can be reduced by recycling the thermal energy. This is done by using the heat released by the condensing steam to warm up the seawater feed stream. Determine the net specific energy of thermal distillation of seawater, if all the thermal energy from the condensing steam is captured for reuse.
d. The steam that condensed into water is still hot at 105 ˚C, and the thermal of this hot product water can additionally be utilized to heat the seawater. If the hot product water passes some of its thermal energy to the seawater and eventually cools down to 50 ˚C, find the net specific energy to desalinate seawater by distillation.
e. Compare and comment on your answers in (b), (c), and (d)
f. The specific energy for reverse osmosis desalination is ~3.5 kWh/m3 . What is the temperature the product water in thermal distillation has to cool down to, in order to pass enough thermal energy to heat up the seawater feed such that the net specific energy in equal to RO desalination? Comment on the technical constrains to execute such a heat exchange.
g. cp and hvap are almost completely insensitive to the salinity of the seawater. I.e., cp and hvap only increases very slightly when the seawater salinity goes up. Contrast this with the dependence of osmotic pressure on solution concentration, and comment an advantage thermal distillation has over reverse osmosis.
4. Consider 1 m3 of 500 mMNaCl solution. Suppose we have a perfectly selective reverse osmosis membrane (i.e., allows only the permeation of water, completely rejects salts). Use temperature T = 25 ˚C.
Part I
a. Using the Van’t Hoff equation, determine the osmotic pressure of the solution. b. By applying a sufficiently large external hydraulic pressure, we can drive the permeation of water across the RO membrane. After 0.5 m3 of water has permeated across the membrane, determined:
i. the concentration of the retained brine
ii. the osmotic pressure of the brine
iii. the concentration of the product water
iv. the recovery, Y
c. What is the minimum hydraulic pressure that we need to apply to achieve the desalination described in (b)? [Hint: consider the equilibrium conditions at the end of the process]
d. The work done in constant pressure RO desalination, W, is given by
W = P∆V
where P is the applied hydraulic pressure and ∆V is the change in volume of the pressurize saline solution. Calculate the work done in carrying out the separation process described in (b), if the hydraulic pressure applied is the answer to (c). Express you answer in kWh.
e. Convert the answer in (d) to specific energy, the energy consumed to produce 1 m3 of product water.
Part II
f. Instead of performing RO desalination at one constant pressure, we can gradually ramp up the pressure in five steps, with 0.1 m3 of water permeating across in each step. The constant pressure to apply at each step would be the equilibrium osmotic pressure of the concentrated solution at the end of that step (i.e., ∆P = ). Fill out the table below that details the five-step RO.
g. Determine the total work done and the specific energy for the 5-step RO desalination.
h. Compare the answers in (g) to (d) and (e). What effect does increasing the number of steps has on the specific energy?
Part III
i. Each step of the constant pressure RO desalination process can be made even finer. Instead of carrying out 5 steps, suppose the process is divided into 50 equal steps (i.e., ∆V is 0.01 m3 for each step). Determine the specific energy fo
Part IV
j. Use the equation in the lecture slides to determine the minimum energy of separation, Emin, for 50% recovery of the 500 mMNaCl solution.
k. Compare and comment on the specific energies in (g) and (i) to (j). If the number of steps in (i) further increases, will the specific energy go below the answer in (j)?
l. Elaborate on the thermodynamic significance of the specific energies in (e) and (j).