Question

In the manufacture of an active pharmaceutical ingredient (API), the API goes through a final purification step in which it is crystallized , filtered, and washed. The washed crystals contain 47 wt% water. They are fed to a tunnel dryer and leave the dryer at a rate of 165 kg/h containing 5% adhered moisture. Dry air enters the dryer at 145°F and 1 atm, and the outlet air is at 130°F and 1 atm with a relative humidity of 50%. Calculate the rate (kg/h) at which the API enters the dryer and the volumetric flow rate (ft3/h) of inlet air.

Answer 1

Given: The washed crystals contain 47 wt% water

Therefore % Crystal in feed, F = 100- 47 = 53 %

after passing through dryer the % of water = 5%

Therefore % Crystal in product = 100- 5 = 95 %

The flow rate of product = 165 kg/hr

So we can say that the amount (not percentage) of crystal will be same in the feed and the product

So flow rate of feed X % of crystal in feed = Product flow rate X % of crystal in product

F X 53 = 165 X 95 = 15675

F = 295.754 kg/hr

We may assume that flow rate of dry air = D Kg / hour, amount of water in air = W Kg / hour

flow rate of outlet air = (D+W) kg/hr

Again we can say that the total amount of water + crystal in the feed = total amount of water + crystal in product,

D + 295.754 = 165 + (D+W)

W = 130.754 kg/hr

also the temperature is

T_out = 135 ^oF = 330.37K

T_in = 145^oF = 335.93 K

Here now we need standard data of pressure of saturated air

P_sat at T = 16500 Pa

P_total = 1 atm = 101325 Pa

W/D = 0.5 X P_sat / P_total

Putting values

D = 130.754 X 101325 / (0.5 X 16500) = 1605.896 kg/hr

using ideal gas equation

PV=nRT

P = pressure

V = volume

n = mass / Molecular weight

R = gas constant = 0.0821 L atm / mol K

T = tempearature = 335.93 K (Tin)

Rearranging

P X molecular weight /RT = Mass / Volume = density

Molecular weight of air = 28.97 g / mole

Density of air at T_in = P M_w / RT = 1 X 28.97 / (0.0821 X 335.93) = 1.05 g/L = 1.05Kg / m^3

Volumetric flow rate = D / Density = 1605.896 / 1.05 = 1529.42m³/hr

Now we have to convert m^3 to ft^3

= 1529.42 X3.28³ ft³/hr = 53969.49ft³/hr