Question

Your company has recently developed a microorganism which produces large amounts of an enzyme for oxidizing phenolics. Such an enzyme can be used in a fixed-bed reactor to improve the taste of drinking water. For such a use, it must be unusually pure. To isolate the enzyme, you plan to adsorb it on a custom-synthesized ion-exchange resin. The isotherm of the resin is such that, at a liquid velocity of 10 cm/hr, you get no solute out of the bed for 3 hr and the feed concentration at 4 hr. The outlet concentration between these limits is nearly linear. Everything's great. Then because of unexpected demand, you are asked to double the velocity of the feed. Your experiments show that the slope of the linear region of a plot of exit concentration versus time varies inversely with velocity. How long should you run the bed?

Answer 1

To determine how long you should run the bed at the doubled velocity, we need to analyze the information provided and make some calculations.

From the given information, we know that at a liquid velocity of 10 cm/hr, there is no solute coming out of the bed for 3 hours, and at 4 hours, the feed concentration is reached. This suggests that the breakthrough time, which is the time it takes for the solute to start appearing in the outlet, is between 3 and 4 hours.

Now, when the velocity is doubled, the slope of the linear region of the plot of exit concentration versus time varies inversely with velocity. This means that as the velocity increases, the slope decreases.

To estimate the breakthrough time at the doubled velocity, we can use the inverse relationship between velocity and slope. Let's assume the original slope at 10 cm/hr is S. Since the velocity is doubled, the new velocity is 20 cm/hr, and the new slope can be represented as 1/2S.

Now, we need to find the time it takes for the solute to reach the feed concentration at the doubled velocity. Let's call this time T.

Using the information given, we can set up the following equation:

(1/2S) * T = 4 hours

Solving for T, we get:

T = (4 hours) * (2S)

T = 8S hours

Therefore, at the doubled velocity of 20 cm/hr, you should run the bed for 8 times the original breakthrough time, which is 8S hours.

It's important to note that the value of S is not provided in the given information, so you would need to determine it experimentally or through further analysis to calculate the exact time to run the bed.