Question

Scale-up of Pilot Plant Tests of a Reciprocating-Plate Extraction Column The pilot plant data in Table P6.9 are for the extraction of an antibiotic from whole \begin{tabular}{lccc} & \multicolumn{2}{c}{ Flow rates \((\mathbf{m l} / \mathbf{m i n})\)} & \\ \cline { 2 - 4 } Run number & Broth & Chloroform & Antibiotic concentration in raffinate (mg/liter) \\ \hline 1 & 45 & 135 & 2 \\ 2 & \(67.5\) & 135 & 3 \\ 3 & 125 & 135 & 30 \\ 4 & 80 & 120 & 5 \\ 5 & 100 & 150 & 7 \\ 6 & 120 & 180 & 9 \\ 7 & 150 & 225 & 25 \end{tabular} fermentation broth using the solvent chloroform in a reciprocating-plate extraction column. The concentration of the antibiotic was \(1.4 \mathrm{~g} / \mathrm{liter}\) in the broth. The column had a diameter of \(2.54 \mathrm{~cm}\), and the height of the plates was \(3.05 \mathrm{~m}\). The partition coefficient \(K\) for the antibiotic is known to be \(2.68\). For each pilot run, determine the diameter and height of the plates for the plant column that would be required for processing 50,000 liters of broth in \(12 \mathrm{~h}\) to give an exit raffinate concentration of antibiotic of \(10 \mathrm{mg} / \mathrm{liter}\), assuming a concentration of antibiotic in the feed broth of \(1.0 \mathrm{~g} / \mathrm{liter}\) (a spreadsheet is convenient for these calculations). Without doing a complete economic analysis, in your judgment which scaled-up pilot run appears to be optimum? (Data from A. E. Karr, W. Gebert, and M. Wang, Can. J. Chem. Eng., vol. 58, p. \(249,1980 .)\)

Short answer

In order to answer this question, it will be necessary to calculate the volume flow rate of the plant, the flow rates of the plant for each pilot run, and the new dimensions (diameter and height) of the plant column. Then, it will be needed to make an informed judgement about which pilot run seems to be the optimum for scaling up based on the required extraction rate and the calculated dimensional changes.

Step-by-step solution

Calculate The Volume Flow rate

The volume flow rate of the broth for the plant per minute should be calculated first. This can be done using a simple conversion from hours to minutes: Volume flow rate = total volume needed / total time = 50000 liters / (12 hours * 60 minutes) = 69.44 liters/min.

Determine The Flow Rates For Each Run

Next, determine the broth and chloroform flow rates for each pilot run. The flow rates for all the pilot runs should be scaled up in the same proportion as the volume flow rate. This means each pilot run's broth and chloroform volume flow rate should be scaled up by multiplying with the factor 69.44 liters/min / pilot run's broth flow rate.

Calculate The Cross-Sectional Area

The next step is to calculate the cross-sectional area for each run. This is done using the formula for cross-sectional area of a cylinder \(A = \frac{D^2\pi}{4}\), where \(D\) is diameter. The diameter \(D\) for the plant can then be obtained by taking the square root of the result \(D = \sqrt{\frac{4A}{\pi}}\)

Calculate The Height

To obtain the height of the plates for the plant, one can use the relation between the heights and flow rates of the pilot plant and the plant: (height of plant) / (height of pilot plant) = (flow rate of plant) / (flow rate of pilot plant). By substituting the known values, we can solve for the height of the plates for the plant.

Find The Optimum Run

Finally, to find the optimum pilot run for scaling up, we need to consider the one that offers the highest extraction rate (lowest antibiotic concentration in raffinate) whilst requiring the lowest increase in diameter and height of plates. These judgments should be based on the calculated values obtained in the previous steps.

Key concepts

Pilot Plant Testing

Pilot plant testing is a critical phase in the development and scale-up of a new extraction process such as antibiotic extraction from fermentation broth. It bridges the gap between laboratory-scale research and full production scale. During pilot plant testing, the process is operated on a smaller scale, typically a reduced volume of materials or a miniature version of the plant, to validate the feasibility of the full-scale process.

This testing phase allows engineers to collect data on process dynamics, energy balance, material balance, and scale-up parameters. For instance, flow rates, temperature profiles, solvent efficacy, and other operational conditions are scrutinized to ensure the process can be scaled up successfully without compromising the quality or yield of the product.

Pilot plant testing also involves troubleshooting and optimization, allowing for identification and correction of any potential issues before the process is implemented on a larger scale, thus mitigating risks and helping to safeguard investments.

Antibiotic Extraction

Antibiotic extraction is the process of isolating active medicinal compounds from a fermentation broth. Antibiotics are typically produced through microbial fermentation and need to be separated from a complex mixture containing different components. The extraction of antibiotics from this mixture is a delicate process, as it involves retaining the antibiotic's efficacy and purity while removing impurities.

In the exercise provided, chloroform is used as a solvent to extract the antibiotic from the broth via a reciprocating-plate extraction column. This process separates the desirable antibiotic molecules based on their differing solubilities in water and organic solvents, a principle known as partitioning. Maintaining the optimal partition coefficient during this process is crucial as it directly influences the purity and yield of the extracted antibiotic.

Reciprocating-Plate Extraction Column

A reciprocating-plate extraction column is a type of extraction equipment used for liquid-liquid extraction. It is made up of several perforated plates that reciprocate to enhance contact between the two immiscible liquid phases, improving mass transfer. This contact is critical for the transfer of solute (antibiotic in this case) from the broth to the chloroform solvent.

The reciprocating motion of the plates generates turbulence which increases the surface area for mass transfer and improves the efficiency of the extraction process. Effective design of these columns involves optimizing parameters such as plate diameter and spacing, which directly affect the extraction rates and ultimately the concentration of the antibiotic in the raffinate (the residual liquid left after the extraction).

Partition Coefficient

The partition coefficient (\(K\)) is a fundamental parameter in solvent extraction processes, such as antibiotic extraction. It describes the ratio of concentrations of a compound in a mixture of two immiscible solvents at equilibrium. In mathematical terms, for a compound distributed between two phases, it's defined as:\[\begin{equation}K = \frac{\text{Concentration in organic phase}}{\text{Concentration in aqueous phase}}\end{equation}\]In antibiotic extraction, a favorable partition coefficient means that the antibiotic prefers to reside in the solvent (like chloroform) rather than in the water-based broth. A high partition coefficient makes the extraction process more efficient, which is desirable for scaling up the operation to process larger volumes of fermentation broth while maintaining the quality and yield of the antibiotic.

Volume Flow Rate Calculation

Calculating the volume flow rate is crucial in designing a scaled-up extraction process. It refers to the quantity of fluid (broth, in this case) that passes through a given cross-section of the extraction column per unit time. The volume flow rate can be computed using the formula:\[\begin{equation}\text{Volume flow rate} = \frac{\text{Total volume needed}}{\text{Total time}}\end{equation}\]For the given exercise, the volume flow rate calculation is essential to determine the dimensions of the full-scale plant required to process a specified volume of broth within a given period. This calculation helps ensure that the scaled-up extraction column can handle the larger production volume efficiently without overloading or underutilizing the system.

Cross-Sectional Area of a Cylinder

When scaling up an extraction column, one of the geometrical aspects to consider is the cross-sectional area of the column. For a cylindrical column, the cross-sectional area is essential for determining the flow rates and velocities of the liquids within the column. It is calculated using the formula:\[\begin{equation}A = \frac{D^2\pi}{4}\end{equation}\]where \(D\) is the diameter of the cylinder. The diameter can subsequently be found by rearranging the formula:\[\begin{equation}D = \sqrt{\frac{4A}{\pi}}\end{equation}\]An accurate determination of the cross-sectional area is critical for the column's design because it directly affects the fluid dynamics inside the column and therefore impacts the overall efficiency of the extraction process. For instance, a properly sized cross-sectional area can help maintain the desired flow regimes and mixing patterns, leading to better mass transfer and more efficient extraction.