A supercritical CO2 extraction system is being operated at 30.6 Mpa and 60^∘ C in the extraction

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A supercritical CO2 extraction system is being operated at...

A supercritical $\mathrm{CO}_2$ extraction system is being operated at $30.6 \mathrm{Mpa}$ and $60^{\circ} \mathrm{C}$ in the extraction chamber. The volume of $\mathrm{CO}_2$ leaving the system measured at $101.3 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$ is $10 \mathrm{~L} / \mathrm{min}$. If the extraction chamber is a tube having a diameter of $50.6 \mathrm{~mm}$ and a length of $45 \mathrm{~cm}$., calculate the residence time of the $\mathrm{CO}_2$ in the extraction chamber. Residence time $=$ volume of chamber/volumetric rate of flow in the chamber.

Key Concepts

Residence Time

Residence time is the average amount of time a fluid (or particle) spends within a reactor or processing chamber. It is calculated by dividing the volume of the chamber by the volumetric flow rate of the fluid through that chamber. This concept is central in reactor design and process engineering as it directly influences reaction completeness, mass transfer, and overall process efficiency.

Volumetric Flow Rate Conversion

Volumetric flow rate conversion is the process of relating flow rates measured at one set of conditions (often standard or reference conditions) to the conditions under which a process actually occurs. This conversion typically uses the ideal gas law or other gas property relationships to account for changes in pressure and temperature, which affect the density and volume of the gas.

Ideal Gas Law

The ideal gas law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and amount (in moles) of an ideal gas through the equation PV = nRT. In the context of flow rate conversions and residence time calculations, the ideal gas law enables the correction of volumetric flow rates measured at standard conditions to those applicable at the operating conditions, assuming the gas behaves ideally.

Chamber Volume Calculation

Chamber volume calculation involves determining the internal volume of a reactor or tube, typically using geometric relationships. For a tubular chamber, the volume is calculated using the formula for the volume of a cylinder, V = ?*(d/2)²*L, where d is the diameter and L is the length of the tube. Accurate determination of the chamber volume is crucial for reliable residence time estimation.

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