Air At A Flow Rate Of 170 M²/H, 16 Oc, 1 Atm, Containing 0.5

Air At A Flow Rate 170 M2h 16 Oc 1 Atm And Containing 05 Mol E

Determine the dimensions of a fixed-bed adsorber for removing ethylene acetate from air based on given operational conditions, including flow rate, temperature, pressure, and adsorption characteristics. The calculations should identify the appropriate bed diameter and height, considering a breakthrough time of 8 hours and a superficial gas velocity of 0.3048 m/s at 38°C and 1 atm. Additionally, evaluate the reasonableness of the resulting bed height-to-diameter ratio and suggest modifications to the design basis if necessary.

Paper For Above instruction

Designing efficient fixed-bed adsorbers for gas purification involves characterizing the flow conditions, adsorption capacities, and geometric parameters to ensure optimal removal of contaminants such as ethylene acetate from air streams. This process requires integrating empirical correlations, adsorption isotherm data, and fluid dynamics principles to size the bed appropriately, balancing operational efficiency with economic feasibility.

The problem involves treating an air stream with a flow rate of 1.70 m²/h at 16°C (which corresponds approximately to 38°C for the adsorption process), containing 0.5 mol% ethylene acetate, with no water vapor, using activated carbon with a particle diameter of 3.35 mm. The system is designed to maintain a breakthrough time of 8 hours, which indicates the operational period until the adsorbent becomes saturated and requires regeneration or replacement.

Basic Assumptions and Data Utilization

Given the flow rate, temperature, and pressure conditions, the first step involves calculating the volumetric flow rate at the specified state, considering ideal gas behavior where necessary. The gas velocities are used to estimate the cross-sectional area of the bed, which ultimately defines the bed diameter. The bed height can then be deduced from the total adsorbed amount over the breakthrough period, factoring in the adsorption capacity of the activated carbon.

Step 1: Calculation of Volumetric Flow Rate

The given superficial gas velocity (\(u_s\)) is 0.3048 m/s. Using volumetric flow rate (\(Q\)) relation with superficial velocity and cross-sectional area (\(A\)):

\(Q = u_s \times A\)

where \(A = \pi \times (D/2)^2\). Rearranging provides the relationship to determine the diameter based on flow rate.

Step 2: Estimation of Bed Diameter

From the flow rate \(Q\), measured in volume per time, and the superficial velocity \(u_s\), the bed diameter \(D\) can be calculated. First, convert the volumetric flow rate to consistent units, accounting for conditions at 16°C and 1 atm, possibly adjusting for the actual conditions at 38°C if necessary using ideal gas law corrections.

Assuming ideal gas behavior, the volumetric flow rate at 1 atm and 16°C (289.15 K), considering the gas temperature at 38°C (311.15 K):

\(Q_{38°C} = Q_{16°C} \times \frac{T_{38°C}}{T_{16°C}}\)

Similarly, converting flow rate units to m³/s allows for solving for the diameter D:

D = 2 × sqrt( Q / (π × u_s) )

Plugging in the values yields the distribution of the bed diameter that accommodates the flow at given superficial velocity.

Step 3: Estimation of Bed Height

The amount of ethylene acetate adsorbed over 8 hours determines the quantity of adsorbent needed. Using the adsorption capacity (from available data in Tables 1 and 2), we calculate the total moles of ethylene acetate captured:

\(n_{adsorbed} = C_{initial} \times Q \times t\)

where \(C_{initial}\) is the concentration of ethylene acetate (mol/m³), obtained from the mole percentage and total flow, and \(t\) is 8 hours converted into seconds.

The total adsorbed mass in mols helps determine the required volume of the active adsorbent bed. Using the adsorption capacity per unit mass of activated carbon, the bed height \(H\) is deduced with:

\(H = \frac{V_{adsorbent}}{A}\)

and \(V_{adsorbent}\) is calculated from the total amount adsorbed and the capacity per unit volume.

Step 4: Evaluation of Bed Height-to-Diameter Ratio

Once the dimensions are estimated, check the ratio \(H/D\). Typically, for fixed-bed adsorption systems, an \(H/D\) ratio of 2-4 is desirable for uniform flow and effective utilization. If the ratio exceeds practical limits or leads to an unreasonable bed height or diameter, modifications to the design basis, such as increasing flow rate or selecting a different adsorbent particle size, should be considered.

Potential Design Changes

If the calculated bed height-to-diameter ratio is unreasonably high, indicating an excessively tall and narrow bed, alternative approaches include increasing the bed diameter (to reduce height), reducing the flow rate, or employing staged adsorption units. Adjustments to the inlet flow velocity or using a different particle size to influence pressure drop and mass transfer rates can also be advantageous.

Conclusion

Accurate calculation of the adsorber dimensions demands integrating process data with empirical correlations for bed design, including packing characteristics, flow dynamics, and adsorption capacities. The approach described enables designing a feasible adsorption system, while evaluating the \(H/D\) ratio guides practical implementation considerations. Should the initial dimensions prove impractical, parameter modifications such as adjusting flow rates, particle sizes, or operational strategies become necessary to optimize system performance.

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