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Chapter 10: Problem 9

Consider an aqueous feedstock with \(10 \mathrm{wt} \%\) organics (take glucose for the calculations). This solution is gasified at \(600^{\circ} \mathrm{C}\) and \(25.0 \mathrm{MPa}\) (abs.), and the reactor effluent is heat exchanged with the feed at an efficiency of \(70 \%\). Estimate the amount of energy that has to be provided to the reactor per \(\mathrm{kg}\) of (wet) feed. You may assume that the reaction reaches equilibrium.

Short Answer

Expert verified
Question: Estimate the amount of energy required to gasify an aqueous feedstock containing 10 wt% organics (glucose) at 600°C and 25 MPa, with a heat exchange efficiency of 70%. Answer: To estimate the amount of energy required, first determine the glucose gasification reaction, calculate the equilibrium constants and moles of each component, determine the energy required for the reaction to reach equilibrium, and finally calculate the provided energy per kg of wet feed considering the heat exchange efficiency.

Step by step solution

01

Determine the reaction for glucose gasification

The gasification reaction of glucose (C6H12O6) can be represented as: C6H12O6 + nH2O -> mCO2 + nH2 where n and m are the stoichiometric coefficients.
02

Calculate the equilibrium constants and moles of each component

At the given conditions (600°C and 25 MPa), we can determine the equilibrium constants for the reaction (use available thermodynamic data or software like FACTSAGE). With the equilibrium constants, we can calculate the values of m and n, giving us the moles of each component (CO2 and H2) at equilibrium.
03

Determine the energy required for the reaction

The energy required for the glucose gasification reaction to reach equilibrium is the change in the Gibbs free energy (ΔG) times the moles of glucose in the feed: ΔG = -RT ln(K_eq) where R is the universal gas constant, T is the temperature in Kelvin (873 K), and K_eq is the equilibrium constant. We can determine the amount of energy required per mole from the Gibbs free energy using the mass of glucose in the feedstock (10 wt% or 0.1 kg/kg feed).
04

Calculate the provided energy per kg of wet feed

Given that the heat exchange efficiency is 70%, we can determine the amount of energy required per kg of wet feed as: Energy_required = ΔG * moles_of_glucose * (1/0.7) This will give us the amount of energy that has to be provided to the reactor per kg of wet feed.

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