Worked Example: Claus Sulfur Recovery Unit (SRU) Stoichiometric Air Demand, Reaction Furnace Flame Temperature & Multi-Bed Converter Yield

1. Problem Statement & SRU Process Flowsheet

An acid gas removal unit (MDEA amine sweetening) in a sour gas processing facility discharges an acid gas stream rich in hydrogen sulfide ($\text{H}_2\text{S}$). To prevent catastrophic atmospheric sulfur emissions and recover commercial bright yellow elemental sulfur, the plant designs a Modified Claus Sulfur Recovery Unit (SRU) followed by a Tail Gas Treating Unit (TGTU).

 Acid Gas Feed
 [72% H2S, 1200 kmol/h] ──┐
                          v
 Combustion Air ──────> [ Reaction Furnace ] ──(1240°C)──> [ Waste Heat Boiler ] ──> [ Condenser 1 ] ──(Liq Sulfur)
 [21% O2, 79% N2]             | (Partial Oxidation)                | (HP Steam 40 barg)        |
                              v                                                                v
                        [ Reheater 1 ] ──> [ Catalytic Converter 1 ] ───────────────> [ Condenser 2 ] ──(Liq Sulfur)
                              |                    | (Al2O3 Catalyst, 240°C)                   |
                              v                    v                                           v
                        [ Reheater 2 ] ──> [ Catalytic Converter 2 ] ───────────────> [ Condenser 3 ] ──(Liq Sulfur)
                              |                    | (Al2O3 Catalyst, 215°C)                   |
                              v                    v                                           v
                        [ Reheater 3 ] ──> [ Catalytic Converter 3 ] ───────────────> [ Condenser 4 ] ──(Liq Sulfur)
                                                   | (TiO2 Catalyst, 195°C)                    |
                                                   v                                           v
                                        [ Tail Gas to TGTU ] <─────────────────────────────────┘

Acid Gas Feedstock Composition & Operating Conditions

• Acid Gas Flow Rate ($\dot{n}_{\text{feed}}$): $1,200.0\text{ kmol/h}$ ($26.45\text{ MMSCFD}$)
• Feed Temperature ($T_{\text{feed}}$): $45.0\text{ }^\circ\text{C}$ ($318.15\text{ K}$)
• Feed Pressure ($P_{\text{feed}}$): $1.80\text{ barg}$ ($2.81\text{ bar abs}$)
• Combustion Air Pre-heat Temperature ($T_{\text{air}}$): $120.0\text{ }^\circ\text{C}$ ($393.15\text{ K}$)
• Combustion Air Composition: $21.0\text{ mol}\% \text{ O}_2$, $79.0\text{ mol}\% \text{ N}_2$ (ambient moisture $= 1.5\text{ mol}\%$)
• Acid Gas Feed Composition (mol%):

Design Objectives

1. Calculate the stoichiometric combustion air flow rate ($\text{Nm}^3/\text{h}$) to oxidize exactly one-third of the $\text{H}_2\text{S}$ to $\text{SO}_2$ while completely incinerating the hydrocarbon contaminant ($\text{CH}_4$).
2. Compute the adiabatic flame temperature ($T_{\text{flame}}$) in the reaction furnace.
3. Calculate steam generation in the Waste Heat Boiler (WHB) at $40\text{ barg}$.
4. Determine the stage-by-stage sulfur recovery across the thermal stage and the three catalytic converters.
5. Audit overall sulfur recovery against EPA 40 CFR 60 Subpart Ja ($99.8\%$ recovery requirement) and define Tail Gas Treating Unit (TGTU) parameters.

2. Thermochemical Reactions & Stoichiometry

2.1 The Two-Step Claus Reaction Principle

The Claus process relies on burning one-third of the feed $\text{H}_2\text{S}$ to generate sulfur dioxide ($\text{SO}_2$), which then reacts with the remaining two-thirds of the $\text{H}_2\text{S}$ to produce elemental sulfur vapor:

$$\text{Step 1 (Thermal Oxidation):} \quad \text{H}_2\text{S} + 1.5\text{ O}_2 \longrightarrow \text{SO}_2 + \text{H}_2\text{O} \quad (\Delta H_{298}^\circ = -518.0\text{ kJ/mol})$$

$$\text{Step 2 (Claus Equilibrium):} \quad 2\text{ H}_2\text{S} + \text{SO}_2 \rightleftharpoons \frac{3}{x} \text{S}_x + 2\text{ H}_2\text{O} \quad (\Delta H_{298}^\circ = -145.6\text{ kJ/mol S})$$

$$\text{Overall Reaction:} \quad 3\text{ H}_2\text{S} + 1.5\text{ O}_2 \longrightarrow \frac{3}{x} \text{S}_x + 3\text{ H}_2\text{O} \quad (\Delta H_{\text{overall}}^\circ = -663.6\text{ kJ/mol})$$

2.2 Hydrocarbon Contaminant Destruction

Methane present in the feed consumes oxygen voraciously:

$$\text{CH}_4 + 2\text{ O}_2 \longrightarrow \text{CO}_2 + 2\text{ H}_2\text{O} \quad (\Delta H_{298}^\circ = -802.3\text{ kJ/mol})$$

3. Step-by-Step Stoichiometric Calculations

Step 1: Net Oxygen Demand ($\dot{n}_{\text{O}_2}$)

Oxygen for $\text{H}_2\text{S}$ Oxidation to $\text{SO}_2$:

To satisfy the stoichiometric Claus ratio of $2:1$ ($\text{H}_2\text{S} : \text{SO}_2$), exactly one-third of the feed $\text{H}_2\text{S}$ must be oxidized to $\text{SO}_2$: $$\dot{n}_{\text{H}_2\text{S, oxidized}} = \frac{864.0\text{ kmol/h}}{3} = 288.0\text{ kmol/h}$$

From the oxidation stoichiometry ($1.5\text{ mol O}_2 / \text{mol H}_2\text{S}$): $$\dot{n}_{\text{O}_2,\text{H}_2\text{S}} = 288.0 \times 1.5 = \mathbf{432.0\text{ kmol/h}}$$

Oxygen for Hydrocarbon Destruction ($\text{CH}_4$):

$$\dot{n}_{\text{O}_2,\text{CH}_4} = 12.0\text{ kmol/h} \times 2.0 = \mathbf{24.0\text{ kmol/h}}$$

Total Net Pure Oxygen Required:

$$\dot{n}_{\text{O}_2,\text{total}} = 432.0 + 24.0 = \mathbf{456.0\text{ kmol/h}}$$

Step 2: Combustion Air Demand & Blower Sizing

Air contains $21.0\text{ mol}\% \text{ O}_2$: $$\dot{n}_{\text{air, dry}} = \frac{456.0\text{ kmol/h}}{0.210} = \mathbf{2,171.4\text{ kmol/h}}$$

Associated nitrogen ($\text{N}_2$): $$\dot{n}_{\text{N}_2} = 2,171.4 \times 0.790 = 1,715.4\text{ kmol/h}$$

Accounting for $1.5\%$ ambient moisture in atmospheric air: $$\dot{n}_{\text{air, wet}} = \frac{2,171.4}{1.0 - 0.015} = \mathbf{2,204.5\text{ kmol/h}}$$

Standard Volumetric Flow Rate:

At standard reference conditions ($0\text{ }^\circ\text{C}, 1.01325\text{ bar}$, molar volume $= 22.414\text{ Nm}^3/\text{kmol}$): $$\dot{V}_{\text{air, standard}} = 2,204.5 \times 22.414 = \mathbf{49,412\text{ Nm}^3/\text{h} \quad (30,700\text{ SCFM})}$$

Process Control Note: The main combustion air blower delivers $90\text{--}95\%$ of this flow under flow control. A fast-acting trim air valve ($5\text{--}10\%$ of flow) is modulated by an optical $\text{H}_2\text{S}/\text{SO}_2$ tail gas analyzer to maintain the precise $2.00 : 1.00$ tail gas ratio entering the catalytic beds.

Step 3: Reaction Furnace Adiabatic Flame Temperature

The total sensible enthalpy liberated by partial combustion heats the burner flue gases:

$$\sum \dot{n}_i \cdot \Delta H_{f,\text{reactants}}^\circ = \sum \dot{n}_j \cdot \Delta H_{f,\text{products}}^\circ + \int_{298}^{T_{\text{flame}}} \left( \sum \dot{n}_j C_{p,j}(T) \right) dT$$

Heat of Combustion Released:

• $\text{H}_2\text{S} \to \text{SO}_2$: $288.0\text{ kmol/h} \times 518,000\text{ kJ/kmol} = 1.4918 \times 10^8\text{ kJ/h}$
• $\text{CH}_4 \to \text{CO}_2$: $12.0\text{ kmol/h} \times 802,300\text{ kJ/kmol} = 9.628 \times 10^6\text{ kJ/h}$
• Thermal Claus Reaction ($\approx 68\%$ sulfur formed in furnace as $\text{S}_2$): $$288.0\text{ kmol/h SO}_2 \times 0.68 \times 145,600\text{ kJ/kmol} = 2.851 \times 10^7\text{ kJ/h}$$
• Total Heat Liberated ($\Delta H_{\text{comb}}$): $1.8732 \times 10^8\text{ kJ/h} \approx 52,033\text{ kW}$

Flue Gas Inventory Entering WHB:

• $\text{N}_2$: $1,715.4\text{ kmol/h}$
• $\text{H}_2\text{O}$: $42.0\text{ (feed)} + 288.0\text{ (oxid)} + 24.0\text{ (CH}_4\text{)} + 391.7\text{ (Claus)} = 745.7\text{ kmol/h}$
• $\text{CO}_2$: $282.0\text{ (feed)} + 12.0\text{ (CH}_4\text{)} = 294.0\text{ kmol/h}$
• $\text{SO}_2$: $288.0 - 195.8 = 92.2\text{ kmol/h}$
• $\text{H}_2\text{S}$ (unreacted): $864.0 - 288.0 - 391.7 = 184.3\text{ kmol/h}$
• $\text{S}_2$ vapor: $293.8\text{ kmol/h}$
• Total Furnace Flue Gas: $3,325.4\text{ kmol/h}$

Average heat capacity of the mixture at high temperature: $\bar{C}_p \approx 39.5\text{ kJ/(kmol}\cdot\text{K)}$.

Solving for Adiabatic Flame Temperature ($T_{\text{flame}}$):

$$\Delta T = \frac{\Delta H_{\text{comb}}}{\sum \dot{n}_j \bar{C}_{p,j}} = \frac{1.8732 \times 10^8\text{ kJ/h}}{3,325.4 \times 39.5} = \frac{1.8732 \times 10^8}{131,353} = 1,426\text{ K} \approx 1,153\text{ }^\circ\text{C}$$

Accounting for air pre-heat ($120\text{ }^\circ\text{C}$): $$T_{\text{flame}} = \mathbf{1,240.0\text{ }^\circ\text{C} \quad (2,264\text{ }^\circ\text{F})}$$

Combustion Stability Check: $1,240\text{ }^\circ\text{C} \ge 1,050\text{ }^\circ\text{C}$ required minimum. The furnace easily achieves stable self-sustaining combustion without auxiliary fuel gas firing, ensuring complete thermal destruction of benzene, toluene, and xylene (BTX) contaminants.

Step 4: Waste Heat Boiler (WHB) Steam Generation

The reaction furnace gases enter the WHB at $1,240\text{ }^\circ\text{C}$ and are rapidly quenched to $315\text{ }^\circ\text{C}$ ($588\text{ K}$) to freeze the chemical equilibrium and prevent reverse Claus dissociation:

$$\Delta T_{\text{whb}} = 1240 - 315 = 925\text{ }^\circ\text{C}$$

Thermal Duty Removed:

$$Q_{\text{whb}} = 3,325.4\text{ kmol/h} \times 38.2\text{ kJ/(kmol}\cdot\text{K)} \times 925\text{ K} = 1.175 \times 10^8\text{ kJ/h} \approx \mathbf{32.64\text{ MW}}$$

High-Pressure Steam Generation ($40.0\text{ barg}$, Saturation Temp $252.7\text{ }^\circ\text{C}$):

Using boiler feed water pre-heated to $110\text{ }^\circ\text{C}$: * Enthalpy of saturated steam ($41\text{ bar abs}$): $h_g = 2,800.5\text{ kJ/kg}$ * Enthalpy of BFW ($110\text{ }^\circ\text{C}$): $h_f = 461.3\text{ kJ/kg}$ * Latent heat demand: $\Delta h_{\text{evap}} = 2,800.5 - 461.3 = 2,339.2\text{ kJ/kg}$

$$\dot{m}_{\text{steam}} = \frac{1.175 \times 10^8\text{ kJ/h}}{2,339.2\text{ kJ/kg}} = \mathbf{50,230\text{ kg/h} \quad (50.23\text{ metric tons/h})}$$

The Claus WHB operates as a massive high-pressure steam boiler, powering facility amine pumps and regenerator reboilers!

Step 5: Stage-by-Stage Sulfur Recovery Balance

Pure elemental sulfur production from the feed $\text{H}_2\text{S}$ ($864.0\text{ kmol/h} = 27,700\text{ kg/h}$ as elemental sulfur):

• Total Sulfur in Feed: $27,700\text{ kg/h} = 664.8\text{ metric tons/day (TPD)}$

6. Environmental Audit & Tail Gas Treating (EPA NSPS Subpart Ja)

Unrecovered Sulfur in Claus Tail Gas:

$$100.0\% - 98.2\% = 1.8\% \text{ loss}$$

$$\text{Sulfur Loss Rate} = 27,700 - 27,205 = 495\text{ kg/h} \quad (11.88\text{ TPD})$$

If routed directly to a thermal incinerator stack without further treatment: $$\dot{m}_{\text{SO}_2\text{, emitted}} = 495\text{ kg S/h} \times \frac{64.06}{32.06} = \mathbf{989\text{ kg/h SO}_2 \quad (8,664\text{ metric tons/year})}$$

Stack $\text{SO}_2$ concentration would exceed $2,800\text{ ppmv}$.

Regulatory Mandate:

Under EPA 40 CFR 60 Subpart Ja, large sulfur recovery plants must achieve: * Minimum Sulfur Recovery: $\ge 99.8\%$ * Maximum Stack $\text{SO}_2$ Emission: $\le 250\text{ ppmv}$ (dry basis, $0\%\text{ O}_2$)

Tail Gas Treating Unit (TGTU - SCOT Process) Integration:

To bridge the gap from $98.2\%$ to $99.9\%$, a Shell Claus Offgas Treating (SCOT) unit is added: 1. Hydrogenation Reactor ($300\text{ }^\circ\text{C}$, Co-Mo Catalyst): All unreacted $\text{SO}_2$, elemental sulfur vapor, $\text{COS}$, and $\text{CS}_2$ in the tail gas are hydrogenated back to $\text{H}_2\text{S}$: $$\text{SO}_2 + 3\text{ H}_2 \longrightarrow \text{H}_2\text{S} + 2\text{ H}_2\text{O}$$ 2. Quench Column: Flue gas cooled to $38\text{ }^\circ\text{C}$, condensing excess water vapor. 3. Selective MDEA Amine Absorber: Formulated MDEA selectively captures $>99.5\%$ of the $\text{H}_2\text{S}$ while slipping $>90\%$ of the $\text{CO}_2$. 4. Recycle to Furnace: Concentrated $\text{H}_2\text{S}$ is recycled back to the Claus reaction furnace burner.

Final Facility Performance with TGTU:

• Overall Sulfur Recovery: $99.92\%$
• Stack $\text{SO}_2$ Concentration: $85\text{ ppmv}$ (Well below the $250\text{ ppmv}$ EPA limit)
• Total Commercial Sulfur Recovered: $664.2\text{ metric tons/day}$ of $99.9\%$ pure molten sulfur.