Worked Example: Sizing an MDEA Amine Sweetening Unit for CO2 and H2S Acid Gas Removal

Acid gas removal (gas sweetening) is mandatory for raw natural gas containing carbon dioxide ($\text{CO}_2$) and hydrogen sulfide ($\text{H}_2\text{S}$). Carbon dioxide is non-combustible and forms corrosive carbonic acid in pipelines, while $\text{H}_2\text{S}$ is an extremely lethal toxic gas that causes rapid sulfide stress corrosion cracking (SSCC) in carbon steels.

Among commercial alkanolamines, Methyldiethanolamine (MDEA) is widely favored for bulk $\text{CO}_2$ removal and selective $\text{H}_2\text{S}$ capture due to its high resistance to thermal degradation, non-corrosive nature, and substantially lower regeneration energy compared to primary (MEA) or secondary (DEA) amines.

This worked example details the process sizing of an industrial MDEA sweetening unit treating $15.0\text{ MMSCFD}$ of sour natural gas at $60.0\text{ barg}$.

1. Operating Problem Statement & Design Basis

A sour gas production field delivers raw natural gas to a central processing facility with the following specifications:

Sour Feed Gas Properties:

• Gas Flow Rate ($Q$): $15.0\text{ MMSCFD}$ ($17,698.0\text{ Sm}^3/\text{h}$)
• Operating Pressure ($P$): $60.0\text{ barg}$ ($61.01\text{ bar(a)} = 884.9\text{ psia}$)
• Inlet Gas Temperature ($T$): $40.0^\circ\text{C}$ ($104.0^\circ\text{F} = 313.15\text{ K}$)
• Carbon Dioxide Content: $4.50\text{ mol}\%$
• Hydrogen Sulfide Content: $50.0\text{ ppmv}$ ($70.9\text{ mg/Sm}^3$)
• Gas Specific Gravity: $0.65$ ($\rho_g \approx 47.5\text{ kg/m}^3$)

Product Sales Gas Quality Targets:

• Treated Gas $\text{CO}_2$: $\le 2.00\text{ mol}\%$ (pipeline tariff limit)
• Treated Gas $\text{H}_2\text{S}$: $\le 4.00\text{ ppmv}$ ($5.7\text{ mg/Sm}^3$)

Solvent Selection & Operating Limits:

• Solvent Type: Aqueous Methyldiethanolamine (MDEA)
• Solvent Concentration: $45.0\text{ wt}\%$ MDEA ($55.0\text{ wt}\%$ water)
• MDEA Molar Mass ($M$): $119.16\text{ g/mol}$ ($\text{kg/kmol}$)
• Solvent Density ($\rho_{sol}$): $1,035\text{ kg/m}^3$ ($8.64\text{ lb/gal}$)
• Design Rich Amine Loading ($\alpha_{rich}$): $0.42\text{ mol acid gas / mol MDEA}$
• Design Lean Amine Loading ($\alpha_{lean}$): $0.01\text{ mol acid gas / mol MDEA}$
• Net Working Capacity ($\Delta \alpha$): $0.42 - 0.01 = \mathbf{0.41\text{ mol acid gas / mol MDEA}}$

2. Step 1: Acid Gas Removal Mass Balance

Total molar feed rate of the raw gas at standard conditions ($V_m = 23.6409\text{ Sm}^3/\text{kmol}$):

$$\dot{n}_{gas} = \frac{17,698.0\text{ Sm}^3/\text{h}}{23.6409\text{ Sm}^3/\text{kmol}} = \mathbf{748.62\text{ kmol/h}}$$

A. Carbon Dioxide Balance:

• Inlet $\text{CO}_2$ Flow: $748.62 \times 0.0450 = 33.69\text{ kmol/h}$
• Target Sales Gas $\text{CO}_2$ ($2.00\%$): Permissible slip $= 748.62 \times 0.0200 = 14.97\text{ kmol/h}$
• $\text{CO}2$ Removed ($\dot{n}$): $33.69 - 14.97 = \mathbf{18.72\text{ kmol/h}}$ ($823.9\text{ kg/h}$)

B. Hydrogen Sulfide Balance:

• Inlet $\text{H}_2\text{S}$ Flow: $748.62 \times (50 \times 10^{-6}) = 0.0374\text{ kmol/h}$
• Target Sales Gas $\text{H}_2\text{S}$ ($4\text{ ppmv}$): Permissible slip $= 748.62 \times (4 \times 10^{-6}) = 0.0030\text{ kmol/h}$
• $\text{H}2\text{S}$ Removed ($\dot{n}$): $0.0374 - 0.0030 = \mathbf{0.0344\text{ kmol/h}}$ ($1.17\text{ kg/h}$)

C. Total Acid Gas to be Absorbed:

$$\dot{n}_{AG} = \dot{n}_{CO2} + \dot{n}_{H2S} = 18.72 + 0.0344 = \mathbf{18.75\text{ kmol/h}} \quad (\mathbf{41.34\text{ lbmol/h}})$$

3. Step 2: Amine Solvent Circulation Rate

To capture $18.75\text{ kmol/h}$ of acid gas at a net loading $\Delta \alpha = 0.41\text{ mol AG / mol MDEA}$:

A. Pure MDEA Molar Circulation Rate:

$$\dot{n}_{MDEA} = \frac{\dot{n}_{AG}}{\Delta \alpha} = \frac{18.75\text{ kmol/h}}{0.41} = \mathbf{45.73\text{ kmol/h}}$$

B. Pure MDEA Mass Flow Rate:

$$\dot{m}_{MDEA,pure} = 45.73\text{ kmol/h} \times 119.16\text{ kg/kmol} = \mathbf{5,449.2\text{ kg/h}}$$

C. Total Aqueous Solution Mass Flow Rate ($45.0\text{ wt}\%$):

$$\dot{m}_{sol} = \frac{5,449.2\text{ kg/h}}{0.45} = \mathbf{12,109.3\text{ kg/h}} \quad (26,696.5\text{ lb/h})$$

D. Volumetric Circulation Rate:

Using solution density $\rho_{sol} = 1,035\text{ kg/m}^3$:

$$L_{amine} = \frac{12,109.3\text{ kg/h}}{1,035\text{ kg/m}^3} = \mathbf{11.70\text{ m}^3/\text{h}}$$

Converting to US Gallons per Minute (GPM):

$$L_{amine}\text{ [GPM]} = \frac{11.70\text{ m}^3/\text{h} \times 264.172\text{ gal/m}^3}{60\text{ min/h}} = \mathbf{51.5\text{ GPM}}$$

(If operating at higher rich loading $\alpha_{rich} = 0.45$, circulation rate drops to $\approx 40.5\text{ GPM}$.)

4. Step 3: Absorber Column Diameter Sizing

The contactor column must accommodate the upward gas flow without causing entrainment flooding.

A. Gas Superficial Flooding Velocity via Souders-Brown:

With $\rho_g = 47.5\text{ kg/m}^3$ ($2.965\text{ lb/ft}^3$) and $\rho_L = 1,035\text{ kg/m}^3$ ($64.61\text{ lb/ft}^3$), and $K_{SB} = 0.16\text{ ft/s}$:

$$v_{flood} = 0.16 \cdot \sqrt{\frac{64.61 - 2.965}{2.965}} = 0.16 \cdot \sqrt{20.79} = 0.16 \times 4.56 = \mathbf{0.73\text{ ft/s}} \quad (0.223\text{ m/s})$$

B. Design Gas Velocity ($70\%$ of flooding):

$$v_{design} = 0.70 \times 0.73\text{ ft/s} = \mathbf{0.51\text{ ft/s}} \quad (0.155\text{ m/s})$$

C. Actual Gas Volumetric Flow Rate:

$$Q_{actual} = 17,698\text{ Sm}^3/\text{h} \times \left( \frac{1.01325}{61.01} \right) \left( \frac{313.15}{288.15} \right) \left( \frac{0.89}{1.0} \right) = \mathbf{284.5\text{ m}^3/\text{h}} = \mathbf{2.79\text{ ft}^3/\text{s}}$$

D. Column Inside Diameter:

$$A_{col} = \frac{2.79\text{ ft}^3/\text{s}}{0.51\text{ ft/s}} = 5.47\text{ ft}^2 \implies D_{calc} = \sqrt{\frac{4 \times 5.47}{\pi}} = 2.64\text{ ft} = \mathbf{31.7\text{ in}} \quad (0.805\text{ m})$$

Selection: Select standard $36.0\text{ inch}$ ($914\text{ mm}$) vessel diameter with 24 valve trays or equivalent structured packing bed.

5. Step 4: Regenerator Stripper Reboiler Thermal Duty

Amine regeneration reboiler duty consists of three primary thermal demands:

graph TD
    A[Total Reboiler Duty: ~718 kW] --> B[Sensible Heat: 185 kW]
    A --> C[Heat of Reaction: 240 kW]
    A --> D[Stripping Steam Vaporization: 293 kW]

1. Sensible Heat ($Q_{sensible}$):

2. Heating rich amine from cross-exchanger outlet ($98^\circ\text{C}$) to stripper bottoms ($121^\circ\text{C}$): $$Q_{sens} = \dot{m}_{sol} \cdot c_p \cdot \Delta T = \frac{12,109}{3,600} \times 3.65 \times (121 - 98) = \mathbf{185.0\text{ kW}}$$

3. Heat of Acid Gas Desorption ($Q_{rxn}$):

4. Endothermic reaction enthalpy for MDEA-$\text{CO}2$ ($\Delta H$): } \approx 46.5\text{ MJ/kmol $$Q_{rxn} = \frac{18.72\text{ kmol/h} \times 46,500\text{ kJ/kmol}}{3,600\text{ s/h}} = \mathbf{241.8\text{ kW}}$$

5. Stripping Steam Generation ($Q_{steam}$):

6. Stripping steam required to maintain low $\text{CO}_2$ partial pressure in the stripper: $$Q_{steam} \approx \mathbf{291.7\text{ kW}}$$

Total Reboiler Heat Duty ($Q_{total}$):

$$Q_{total} = 185.0 + 241.8 + 291.7 = \mathbf{718.5\text{ kW}}$$

In imperial energy units: $$Q_{total} = 718.5\text{ kW} \times 3,412.14 = \mathbf{2.45\text{ MMBtu/h}}$$

Low-Pressure (LP) Steam Consumption:

Using saturated utility steam at $3.5\text{ barg}$ ($148^\circ\text{C}$, $\lambda = 2,085\text{ kJ/kg}$):

$$\dot{m}_{steam} = \frac{718.5\text{ kW} \times 3,600\text{ s/h}}{2,085\text{ kJ/kg}} = \mathbf{1,240.5\text{ kg/h}} \quad (\mathbf{2,735\text{ lb/h}})$$

6. Step 5: Sulfur Recovery & Environmental Rating

The mass of $\text{H}_2\text{S}$ removed from the gas stream is:

$$\dot{m}_{H2S} = 1.17\text{ kg/h} \implies \text{Elemental Sulfur Equivalent} = 1.17 \times \left( \frac{32.065}{34.08} \right) = 1.10\text{ kg/h}$$

Daily sulfur production:

$$\dot{m}_{sulfur} = 1.10\text{ kg/h} \times 24\text{ h/day} = \mathbf{26.4\text{ kg/day}} \quad (\mathbf{0.026\text{ tonnes/day}})$$

Technology Recommendation:

• Because sulfur production is far below the $1.0\text{ tonne/day}$ threshold required to economically justify a Claus Sulfur Recovery Unit (SRU), the acid gas overhead from the amine regenerator is routed to a non-regenerable solid scavenger bed (iron sponge / Triazine) or catalytic thermal oxidizer.

7. Engineering Summary & Comparison