1. Pseudocritical Property Formulation (Wichert-Aziz Corrections)
Acid gas mixtures containing high fractions of \(\text{H}_2\text{S}\) and \(\text{CO}_2\) deviate substantially from standard hydrocarbon gas compressibility behavior due to strong intermolecular dipole moments and hydrogen bonding tendencies. The unadjusted pseudocritical temperature \(T_{pc}\) and pressure \(P_{pc}\) are calculated via Kay's rule:
\[ T_{pc} = \sum y_i T_{c,i} \qquad P_{pc} = \sum y_i P_{c,i} \]
The Wichert-Aziz (1972) method applies a correction factor \(\epsilon\) (in Kelvin) based on the combined acid gas mole fraction \(A = y_{\text{H}_2\text{S}} + y_{\text{CO}_2}\) and \(\text{H}_2\text{S}\) fraction \(B = y_{\text{H}_2\text{S}}\):
\[ \epsilon = 120 \left( A^{0.9} - A^{1.6} \right) + 15 \left( B^{0.5} - B^{4.0} \right) \]
The modified pseudocritical values are:
\[ T'_{pc} = T_{pc} - \epsilon \qquad P'_{pc} = \frac{P_{pc} T'_{pc}}{T_{pc} + B(1 - B)\epsilon} \]
2. Multistage Polytropic Compression & API 618 Temperature Limit
To prevent localized thermal degradation of lubricating oils and catastrophic cylinder valve fatigue, API 618 mandates that the discharge temperature of each compression stage shall not exceed \(135^\circ\text{C}\) (\(275^\circ\text{F}\)). For a stage operating with compression ratio \(r_p = P_{\text{out}} / P_{\text{in}}\), the discharge temperature is:
\[ T_{\text{disch}} = T_{\text{suct}} \cdot r_p^{\frac{\gamma - 1}{\gamma \cdot \eta_p}} \]
where \(\gamma \approx 1.26\text{--}1.29\) for acid gas mixtures, and \(\eta_p\) is polytropic efficiency (\(75\text{--}82\%\)). The specific polytropic head \(H_p\) and shaft power \(W_{\text{shaft}}\) are evaluated as:
\[ H_p = Z_{\text{avg}} \frac{R}{MW} T_{\text{suct}} \left( \frac{n}{n-1} \right) \left[ r_p^{\frac{n-1}{n}} - 1 \right] \qquad W_{\text{shaft}} = \frac{\dot{m} \cdot H_p}{\eta_p \cdot \eta_{\text{mech}}} \]
3. Carroll & Mather Water Solubility Minima & Dehydration Envelope
A critical physical phenomenon in acid gas compression is that the water carrying capacity (\(W_{\text{sat}}\)) does not decrease monotonically with pressure. As investigated by Carroll & Mather (1995), water solubility reaches an absolute minimum at intermediate pressures between \(30\ \text{bar}\) and \(50\ \text{bar}\) before rising sharply as the acid gas transitions into the dense supercritical fluid phase:
\[ W_{\text{sat}} = f(P, T, y_{\text{H}_2\text{S}}, y_{\text{CO}_2}) \]
If the acid gas is not dehydrated, liquid water drops out inside the 2nd or 3rd stage suction scrubbers, forming aggressive aqueous \(\text{H}_2\text{S}\) and carbonic acid that induce rapid hydrogen-induced cracking (HIC) and sulfide stress corrosion (SSC).
4. Supercritical Dense-Phase Wellbore Hydraulics
At surface discharge pressures exceeding \(100\text{--}150\ \text{barg}\), acid gas compresses into a dense, liquid-like phase (\(\rho \approx 550\text{--}750\ \text{kg/m}^3\)). The hydrostatic fluid column in the vertical injection wellbore provides natural pressure assist at the sandface:
\[ P_{\text{sandface}} = P_{\text{wellhead}} + \frac{\rho_{\text{dense}} \cdot g \cdot TVD}{10^5} \quad [\text{barg}] \]
This hydrostatic boost significantly reduces the required surface compressor discharge pressure.