1. Geomechanical Operating Pressure Boundaries (API RP 1170)
Unlike porous sandstone reservoirs bounded by capillary rock seals, salt cavern structural integrity is governed by the rheological creep and dilatancy properties of solid crystalline halite (\(\text{NaCl}\)). Two mandatory pressure limits define the safe operating envelope:
- Maximum Allowable Operating Pressure (\(P_{\text{max}}\)): Constrained by the lithostatic overburden fracture gradient at the casing shoe depth (\(D_{\text{shoe}}\)) to prevent tensile rock fracturing: \[ P_{\text{max}} = g_{\text{litho}} \cdot D_{\text{shoe}} \qquad (g_{\text{litho}} \le 0.80\text{--}0.85\ \text{psi/ft} \approx 0.018\text{--}0.019\ \text{bar/m}) \]
- Minimum Cushion Pressure (\(P_{\text{min}}\)): Enforced to maintain sufficient internal pneumatic pressure to counteract the inward deviatoric rock stress, suppressing rapid halite creep convergence and roof spalling: \[ P_{\text{min}} = g_{\text{creep}} \cdot D_{\text{shoe}} \qquad (g_{\text{creep}} \ge 0.25\text{--}0.30\ \text{psi/ft} \approx 0.0056\text{--}0.0068\ \text{bar/m}) \]
2. Real Gas Inventory Mass Balance & Working Gas Capacity
Because cavern geometric volume (\(V_{\text{cav}}\)) remains constant during cyclic operation, the total moles of gas in place at any pressure is governed by the real gas law:
\[ n(P) = \frac{P \cdot V_{\text{cav}}}{Z(P, T) \cdot R \cdot T} \]
The Total Gas Capacity (\(V_{\text{total}}\)) at \(P_{\text{max}}\) and Cushion Gas Inventory (\(V_{\text{cushion}}\)) at \(P_{\text{min}}\) evaluate the usable Working Gas Capacity (\(V_{\text{working}}\)):
\[ V_{\text{working}} = V_{\text{cav}} \left[ \frac{P_{\text{max}}}{Z(P_{\text{max}}, T) \cdot R \cdot T} - \frac{P_{\text{min}}}{Z(P_{\text{min}}, T) \cdot R \cdot T} \right] \cdot V_{\text{std}} \]
where \(V_{\text{std}} = 23.644\ \text{Sm}^3/\text{kmol}\). The working-to-cushion ratio \(W/C = V_{\text{working}} / V_{\text{cushion}}\) in salt caverns typically exceeds \(2.0\text{ to }3.5\), compared to only \(0.8\text{--}1.2\) in depleted gas fields.
3. Thermodynamic Expansion Cooling during Peak Withdrawal
Rapid gas withdrawal causes the cavern inventory to undergo near-adiabatic expansion, resulting in a temperature drop (\(\Delta T_{\text{decay}}\)) driven by real-gas Joule-Thomson expansion and work of decompression:
\[ \frac{dT}{dt} = \frac{T}{V_{\text{cav}}} \left( \frac{\partial Z}{\partial T} \right)_P \frac{dP}{dt} + \frac{U A (T_{\text{rock}} - T)}{\dot{m} C_v} \]
Over a sustained 10-to-20 day peak withdrawal event, gas temperature inside the cavern can plunge by \(15^\circ\text{C}\) to \(25^\circ\text{C}\). Surface heating facilities must supply heat duty to prevent downstream pipeline hydrate formation:
\[ \dot{Q}_{\text{heater}} = \dot{m}_{\text{with}} \cdot C_p \cdot \left( T_{\text{sales,spec}} - T_{\text{wellhead}} \right) \quad [\text{kW}] \]