Assessing LNG feed gas depressurisation
Methods and models for estimating time-dependent profiles of mass discharge rates, pressures, and temperatures for LNG feed gas non-adiabatic depressurisation cases.
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Depressuring systems are generally installed in LNG facilities and process plants operating at high pressures to timely reduce pressures of isolated segments when necessary. These systems can be used to reduce the risks of vapour cloud explosion or jet fire in an emergency, such as fire, seal failure, flange leakage, or other containment losses. API Standard 521 discusses depressurisation time and pressure targets.
In LNG facilities, the transient discharges from depressuring are routed to a (wet or dry) flare system and typically result in major flare loads, which need to be considered in the flare design philosophy and flare system operating capacity. The system can reach much lower temperatures while depressurising, and these temperatures need to be evaluated for selecting the materials of construction.
Typically, commercial simulators/programs are used to calculate the peak flow rate and minimum (or maximum in case of fire or non-adiabatic) temperature from depressurisation. However, the calculation methods in the simulators may remain unclear to some users as algorithm details are not directly illustrated. Against this backdrop, simple calculation methods or models are described, which can be solved in spreadsheets and mainly derived from applying thermodynamic principles to estimate the transient profiles of gas phase depressuring systems. This model could help in understanding the thermodynamics of depressurisation, and the results from this model may be used as references for checking the results from a new simulator or a new version of a known simulator. While depressurised segments contain gas phase, liquid phase, or multiphase systems, the model discussed herein is applicable to depressurised segments with single or multicomponent gas phase only and will need to be expanded for a multiphase system.
In addition to emergency situations such as fire requiring the segment in the fire zone to be depressurised, de-inventory of the same segment can also be expected during normal shutdown and maintenance or in the event of inadvertent opening of the depressuring valve. In these cases of depressurisation without external heat input, for gases such as LNG feed gas in the region of positive Joule Thompson (JT) coefficients, the adiabatic expansion from a well-insulated segment will result in the maximum temperature drop and generally becomes the governing scenario for specifying the minimum metal design temperature requirement of the system. This design requirement is essential for plants such as LNG facilities with gas streams at low normal operating temperatures.
The total volume (V, ft³) of an isolated segment to be depressurised typically involves the volumes of equipment items and piping between the isolation valves, which are typically automatic or remotely operated on-off valves. The total volume remains unchanged during the depressurisation, but the fluid mass (M, lbm) inside the volume will decrease. Equations 1, 2 and 3 describe the time-dependent M during depressurisation:
where ρ is the gas density (lb/ft³) and m is the mass flow rate (lb/hr). The transient mass flow rate m out of the isolated segment varies with the segment pressure (P) and the outlet or backpressure of the depressuring orifice discharging to a flare system. For most of the high-pressure or LNG plant segments to be depressurised, the initial pressures (Po) are much higher than the typically targeted pressure of 100 psig, and the flare backpressure during the depressurisation is typically much lower than 100 psig. Higher flare backpressures generally could occur during major or multiple relief scenarios. However, the associated backpressures typically stay below 100 psig, and activating the depressurising system in these relief events may be considered less likely.
For cases where the depressurising orifice back pressure is well below the choked or critical flow pressure, m can be estimated by assuming choked flow across a resistance coefficient/factor. The depressurisation feature in the commercial simulator provides several options for flow rate calculation, and using a flow coefficient CV for a valve is one of these options. For consistent comparison, the same CV equation (Equation 2) in the simulator is used in the spreadsheet models for calculating the depressurised rates in the choked flow region.
Equation 2 provided by a control valve vendor contains the control valve coefficient (Cv), P pressure (PSIA), G – specific gravity relative to air, T – temperature (°R), and Z – compressibility factor.
K is the product of a unit conversion constant and a valve critical flow factor from the vendor. The same type of equation is also used in the commercial simulator to get the results for comparison purposes.
For adiabatic depressurisation, the gas in the segment can be modelled as essentially reversible, isentropic or polytropic expansion. For real gases, pressure and specific volume (υ,ft³/lb) are often related by Equation 3¹, especially for some limited pressure ranges (1,000-100 psig in this example), and the gas pressures (P) and the specific volumes (υ,ft3/lb) can be generally expressed as Equation 3.
n is the isentropic expansion coefficient or reversible polytropic exponent (RPE) derived from actual P and υ data of real gases. For ideal gas, n equals to Cp / Cv or Cp / (Cp – R), the ratio of heat capacity at constant pressure to heat capacity at constant volume. To evaluate the value of n for real gases, the actual P and υ data along the isentropic path are needed. They are available from several sources, including published data or estimated from the selected applicable equation of state or other property packages.
For the option to generate isentropic P and υ data from a known or commercially proven simulator, a dry LNG feed gas at initial conditions of 1,000 psig and 80°F is used as an example for illustrating the calculation models for depressurisation. This feed gas is primarily methane, and other components in small percentages are hydrocarbons from ethane to iso-pentane (C₂ to i-C₅), nitrogen, and traces of CO₂. Figure 1 shows the isentropic P and υ data generated from a commercial simulator using Peng-Robinson (PR) property package. As shown, the P and υ data along the isentropic path can be well correlated with Equation 4, and the resulting R-squared (R2) or coefficient of determination essentially equals to one, indicating a good fit, at least for this LNG feed gas example.
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