## Reduced Order Systems Model Predicting the Effects of Boil Off Gasses in Liquified Natural Gas Tanks

lng tank pressure prediction with reduced order thermodynamics model

Ed Wettlaufer – Sr Technical Specialist, Altair Engineering, April 19, 2023

Introduction

Natural gas is recovered from rock formations below the surface of the earth and is a byproduct of oil exploration and processing.  To transport it over long distances it can be liquified as a cryogenic fluid at a temperature of -163C to increase its density.  The tanks which are used to store the liquified gas (LNG) inevitably transfer small amounts of heat to the fluid resulting in a transformation to gas as it reaches its boiling point.  This Boil-Off-Gas increases the pressure inside the storage tank and must be managed to maintain the integrity of the tank.  Sea going vessels manage the BOG, using it as fuel, through combustion in the ship’s engines.  This paper describes a Systems Modeling approach using Reduced Order Models (ROM) to calculate the state variables of the system, such as pressure, volume, and temperature.

Challenges

Several environmental variables can make these calculations exceedingly complicated.  Ambient temperature, modes of heat transfer, species other than methane in the mixture, the states of the liquid and gas inside the tank and agitation are several of the variables which contribute to BOG production.

The modeling assumptions are:

• Heat ingress from the surroundings are lumped in a single factor
• The components are saturated
• Mixing or agitation is neglected
• Methane (CH4) is the only species in the tank
• The temperature within the tank is uniform
• Expansion or deformation of the tank is ignored

Problem Formulation

To calculate the pressure as a function of time the Benedict-Webb-Rubin (BWR) equation of state [1] was used as the fundamental physics governing the prediction.  Elements of the physical environment were decomposed to build sub-systems comprising an overall systems model for the simulation.  Enthalpy, Specific Volume, and Saturation tables are used to calculate the initial conditions entered by the user.

Figure 1 - BWR EOS

The constant coefficients [2] in the BWR equation are experimentally determined for the working fluid and shown in fig 3.

Figure 2 - Altair Activate Initial Conditions Model

There are several “leak paths” for heat in this system.  In leu of attempting to capture the intricacies of these items, the model uses a boil off gas rate per day.  This is a ROM of the tank’s thermodynamic interaction with the environmental surroundings.

Figure 3 - BWR Model

The simulation time was set to 10 days and with the initial conditions set, the model, using the BOG rate, calculates the state after one second, and these new values assume the role of initial conditions for the next time step.  Using the BWR model, the simulation executes 10 days’ worth of iterations arriving at a final state in about 10 seconds.

Figure 4 - Tank Pressure

Conclusion

A Systems Modeling approach provides a means to deconstruct the apparatus into sub-systems of interest enabling the analyst to spend effort on modeling critical areas and less time on non-critical areas using reduced order models.  This model predicts the pressure created as a result of Boil-Off-Gasses in an LNG tank.  While these gases are vented and managed, the model predicts the worst case rise in pressure.  The model also calculates all the other variables in the BWR equation which could provide guidance for Engineering decisions in other areas of the system.

1. Benedict, Manson; Webb, George B.; Rubin, Louis C. (1940), "An Empirical Equation for Thermodynamic Properties of Light Hydrocarbons and Their Mixtures: I. Methane, Ethane, Propane, and n-Butane", Journal of Chemical Physics, 8 (4): 334–345.
2. Starling, Kenneth E. (1973), Fluid Properties for Light Petroleum Systems, Gulf Publishing Company, p. 270.