## Equilibrium and Non-Equilibrium Thermodynamics of Natural Gas Processing

##### Abstract

The objective of this work has been to study equilibrium and non equilibrium situations during high pressure gas processing operations with emphasis on utilization of the high reservoir pressure. The well stream pressures of some of the condensate and gas fields in the North Sea are well above 200 bar. Currently the gas is expanded to a specified processing condition, typically 40-70 bar, before it is recompressed to the transportation conditions. It would be a considerable environmental and economic advantage to be able to process the natural gas at the well stream pressure. Knowledge of thermodynamic- and kinetic properties of natural gas systems at high pressures is needed to be able to design new high pressure process equipment.
Nowadays, reactive absorption into a methyldiethanolamine (MDEA)solution in a packed bed is a frequently used method to perform acid gas treating. The carbon dioxide removal process on the Sleipner field in the North Sea uses an aqueous MDEA solution and the operation pressure is about 100 bar. The planed carbon dioxide removal process for the Snøhvit field in the Barents Sea is the use of an activated MDEA solution.
The aim of this work has been to study high-pressure effects related to the removal of carbon dioxide from natural gas. Both modelling and experimental work on high-pressure non-equilibrium situations in gas processing operations have been done.
Few experimental measurements of mass transfer in high pressure fluid systems have been published. In this work a wetted wall column that can operate at pressures up to 200 bar was designed and constructed. The wetted wall column is a pipe made of stainless steel where the liquid is distributed as a thin liquid film on the inner pipewall while the gas flows co- or concurrent in the centre of the pipe. The experiments can be carried out with a well-defined interphase area and with relatively simple fluid mechanics. In this way we are able to isolate the effects we want to study in a simple and effective way.
Experiments where carbon dioxide was absorbed into water and MDEA solutions were performed at pressures up to 150 bar and at temperatures 25 and 40°C. Nitrogen was used as an inert gas in all experiments.
A general non-equilibrium simulation program (NeqSim) has been developed. The simulation program was implemented in the object-oriented programming language Java. Effort was taken to find an optimal object-oriented design. Despite the increasing popularity of object-oriented programming languages such as Java and C++, few publications have discussed how to implement thermodynamic and fluid mechanic models. A design for implementation of thermodynamic, mass transfer and fluid mechanic calculations in an object-oriented framework is presented in this work.
NeqSim is based on rigorous thermodynamic and fluid mechanic models. Parameter fitting routines are implemented in the simulation tool and thermodynamic-, mass transfer- and fluid mechanic models were fitted to public available experimental data. Two electrolyte equations of state were developed and implemented in the computer code. The electrolyte equations of state were used to model the thermodynamic properties of the fluid systems considered in this work (non-electrolyte, electrolyte and weak-electrolyte systems).
The first electrolyte equation of state (electrolyte ScRK-EOS) was based on a model previously developed by Furst and Renon (1993). The molecular part of the equation was based on a cubic equation of state (Scwarzentruber et.al. (1989)’s modification of the Redlich-Kwong EOS) with the Huron-Vidal mixing rule. Three ionic terms were added to this equation – a short-range ionic term, a long-range ionic term (MSA) and a Born term. The thermodynamic model has the advantage that it reduces to a standard cubic equation of state if no ions are present in the solution, and that public available interaction parameters used in the Huron-Vidal mixing rule could be utilized. The originality of this electrolyte equation of state is the use of the Huron-Vidal mixing rule and the addition of a Born term. Compared to electrolyte models based on equations for the gibbs excess energy, the electrolyte equation of state has the advantage that the extrapolation to higher pressures and solubility calculations of supercritical components is less cumbersome. The electrolyte equation of state was able to correlate and predict equilibrium properties of CO2-MDEA-water solutions with a good precision. It was also able to correlate high pressure data of systems of methane-CO2-MDEA and water.
The second thermodynamic model (electrolyte CPA-EOS) evaluated in this work is a model where the molecular interactions are modelled with the CPA (cubic plus association) equation of state (Kontogeorgios et.al., 1999) with a classical one-parameter Van der Walls mixing rule. This model has the advantage that few binary interaction parameters have to be used (even for non-ideal solutions), and that its extrapolation capability to higher pressures is expected to be good. In the CPA model the same ionic terms are used as in the electrolyte ScRK-EOS.
A general non-equilibrium two-fluid model was implemented in the simulation program developed in this work. The heat- and mass-transfer calculations were done using an advanced multicomponent mass transfer model based on non-equilibrium thermodynamics. The mass transfer model is flexible and able to simulate many types of non-equilibrium processes we find in the petroleum industry. A model for reactive mass transfer using enhancement factors was implemented for the calculation of mass transfer of CO2 into amine solutions. The mass transfer model was fitted to the available mass transfer data found in the open literature.
The simulation program was used to analyse and perform parameter fitting to the high pressure experimental data obtained during this work. The mathematical models used in NeqSim were capable of representing the experimental data of this work with a good precision. From the experimental and modelling work done, we could conclude that the mass transfer model regressed to pure low-pressure data also was able to represent the high-pressure mass transfer data with an acceptable precision. Thus the extrapolation capability of the model to high pressures was good.
For a given partial pressure of CO2 in the natural gas, calculations show a decreased CO2 capturing capacity of aqueous MDEA solutions at increased natural gas system pressure. A reduction up to 40% (at 200 bar) compared to low pressure capacity is estimated. The pressure effects can be modelled correctly by using suitable thermodynamic models for the liquid and gas. In a practical situation, the partial pressure of CO2 in the natural gas will be proportional to the total pressure. In these situations, it is shown that the CO2 capturing capacity of the MDEA solution will be increased at rising total pressures up to 200 bar. However, the increased capacity is not as large as we would expect from the higher CO2 partial pressure in the gas.
The reaction kinetics of CO2 with MDEA is shown to be relatively unaffected by the total pressure when nitrogen is used as inert gas. It is however important that the effects of thermodynamic and kinetic non- ideality in the gas and liquid phase are modelled in a consistent way. Using the simulation program NeqSim – some selected high-pressure non-equilibrium processes (e.g. absorption, pipe flow) have been studied. It is demonstrated that the model is capable of simulating equilibrium- and non-equilibrium processes important to the process- and petroleum industry.