High-pressure experimental vapour-liquid-liquid equilibrium measurements and modelling for natural gas processing: Equipment validation, and the system CH4+nC6H14+H2O
Graphical abstract
Introduction
With the expansion of subsea processing capabilities, underwater natural gas production facilities have recently been proposed by Equinor [1]. The Gas-2-PipeTM (G2P) process considers two main steps: pre-separation of gas-condensate-water mixtures, followed by compression and dehydration of the resultant wet gas to produce on-spec natural gas. Subsea separation and processing offer several advantages over traditional approaches, mostly related to limitations and risks inherent to multiphase pipelines. These advantages include: [2].
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Increased product recovery and energy efficiency
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Reduced capital and operating expenditure
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Extended operational lifetimes
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Increased number of viable reserves
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Improved flow assurance
Due to the proximity to the reservoir and depending on installation depth and location, higher pressures and colder temperatures would likely occur. For this reason, new experimental data are measured. The importance of experimental data cannot be overstated, as was highlighted in a statement by Prof. Dominique Richon: [3].
“Some people think that experimental work, compared to modelling and simulation, is more tedious, more expensive, and less appreciated in our community. However, numerous e-mail exchanges have confirmed my feeling that good thermodynamic data are absolutely necessary, because process design relies on accurate modelling and accurate modelling relies on reliable experimental data.”
In our previous studies [4,5] we measured two-phase experimental data related to the dehydration step in the G2P™ process. The present study is concerned with thermodynamic behaviour of mixtures representative of the three-phase pre-separation step. Systems containing methane (C1), n-hexane (nC6) and water (H2O) have been investigated using a vapour-liquid-liquid equilibrium (VLLE) experimental apparatus [6] which has been modified since previous publication. In this work we firstly present binary VLE data, which are used for the verification of the experimental apparatus. Several data sets are available for C1+H2O meaning that comparisons can be made with a relatively high degree of certainty. C1+nC6 is equally well-studied with over 70 data sets found in NIST TDE [7], although there were fewer data sets available in the temperature range of interest to this study.
In the selection of data presented in Table 1, preference was given to sources where both the liquid and vapour phases (i.e. TPxy data) were reported. Due to the design of experimental apparatus, it is however more typical to see only the liquid phase composition reported.
LLE data for n-alkane + H2O systems have been reviewed in detail by Maçzyński et al. [18] where the solubility of n-alkanes in water exhibits a minimum at room temperature and ambient pressure. It cannot be determined whether the solubility minimum holds for high-pressure data, as those measured by Tsonopoulos & Wilson [19] (0.3–3.5 MPa) were at temperatures above where such a minimum may exist.
While several binary VLE and LLE data can be found in the open literature, surprisingly few data sources are available for ternary and multicomponent VLE and VLLE systems. The literature data for systems containing methane, water and an n-alkane are given in Table 2.
Gillespie & Wilson [20] detected two liquid phases (VLLE) T ε [366, 422] K and P ε [3.1, 6.2] MPa. Meanwhile at higher pressures (≥13.8 MPa) for T ε [366, 422] K and all pressures at other temperatures (311, ≥476 K), only vapour and an aqueous phase (VLE) are reported. In the three-phase region it is observed that vapour content of nC5 was quite erratic. Susilo et al. [21] also included data for neohexane, tert-butyl methyl ether and methylcyclohexane. The uncertainty of their data was explicitly not stated, but the standard deviations for all measurements were provided. Three-phase behaviour is found in all cases here [21], although both the temperature and pressure ranges are lower than those studied by Gillespie and Wilson [20]. In both the previous cases, the experimental feed compositions were not reported. Ng and Chen [22] measured three-phase data only and did report experimental feed conditions. Their uncertainty is given as ±0.003 for major components and it is stated that “minor components are thought to be within ±10% of the reported value”. The main aim of this study, following verification of the apparatus with binary measurements, is to produce new VLLE data for C1+nC6+H2O at temperatures and pressures of interest to subsea separation processes. Of interest also, is evaluating the ability of relevant thermodynamic models to model these new multiphase data.
Several thermodynamic models may be used for natural gas and condensate processing applications. Various equations of state, activity coefficient models and even machine learning applications are found in the literature. For this study we are specifically interested in models such as the simplified Perturbed-Chain Statistical Associating Fluid Theory (sPC-SAFT) [23] and the Cubic-Plus-Association (CPA) [24,25] equations of state which offer prediction at high pressure and were developed specifically to describe mixtures which contain hydrogen-bonding compounds like water. Standard literature versions of these models have been used in this study. A summary of the models is provided in the Supporting Information, while complete reviews are available in other sources: CPA [26,27] and SAFT-type equations of state [[28], [29], [30], [31], [32]].
In a recent study by Liang et al. [33], both CPA and sPC-SAFT were evaluated against experimental data related to gas hydrate systems which typically contain water, hydrocarbons and MeOH/glycols. It was found that both models exhibit “equally good performance”. Tzirakis et al. [34] evaluated CPA for the correlation of several three-phase MEG-related systems. The magnitude of prediction errors varied significantly across the three phases, with low errors (typically <2%) for the main components in each phases up to very large errors (∼350%) for trace components (such as H2O in the HC-rich phase). Other interesting/relevant applications of (s)PC-SAFT include: prediction of natural gas and gas condensate dew points and liquid drop out [35,36], hydrate fluid-phase equilibria modelling [37], modelling of n-alkanes and water mixtures [38], and LLE of petroleum fluids [39].
Multicomponent data are not typically used for fine-tuning models. It is however still important to understand the model accuracy for complex mixtures in order to make informed process design decisions and the requirement for additional multicomponent data was highlighted by Liang et al. [33]. To this end it is also crucial to understand the uncertainty of experimental data (and how it was determined), such that an informed comparison of the differences between the model/design and data can be made. An increased drive in recent years has led to the forced reporting of experimental uncertainty in major academic journals. Quality control has been implemented by NIST, whereby experimental data are now thoroughly checked before publication [40].
Section snippets
Experimental methodology
A series of binary and ternary VLE and VLLE measurements have been made using an analytical isothermal equilibrium cell. The apparatus was originally designed and commissioned by Frost et al. [6,41] and following modifications, the apparatus was recommissioned. A new gas chromatograph (GC) has been installed, which meant that the analytical accuracy of the apparatus needed to be verified. The experimental apparatus is presented in Fig. 1.
Validation of experimental apparatus
The experimental data for the verification/validation of the apparatus are split up into liquid phase and vapour phase composition for C1+H2O and C1+nC6, and are presented in Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7 respectively. The respective data are reported in Appendix A (Table A 1, Table A 2).
Conclusions
An older experimental apparatus has been recommissioned. Validation data have been measured for two binary systems: C1+H2O at 313 K and C1+nC6 at 303 K. The data compare favourably with other experimental data available in the literature and the uncertainty of the analytical methods were estimated at ± 9% with a 95% confidence interval.
81 new ternary VLLE data have been produced for the C1+nC6+H2O system using three different feed compositions and three different temperatures (303, 313 and
Acknowledgements
The authors gratefully acknowledge the financial support from Equinor A/S (Norway) for this work as part of the research project ‘Thermodynamics of Petroleum Fluids relevant to Subsea Processing’ as part of the ‘Chemicals for Gas Processing’ research programme.
Nomenclature
- a0
- Attractive energy term (CPA) [bar cm6 / mol2]
- AARD
- Average absolute relative deviation
- b
- Co-volume (CPA) [cm3/mol]
- β
- Association volume (CPA) [dimensionless]
- BIP
- Binary interaction parameter (CPA/sPC-SAFT) also kij
- c1
- attractive energy temperature-correction (CPA) [dimensionless]
- CG
- carrier gas (for GC)
- CI
- Confidence interval (multiplier)
- CPA
- Cubic-Plus-Association equation of state
- ε
- association energy (CPA) [bar cm6 / mol]
- ε
- energy (depth of the pair potential) (sPC-SAFT) [J]
- εAB
- energy of association (sPC-SAFT)
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