(441b) Calculating Dew Points for Natural Gas Containing Water and/or Selected Production Chemicals

Calculating Dew Points
for Natural Gas containing Water and/or selected Production Chemicals

Eirini
K.Karakatsani¹ and Georgios M. Kontogeorgis¹

¹Technical University of Denmark, Department of
Chemical and Biochemical Engineering, Center for Energy Resources Engineering
(CERE)

Corresponding author e-mail: eirka@kt.dtu.dk

1.   
Introduction

The water content of natural gas (NG) often
poses problems during the production, transportation and distribution of the gas.
Small quantities of undesired dissolved water may condense leading to the
formation of condensed water, hydrates and/or ice.  Such condensed phases may result in
corrosion, two-phase flow problems, safety hazards and flow assurance issues,
slugging of the flow lines, valves and instrumentation resulting in reduced
capacity and shutdowns, and reduction of the oil recovery efficiency because of
reduction of the reservoir permeability [1]. Accurate thermodynamic models able
to calculate the water vapor concentration in equilibrium with hydrate, ice and
water in natural gas at pipeline operating conditions (253-323K and up to
250bar) are necessary both because experimental data are limited and difficult
to obtain, and because the limits of dehydration techniques (physical
adsorption and condensation) need to be defined. The latter techniques use
chemicals (eg. glycols and alcohols) which also
condensate, adding one more level of challenge when it comes to design of
pipelines and process equipment and thermodynamic modeling of formed mixtures.

Aim of this work is to evaluate and compare the
performance of different carefully selected thermodynamic models
vis-à-vis their capacity to calculate dew points of natural gas mixtures with
and without chemicals. A main focus is put on the further development
of the CPA (Cubic-Plus-Association)
equation of state (EoS) [2] for the applications
under consideration and its comparison to GERG-water  calculation
method, an ISO-standard model specifically designed to correlate water content
and dew points of natural gas [3].

2.   
Results and discussion

In this work appropriate ice and hydrate models have been combined with
the predictive CPA model for calculating the equilibrium conditions of all
possible fluid and condensed phases in a natural gas mixture.

More specifically, the water fugacity in the
ice phase at the desired pressure of the system P is given by the following equation:

which
corrects the saturation fugacity at the same temperature by the Poynting factor, while for the hydrate phase modeling the
well established statistical model proposed by van der
Waals and Platteeuw [4] (vdW-P)
was used together with the simplified approach suggested by Parrish and Prausnitz [5] for the Langmuir constants. According to vdW-P theory the chemical potential of the hydrate phase is
given by the expression: 

where R is the universal gas constant, ν_i is the number of type i cavities per water molecule
(which are:  ν₁= 1/23 and ν₂= 3/23 for structure I
hydrate and ν₁= 2/17 and ν₂= 1/17 for type II hydrates)
and the summation is over all cavity types (both 1 and 2). Finally, the
occupancy of cavity m by a component i, Θ_mi, is
calculated as follow:

Here f_k is
the fugacity of a component k in the
equilibrium vapor phase obtained from an equation of state,
the summation is over all hydrate-forming components while C_mi are the Langmuir
constants. Following the simplified approach, suggested by Parrish and
Prausnitz: 

where
and
are
fitted parameters.

In this work new
and
 parameters were derived for four
main natural gas components (CH₄ , C₂H₆, C₃H₈,
CO₂) using the most recent available phase equilibrium experimental
data (both Hydrate-Ice-Vapour and Hydrate-Liquie-Vapour data), only single
hydrate data where possible, the most recent CPA parameters for NG components
and checking the internal consistency of experimental data before using them (f.ex. Bakker pointed inconsistencies between the data sets
previous used for methane parameters estimation [6]). The new parameters (Table 1) have been tested under many
different conditions (low temperatures, hydrate structure transitions, HVE, HLE,..), where HLE and structural transitions have been found
to be the biggest challenges for the model (see f.ex.
Figure 1 for HLE calculations where
results of GERG-water, SRK, PR and VPT EoS are also
included). It is obvious that the CPA EoS
performs qualitatively better both with and without binary interaction
parameters. It also seems that different thermodynamic models' results scatter
more at high pressures and low temperatures (HPLT), where hydrates usually form
(see f.ex. Figure 2).     

Table 1. Optimized
values of Ami and Bmi for calculating the Langmuir
constants.

Figure 1 (left). Water content of a binary hydrocarbon liquid mixture (0.646 C2H6- 0.354
C3H8 mole fraction) mixture in equilibrium with
hydrate.

Figure 2 (right).  Water content of a binary
hydrocarbon gas mixture (0.9469 CH4- 0.0531 C3H8 mole fraction)
mixture in equilibrium with hydrate.

When inhibitors are included in the NG mixture, results produced by
different thermodynamic models tend to be more similar to each other at low
inhibitor concentrations, while the scatter is more pronounced at high
concentrations, which are often the case nowadays as exploration and production
activities move into colder and deeper regions (see Figure 3). About Figure 3,
it should be noted that the phase behavior of NG mixtures is qualitatively
similar to that of pure methane. Based on the results of this Figure, CPA is
found in better quantitative agreement with experimental data than any other
model.  

Figure 3 (left). Methane hydrate formation in the presence of triethylene glycol (TEG) as inhibitor.

Figure 4 (right).  Water content of CO₂
in equilibrium with hydrates at 137.9bar and different temperatures.

Recently, the accuracy and reliability of different experimental
measurements for the highly asymmetric CO₂-H₂O system at HPLT
conditions have been questioned. F.ex. Haghighi et al.[7] measured water
content for pure CO₂ in equilibrium with hydrates at 137.9 bar and
found it substantially smaller compared to the previously reported values in
GPA RR-99. Although our results do not coincide with those new measurements,
they are in better agreement with them than with the older results reported by
GPA, especially when it comes to CPA results (see Figure 4).

In another case, Seo et al.[8]
measured the solubility of water in liquid CO₂ at 6.1 and 10.1MPa in
the presence of hydrate and observed a weak pressure dependence, contrary to
the previously reported data of Song and Kobayashi. Indeed our models' results
also suggest a weaker pressure dependence than the originally suggested but we
believe that the high temperature data are still correct, referring to VHE
conditions instead of LHE conditions as originally thought (taking into account
the existence of a three-phase line (VLL) which ends at the UCEP) (see. Figure 5). As
seen in the Figure, CPA EoS
result almost coincide with the experimentally reported value of water vapor
composition along the 3-phase line.

Finally, Eslamimanesh et al.[9] performed a
thermodynamic consistency test based on an area approach and studied the reliability
of experimental data of solubility in CO₂-H₂O system.
They found 3 thermodynamically inconsistent data series [10-11] at 298.20K,
333.20K and 353.10K which we compared against our model correlations. VPT EoS was found the one in worse agreement with the specific
data. 

Figure 5. Solubility
of water in the liquid CO2 for the L_CO2-H and L_CO2-L_w
phase between 5.992MPa and 10.34MPa.

Conclusions

The results reveal that CPA is a versatile model that can ?in most
cases- capture the complicated phase behavior of systems with NG mixtures
and/or production chemicals at pipeline operating conditions, when combined
with the vdW-P theory. Even when CPA is purely
predictive (i.e. all binary interaction parameters are set equal to 0) it
provides qualitatively correct results and can be used for calculating the
thermodynamically stable phase, which is often not known in advance. 

Comparison between different models' results and experimental data shows
that there is still a lot to be done both in terms of experimental data
consistency tests and model development.

 References

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