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Loss of Monoethylene Glycol to CO2- and H2S-Rich Fluids: Modeled Using Soave−Redlich−Kwong with the Huron and Vidal Mixing Rule and Cubic-Plus-Association Equations of State Rasmus Risum Boesen,* Peter Jørgensen Herslund, and Henrik Sørensen Calsep A/S, Parallelvej 12, DK-2800 Kongens Lyngby, Denmark ABSTRACT: Produced reservoir fluids often carry formation water, and gas hydrates may form in pipelines transporting the produced fluid, unless an inhibitor is added. Monoethylene glycol (MEG) is one of the most widely used hydrate inhibitors, because loss to the gas phase is typically low. The loss of MEG to CO2-rich fluids can, however, be quite significant and must be accounted for in design and economical evaluations. Accurate thermodynamic models are needed to predict the inhibition effect as well as the loss of the hydrate inhibitor to the non-aqueous phases. In this work, the Soave−Redlich−Kwong (SRK) equation of state with the Huron and Vidal (HV) mixing rule and the cubic-plus-association (CPA) model have been compared for mixtures of gas, H2O, and MEG. The models have been tested on phase equilibrium data for binary mixtures of gases (e.g., C1, CO2, and H2S) and polar components (H2O and MEG) as well as on hydrate inhibition data. Overall, the SRK−HV and CPA models provide similar results, but an exception is gas mixtures rich in CO2, for which notable differences are seen for the MEG concentration in the gas phase.
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INTRODUCTION For more than 30 years, cubic equations of state, such as, for example, the Soave−Redlich−Kwong (SRK) equation, have been the industrial standard for simulating pressure, volume, and temperature (PVT) behavior and phase equilibria of hydrocarbon mixtures. Produced reservoir fluids often carry formation water. To prevent formation of gas hydrates, inhibitors are added, of which the most commonly used are methanol (MeOH) and monoethylene glycol (MEG). Accurate modeling of mixtures of reservoir fluid, water, and hydrate inhibitors is needed to calculate the required inhibitor dosage counting in the loss of inhibitor to the hydrocarbon phases. An advantage of using MEG as an inhibitor over MeOH is that loss to the hydrocarbon phases is often limited and a larger fraction can be recovered. Some reservoir fluids are rich in CO2 and/or H2S, and the mutual solubility between these gases and hydrate inhibitors is higher than that for hydrocarbon gases. The higher mutual solubility makes CO2- and H2S-rich fluids mixed with water and hydrate inhibitors a modeling and operational challenge. Furthermore, it may lead to a significantly higher MEG loss. A thermodynamic model applied for these systems should be valid for temperatures and pressures ranging from reservoir conditions to subsea pipeline conditions and below. The purposes of this work are to (i) compare the performance of the SRK equation with the Huron and Vidal (HV) mixing rule and the cubic-plus-association (CPA) equation of state and validate them against phase equilibrium data for binary systems and hydrate formation data and (ii) highlight that the loss of MEG to the gas phase can reach significant levels in reservoir fluids rich in CO2 and/or H2S and that, for such fluids, the loss of MEG must be taken into account.
and nonpolar components. Such mixtures can however be handled using an advanced mixing rule for the a parameter, such as, for example, the one of Huron and Vidal, which combines the cubic equation with the non-random two-liquid (NRTL) excess Gibbs energy model.1 Another option is to introduce an association term, which accounts explicitly for the hydrogen bonding, as is the case with the CPA model.2,3 In this work, these two approaches are compared for mixtures containing C1, CO2, H2S, H2O, and MEG. For hydrocarbons, H2S, and CO2, the equation of state parameters are calculated from the critical properties, Tc and Pc, and the acentric factor using the classical SRK α formulation. Binary parameters are chosen in such a way that both the SRK−HV and CPA reduce to the classical SRK equation with a constant binary interaction parameter in the absence of polar components. The CPA equation is often applied with parameters a0, b and c1, which do not reduce to the correct values of Tc, Pc, and acentric factor. This will usually result in better prediction of vapor pressures and densities at the expense of matching the critical point. The classical SRK approach with the correct critical properties is heavily used in the oil and gas industry, and this makes it advantageous that the model reduces to the classical SRK equation when no polar components are present. In the SRK−HV calculations, the physically correct Tc, Pc, and acentric factor values are also used for the polar components. In CPA, all self-associating components have five pure component parameters, which have been adopted from refs 3 and 4. Special Issue: 17th International Conference on Petroleum Phase Behavior and Fouling
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EQUATIONS OF STATE Using classical mixing rules, the SRK equation is unable to give a satisfactory description of the complex phase equilibrium of polar © XXXX American Chemical Society
Received: September 15, 2016 Revised: November 30, 2016
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DOI: 10.1021/acs.energyfuels.6b02365 Energy Fuels XXXX, XXX, XXX−XXX
Article
Energy & Fuels Table 1. Number of Data Points Used in Parameter Estimation and Validation for H2O−Gas Systems H2O in gas C1 C2 C3 n-C4 CO2 H2S
gas in H2O
number of points
Tmin (°C)
Tmax (°C)
Pmin (bar)
Pmax (bar)
number of points
Tmin (°C)
Tmax (°C)
Pmin (bar)
Pmax (bar)
244 169 89 139 252 200
0 5 38 38 0 25
250 250 320 238 205 204
5.1 3.2 5.4 1.4 1.0 3.4
1378 2910 2000 694 3500 353
352 172 156 264 575 437
1 1 0 25 0 10
280 300 149 238 260 204
1.0 0.7 0.1 1.0 0.5 1.5
2583 3500 192 1000 3500 207
Table 2. Number of Data Points Used in Parameter Estimation and Validation for MEG−Gas Systems MEG in gas C1 C2 C3 n-C4 CO2 H2S
gas in MEG
number of points
Tmin (°C)
Tmax (°C)
Pmin (bar)
Pmax (bar)
number of points
34 na na na 90 na
5
150
14.8
401
0
150
1.3
63
128 54 35 na 152 45
Tmin (°C)
Tmax (°C)
Pmin (bar)
Pmax (bar)
10 10 25
150 125 125
0.9 1.0 0.8
401 203 203
15 −10
150 125
0.3 0.03
384 68
Figure 1. Absolute average relative deviations (AARDs) between simulations with data for SRK−HV and CPA and experimental data11 for binary systems with H2O.
Figure 2. Absolute average relative deviations (AARDs) between simulations with data for SRK−HV and CPA and experimental data11 for binary systems with MEG.
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HANDLING ACID GASES Modeling mixtures of polar components and the acid gases CO2 and H2S using the CPA equation of state requires special attention. Tsivintzelis et al.6,7 investigated mixtures of CO2 and polar components and found that better results are obtained if CO2 is treated as a solvating component; i.e., it does not self-associate but is able to cross-associate with other components.
Details on the SRK−HV model may be found in ref 5. The g interaction parameters are assumed to be linear functions of the temperature. Together with the non-randomness (αij) parameter, it gives a total of five binary interaction parameters. In CPA, the CR-1 combining rule has been applied for mixtures of associating components. For interactions involving associating components, a temperature-dependent kij has been applied. B
DOI: 10.1021/acs.energyfuels.6b02365 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 3. Comparison of SRK−HV (solid lines) and CPA (dashed lines), with data for H2O in C1 (left) and C1 in H2O (right). Experimental data are selected from refs 16−28.
Figure 4. Comparison of SRK−HV (solid lines) and CPA (dashed lines), with data for H2O in CO2 (left) and CO2 in H2O (right). Experimental data are selected from refs 23 and 29−47.
Figure 5. Comparison of SRK−HV (solid lines) and CPA (dashed lines), with data for H2O in H2S (left) and H2S in H2O (right). Experimental data are selected from refs 48−52.
Austegaard et al.8 investigated the binary mixtures of CO2− H2O and C1−H2O comparing SRK (with the classical mixing rules as well as HV) to the CPA equation. It was also found that it is necessary to account for the cross-association between CO2 and H2O to obtain good results with CPA. Using SRK with classical mixing rules, it was not possible to match both CO2/C1 solubility in H2 O and the H 2O solubility in CO 2/C1 simultaneously. The best overall match of the data was obtained when the HV mixing rule was used with SRK. In this work, both CO2 and H2S are assumed to have a single electron donor site and the modified CR-1 rule (mCR-1)9 is used
to determine the cross-association strength. The cross-association volume is used as an additional binary tuning parameter.
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HYDRATE MODELING The well-known van der Waals−Platteeuw model has been used to calculate the fugacity of H2O in solid hydrate phases as suggested by Munck et al.10 The gas adsorption parameters applied in the hydrate model are not universal but specific to the equation of state used for the fluid phases. Calculation of hydrate formation is a balance between the fugacity of H2O in the hydrate and aqueous phases. At equilibrium C
DOI: 10.1021/acs.energyfuels.6b02365 Energy Fuels XXXX, XXX, XXX−XXX
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Energy & Fuels
Figure 6. Comparison of SRK−HV (solid lines) and CPA (dashed lines), with data for MEG in C1 (left) and C1 in MEG (right). Experimental data are selected from refs 53−58.
Figure 7. Comparison of SRK−HV (solid lines) and CPA (dashed lines), with data for MEG in CO2 (left) and CO2 in MEG (right). Experimental data are selected from refs 53 and 59−63.
ln(f Haqueous ) − ln(f Hhydrate )=0 O O 2
(1)
2
This can be broken into liquid lattice [ln(f Haqueous ) − ln(f Hpure )] − [ln(f Hempty ) O O O 2
− =0
2
liquid ln(f Hpure )] 2O
2
−
[ln(f Hhydrate ) 2O
lattice − ln(f Hempty )] O 2
(2)
The middle term is a melting term for the hypothetical empty hydrate and is independent of the equation of state. The first term is 0 if the aqueous phase is pure water, which shows that all equations of state by definition will give the same contribution to this term if the aqueous phase is pure H2O. The last term is the stabilizing effect of the guest molecules on the hydrate lattice. It depends upon the fugacity of the guest molecules. If the mutual solubility between water and gas is low, the aqueous phase will be almost pure water and the gas phase will only contain an insignificant amount of water. With the same pure component parameters, the fugacity of the non-associating gas component will be practically the same for SRK−HV and CPA. For this reason, the same set of hydrate adsorption parameters can be used with both equations if the gas consists of N2 and/or light hydrocarbons. Especially at high pressure, the mutual solubility between water and the acid gases, CO2 and H2S, is significantly higher than that of water and hydrocarbon gases. The water phase can no longer be assumed to be pure, and the first term in eq 2 no
Figure 8. Comparison of SRK (solid lines) and CPA (dashed lines), with data for H2S in MEG. Experimental data are selected from refs 60, 65, and 66.
longer cancels out. As a consequence, different hydrate adsorption parameters are required for SRK−HV and CPA. The addition of hydrate inhibitor further reduces the fugacity of H2O in the aqueous phase. The simulated fugacity will depend upon the equation of state.
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PARAMETER ESTIMATION The binary HV and CPA parameters between gases and polar components have been tuned to the mutual solubilities using a least-squares method. Data11 covering wide ranges in temperature D
DOI: 10.1021/acs.energyfuels.6b02365 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 9. Comparison of hydrate curves for SRK−HV (solid lines) and CPA (dashed lines), inhibited by MEG: (left) C1 hydrate12−15 and (right) C1 + C3 hydrate.67
Figure 10. Comparison of SRK−HV (solid lines) and CPA (dashed lines) for H2O and MEG concentrations in C1−C3 gas. Gas feed, 90 mol % C1 and 10 mol % C3; liquid feed, 50 wt % MEG in H2O. Data are from Ng and Chen.68
Figure 11. Comparison of SRK−HV (solid lines) and CPA (dashed lines) for H2O and MEG concentrations in C1−CO2 gas. Gas feed, 90 mol % C1 and 10 mol % CO2; liquid feed, 50 wt % MEG in H2O. Data are from Ng and Chen.68
temperatures and loss of hydrate inhibitors to non-aqueous phases correctly. Therefore, in this work, the H2O−MEG interaction parameters have been tuned with emphasis on inhibited methane hydrate data.12−15 An overall comparison of SRK−HV and CPA for binary mixtures is summarized in Figures 1 and 2. The data points were manually filtered to avoid including obviously incorrect data and to ensure a good balance of data point representation over the ranges in the pressure and temperature.
and pressure has been included in an attempt to obtain parameters that are not biased toward certain conditions. A high priority has been given to match the concentration of polar components, H2O and MEG, in the gas phase, which, in some cases, is reflected in a less good match of the corresponding gas solubility in the polar phase. The number of data points and pressure and temperature ranges for the binary systems are summarized in Tables 1 and 2. For engineering calculation purposes, it is of importance to predict hydrate formation E
DOI: 10.1021/acs.energyfuels.6b02365 Energy Fuels XXXX, XXX, XXX−XXX
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Figure 12. Simulations with SRK−HV and CPA, with varying CO2 concentrations at different H2O amounts. The MEG concentration is 50 wt %.
MEG−C1. Figure 6 shows a comparison between CPA and SRK−HV at selected isotherms for the binary MEG−C1 system. The two models give an equally good match of the MEG concentration in the gas phase. This has been given a high priority in the parameter estimation, which is why the CPA match of the C1 solubility in MEG is overestimated. SRK−HV gives a good match of both phases. MEG−CO2. Figure 7 illustrates that the simulated MEG concentration in the CO2-rich phase is similar for CPA and SRK−HV, while CPA gives a better match of the gas solubilities in MEG. MEG−H2S. To our knowledge, there are no published data of the equilibrium composition of the H2S-rich phase for the MEG−H2S binary system. Making the analogy with CO2, it would be expected that cross-association between MEG and H2S plays a role and should be accounted for in CPA. However, as a result of the lack of data, it is not justified to use the crossassociation volume as a tuning parameter. Tsivintzelis et al.64 found that accounting for the cross-association and, thereby, having an extra tuning parameter improved the match of H2S solubility in MEG but treating H2S as a non-associating component gave satisfactory results. Therefore, the latter approach has been used here, and as illustrated by Figure 8, it is possible to match the gas solubility data using the temperature-dependent kij for CPA. Similarly, the lack of experimental data makes it unnecessary to use the HV mixing rule. As illustrated by Figure 8, the data can be matched quite well using the classical mixing rules. H2O−MEG. Predicting the inhibition effect is required to calculate the amount of inhibitor needed to avoid hydrate formation at a given set of operating conditions. Because C1 is the predominant constituent of natural gas, the H2O−MEG interaction parameters have been tuned to inhibited C1 hydrate curves. Figure 9 shows the hydrate curves for MEG concentrations up to 50 wt % for a pure C1 hydrate and up to 60 wt % for a mixed C1−C3 hydrate. Overall, SRK−HV and CPA give similar results. The difference does increase with the inhibitor concentration, but at the highest concentration, the results are still within approximately 0.5 °C.
Figure 13. Simulations with SRK−HV and CPA, with varying H2O amounts. The MEG concentration is 50 wt %.
As seen from Figure 1, the two models perform equally well overall. CPA gives a slightly better match of H2O in gas, while SRK−HV is slightly better for the gas solubility in water.
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BINARY SYSTEMS In this section, simulations of the mutual solubilities in binary systems are shown at selected isotherms to illustrate typical differences and similarities between SRK−HV and CPA. H2O−C1. Figure 3 shows how the two equations of state match the binary H2O−C1 system. At moderate pressures of 50−100 bar, CPA provides more accurate simulations of the water content in the gas, which may be attributed to the more accurate modeling of vapor pressure. As pressure increases, the water content in the C1-rich phase becomes governed by solubility rather than volatility. At these conditions, the SRK− HV model provides a better match of the water content in gas than CPA. Overall, SRK−HV also gives a better match of the C1 solubility in the aqueous phase. Even with a linear temperature dependence of kij, it is not possible with CPA to match the gas solubility as well as with SRK−HV. H2O−CO2. Figure 4 shows how SRK−HV and CPA match the binary H2O−CO2 system. The match of the water content in the CO2-rich phase is very similar, while SRK−HV is slightly better in matching the CO2 solubility in the water phase. H2O−H2S. Figure 5 shows the match of the binary H2O−H2S system. Again, the overall match by SRK−HV and CPA is similar, with the H2S solubility in H2O being matched slightly better with SRK−HV. At lower pressures, the H2O content in the H2S-rich phase is matched slightly better with CPA, but overall, the two models perform equally well.
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MULTICOMPONENT DATA WITH H2O AND MEG In this section, SRK−HV and CPA predictions are compared to data from Ng and Chen68 to see how well they perform in predicting the H2O and MEG contents in a mixed gas in equilibrium with an aqueous liquid phase. Figure 10 shows the H2O and MEG contents in a gas mixture of C1 (90 mol %) and C3 (10 mol %). SRK−HV and CPA give similar results for both MEG and H2O. The same goes for the equilibrium concentrations in a gas mixture of C1 (90 mol %) and CO2 (10 mol %), as illustrated in Figure 11. F
DOI: 10.1021/acs.energyfuels.6b02365 Energy Fuels XXXX, XXX, XXX−XXX
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Energy & Fuels
∼90 mol %, which could be representative of CO2-rich reservoir fluids. More data are needed to validate which model is more accurate, particularly for gases with high CO2 concentrations. Similarly, an increased MEG loss may be expected to reservoir fluid rich in H2S, but a lack of data, particularly for the MEG solubility in H2S, makes it difficult to evaluate the models. The SRK−HV and CPA models are both capable of handling mixtures with polar components. A comparison has been made with data for binary H2O−gas and MEG−gas mixtures as well as multicomponent data. The overall match for the models is comparable over large pressure and temperature intervals. For the CPA equation, better results for binary mixtures of H2O−CO2 and MEG−CO2 are obtained when CO2 is treated as a solvating component and the cross-association volume is used as a tuning parameter. The same applies for the binary mixture of H2O and H2S. No data for MEG solubility in H2S were available; therefore, cross-association between MEG and H2S was not applied. H2O−MEG interaction parameters were tuned to inhibited C1 hydrate curves, and CPA and SRK−HV were shown to give very similar hydrate temperatures up to a concentration of 60 wt % MEG.
At the highest pressures, the data show that the MEG concentration in the C1−CO2 mixture is larger than in the C1−C3 mixture, indicating that the presence of CO2 increases the solubility of MEG. The CO2 concentration in the gas feed is fairly low, but the difference between SRK−HV and CPA is more pronounced than in the C1−C3 mixture, particularly at the highest pressure. It is worth noting that both SRK−HV and CPA underpredict the MEG concentration in the C1−CO2 gas mixture.
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INFLUENCE OF CO2 In the following section, simulations are presented to illustrate the influence of the sour gas component CO2. The simulations are carried out at typical pipeline operating conditions (P = 200 bar and T = 5 °C). The focus here is to calculate the loss of MEG to the gas phase, which is often not considered to be significant as a result of low volatility of MEG. The CO2 concentration is given as mole percent in the gas (mixture of C1 and CO2). H2O amount is given as mole percent of H2O + gas feed, and the MEG concentration is given as weight percent of the aqueous components (H2O + MEG). Figure 12 shows the equilibrium concentration of MEG in the non-aqueous phase when the gas is a mixture of C1 and varying amounts of CO2. As the CO2 concentration increases so does the MEG concentration in the gas. As a result of the relatively low solubility of gas in the aqueous phase, the equilibrium concentration of MEG in the gas is not very sensitive toward the water amount. Figure 12 also shows the corresponding inhibitor loss defined as the percentage of the total amount of inhibitor that is lost to the gas phase. This illustrates that, if the water amount is low, then a significantly higher fraction of the inhibitor is lost to the gas phase, from which it is usually not recovered. Figure 12 shows that SRK−HV and CPA yield similar predictions for the amount of MEG in the pure gases, but for a mixture rich in CO2 (∼40−90 mol % CO2), there is a difference of up to a factor 4 on the concentration of MEG in the gas. This difference is also reflected in the percentage of MEG that is lost, as illustrated in the figure. Figure 13 shows the difference between the inhibitor loss in cases where the gas is either pure C1 or pure CO2. SRK−HV and CPA yield comparable results in both cases. The higher solubility of MEG in CO2 than in C1 is reflected in an inhibitor loss that is orders of magnitude higher. If the water amount is low (
