# Simulation of Dual Mixed Refrigerant Natural Gas Liquefaction Processes Using a Nonsmooth Framework

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## Abstract

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## 1. Introduction

_{2}emissions and no particle emissions upon combustion means that natural gas provides a cleaner alternative to oil and coal. However, a significant challenge with using natural gas is related to its transportation, especially over long distances. Alternative technologies for the transportation of natural gas exist, where the conventional approach is to use pipelines. However, pipeline transportation requires a large initial investment in infrastructure. Moreover, it ties the seller of the gas to a small set of customers at the receiving terminals. Excessive infrastructure and transportation costs for long distances also make pipeline gas difficult to export to the global energy market. Because of this, the recent trend has been towards natural gas liquefaction. The liquefaction of natural gas is a very energy intensive process that requires cooling to about −162 C. Investments in expensive, customized, and proprietary technology are necessary. Together with high operating costs, liquefaction accounts for about 30–40% of the total cost of the Liquefied Natural Gas (LNG) chain [1]. LNG production plants are frequently divided into three main categories: base-load, peak-shaving, and small-scale plants. Single mixed refrigerant (SMR) liquefaction processes are normally considered for small-scale and peak-shaving LNG production where capital costs rather than operational costs are the main concern. In the case of base-load plants, high production volumes with accompanying high operating costs advocate more efficient designs. A popular alternative is the Dual Mixed Refrigerant (DMR) processes due to their high efficiency and flexible design. The added flexibility comes at a cost computationally, however, as DMR processes are significantly more complex to model, simulate, and optimize than SMR processes.

## 2. The Nonsmooth Multistream Heat Exchanger Model

#### Solving the MHEX Model

## 3. Simulation Cases and Results

- Pressure level of the (warm/cold) high pressure refrigerant: ${P}_{\mathrm{HP}(\mathrm{W}/\mathrm{C})}$.
- Pressure level of the (warm/cold) low pressure refrigerant: ${P}_{\mathrm{LP}(\mathrm{W}/\mathrm{C})}$.
- Inlet/outlet temperatures of the high pressure refrigerants (equal to the natural gas stream): ${T}_{\mathrm{HP}}^{\mathrm{IN}/\mathrm{OUT}}$.
- Inlet/outlet temperatures of the low pressure refrigerant streams: ${T}_{\mathrm{LP}}^{\mathrm{IN}/\mathrm{OUT}}$.
- Molar flowrate of the (warm/cold) refrigerants: ${F}_{(\mathrm{W}/\mathrm{C})}$.
- Molar flowrate of component i in (warm/cold) refrigerants: ${f}_{(\mathrm{W}/\mathrm{C}),i}$.

## 4. Example 1

**Case I:**${P}_{\mathrm{LPW}}$, ${P}_{\mathrm{HPC}}$, ${f}_{\mathrm{W},\mathrm{propane}}$, ${T}_{\mathrm{LP},2}^{\mathrm{OUT}}$, $U{A}_{2}$.**Case II:**${P}_{\mathrm{HPW}}$, ${P}_{\mathrm{LPC}}$, ${F}_{\mathrm{C}}$, $\Delta {T}_{\mathrm{min},1}$, $\Delta {T}_{\mathrm{min},2}$.

**Case I.**Solved for a variable WMR composition, an unknown inlet temperature to the CMR compressor, the heat exchanger conductance in MHEX 2, as well as the low pressure level ${P}_{\mathrm{LPW}}$ and high pressure level ${P}_{\mathrm{HPC}}$ of the warm and cold mixed refrigerants, respectively. The refrigerant composition was changed in the model by varying the component molar flowrate of propane ${f}_{\mathrm{W},\mathrm{propane}}$. A solution was obtained after four iterations and a total simulation time of 62.7 s, including initialization. The model converged to a solution with ${P}_{\mathrm{LPW}}=0.57$ MPa, ${P}_{\mathrm{HPC}}=6.53$ MPa and ${T}_{\mathrm{LP},2}^{\mathrm{OUT}}=242.15$ K. The design resulted in a total compression work of 21.33 MW, with heat exchanger conductance values of $U{A}_{1}=2.69$ MW/K and $U{A}_{2}=1.89$ MW/K. The work distribution of the two compressors was 16.79 MW for compressing the CMR and 4.54 MW for compressing the WMR. A new WMR composition was obtained consisting of 53.30 mol % ethane, 26.64 mol % propane and 20.06 mol % n-butane with a corresponding molar flowrate of 1.48 kmol/s. Figure 2 presents the composite curves and driving force plot for the solution.

**Case II.**Solved for the flowrate of the CMR, the minimum approach temperatures in both MHEXs, and the high pressure and low pressure levels of the warm and cold refrigerant mixtures, respectively. A solution was obtained after 13 iterations with ${P}_{\mathrm{HPW}}=1.58$ MPa, ${P}_{\mathrm{LPC}}=0.388$ MPa, ${F}_{\mathrm{C}}=1.952$ kmol/s, and minimum approach temperatures of 5.00 K and 3.15 K for MHEX 1 and 2, respectively. The design resulted in a total compressor work of 20.56 MW, and a heat exchanger conductance value $U{A}_{1}$ of 2.04 MW/K. Compressing the CMR required a total of 14.10 MW, whereas compressing the WMR required only 6.46 MW. The total simulation time, including initialization of the model, was 102.5 s. The composite curves and driving force plots for the process are presented in Figure 3. As can be seen, both solutions have a similar trend, although the cold low pressure refrigerant superheating is noticeably larger in Case I. This results in lower driving forces in MHEX 1, but also introduces a larger temperature difference at the cold end of the process, leading to a higher compression power. A discussion on superheating and its effect on design of DMR processes was made by Kim and Gundersen [29].

## 5. Example 2

**Case I:**${P}_{\mathrm{LPW}}$, ${P}_{\mathrm{HPW}}$, ${P}_{\mathrm{LPC}}$, ${T}_{\mathrm{HP},2}^{\mathrm{OUT}}$, ${T}_{\mathrm{LP},3}^{\mathrm{OUT}}$, ${F}_{\mathrm{C}}$, $\Delta {T}_{\mathrm{min},2}$.**Case II:**${P}_{\mathrm{LPW}}$, ${P}_{\mathrm{HPC}}$, ${T}_{\mathrm{HP},2}^{\mathrm{OUT}}$, ${T}_{\mathrm{LP},3}^{\mathrm{OUT}}$, ${f}_{\mathrm{W},\mathrm{ethane}}$, $\Delta {T}_{\mathrm{min},2}$, $U{A}_{3}$.

**Case I:**Solved for both pressure levels of the WMR, the low pressure level and refrigerant flowrate of the CMR, the feed gas and high pressure refrigerant temperatures out of MHEX 2, the low pressure refrigerant temperature out of MHEX 3, as well as the minimum approach temperature in MHEX 2. A solution was obtained after six iterations and a total simulation time of 83.0 s with ${P}_{\mathrm{LPW}}=0.43$ MPa, ${P}_{\mathrm{HPW}}=1.62$ MPa, ${P}_{\mathrm{LPC}}=0.27$ MPa, ${T}_{\mathrm{HP},2}^{\mathrm{OUT}}=155.34$ K, ${T}_{\mathrm{LP},3}^{\mathrm{OUT}}=151.34$ K, ${F}_{\mathrm{C}}=1.42$ kmol/s, and $\Delta {T}_{\mathrm{min},2}=6.68$ K. The $UA$-values were calculated to be 1.99 MW/K and 2.12 MW/K for MHEXs 1 and 2, respectively. The obtained feasible design resulted in a combined compression work of 14.40 MW, where 9.76 MW was needed to compress the CMR, and 4.64 MW was used to compress the WMR. Figure 5 presents the composite curves and driving force distribution in the MHEXs at the solution.

**Case II:**Solved for the low pressure level of the WMR, high pressure level of the CMR, the natural gas and high pressure refrigerant temperatures out of MHEX 2, the low pressure refrigerant temperature out of MHEX 3, the composition of the WMR, the minimum temperature difference in MHEX 2, and the heat exchanger conductance value for MHEX 3. The model converged after three iterations and a total simulation time of 64.2 s to a solution with ${P}_{\mathrm{LPW}}=0.44$ MPa, ${P}_{\mathrm{HPC}}=4.59$ MPa, ${T}_{\mathrm{HP},2}^{\mathrm{OUT}}=161.03$ K, ${T}_{\mathrm{LP},3}^{\mathrm{OUT}}=157.03$ K, $\Delta {T}_{\mathrm{min},2}=7.88$ K, and $U{A}_{3}=0.33$ MW/K. A new WMR composition was obtained with 49.24 mol % ethane, 33.24 mol % propane, and 17.51 mol % n-butane and a total molar flowrate of 1.59 kmol/s. The feasible design required a total compression power of 14.85 MW, where 10.08 MW was spent compressing the CMR and 4.76 MW was used to compress the WMR. The heat exchanger conductance values were calculated during post-processing to be $U{A}_{1}=2.02$ MW/K and $U{A}_{2}=1.84$ MW/K, respectively. The composite curves and driving force plots for the process are presented in Figure 6.

**Case III:**Included an NGL separator for the extraction of heavier hydrocarbons (see Figure 7). The case solved for the same set of variables as in Case I and with the same initial guesses and parameter values as given in Table 2. As for the previous examples, the model was solved from an initial guess at which Aspen Plus obtained no feasible solutions with the built-in MHEX module. Rich feed gas compositions at a reduced pressure of 4.0 MPa were used to ensure adequate separation. Simulations were carried out at three different compositions with varying methane contents (Table 3).

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

Roman letters | ||

$EBP$ | = | enthalpies of the extended composite curves (W) |

f | = | component molar flowrate (mol/s) |

F | = | total molar flowrate (mol/s) |

$\mathbf{G}$ | = | element of the generalized derivative |

$m{C}_{\mathrm{p}}$ | = | heat capacity flowrate (W/K) |

${n}_{\mathrm{c}}$ | = | total number of components |

T | = | temperature (K) |

$UA$ | = | heat exchanger conductance (W/K) |

P | = | absolute pressure (Pa) |

Q | = | heat duty (W) |

$\mathbf{y}$ | = | equation residuals |

W | = | compressor work (MW) |

Greek letters | ||

$\Delta {T}_{\mathrm{LM}}$ | = | log mean temperature difference (K) |

$\Delta {T}_{\mathrm{min}}$ | = | minimum approach temperature (K) |

$\Delta Q$ | = | enthalpy change (W) |

$\gamma $ | = | variable in the LP-Newton method |

Subscripts and superscripts | ||

2p | = | two-phase substream |

BP | = | bubble point |

C | = | cold stream |

DP | = | dew point |

in/out | = | inlet/outlet temperature of a substream |

IN/OUT | = | inlet/outlet temperature of a process stream |

H | = | hot stream |

HP | = | high pressure refrigerant |

LP | = | low pressure refrigerant |

p | = | pinch candidate |

sub | = | subcooled substream |

sup | = | superheated substream |

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**Figure 1.**The Dual Mixed Refrigerant (DMR) model with cascading PRICO cycles for the warm and cold mixed refrigerant streams.

**Figure 2.**(

**a**) Composite curves for the feasible design in Case I. (

**b**) The corresponding driving force plot.

**Figure 3.**(

**a**) Composite curves for the feasible design in Case II. (

**b**) The corresponding driving force plot.

**Figure 5.**(

**a**) Composite curves for the feasible design in Case I. (

**b**) The corresponding driving force plot.

**Figure 6.**(

**a**) Composite curves for the feasible design in Case II. (

**b**) The corresponding driving force plot.

**Table 1.**Multistream heat exchanger (MHEX) and refrigerant stream data for Example 1. For unknown variables, the value listed is an initial guess.

Property | Value | Property | Value |
---|---|---|---|

$\eta $ | 0.8 | $U{A}_{2}$ (MW/K) | 3.0 |

$\Delta {T}_{\mathrm{min},1}$ (K) | 3.0 | $\Delta {T}_{\mathrm{min},2}$ (K) | 3.0 |

${F}_{\mathrm{W}}$ (kmol/s) | 1.65 | ${F}_{\mathrm{C}}$ (kmol/s) | 1.55 |

${P}_{\mathrm{HPW}}$ (MPa) | 1.67 | ${P}_{\mathrm{HPC}}$ (MPa) | 4.30 |

${P}_{\mathrm{LPW}}$ (MPa) | 0.42 | ${P}_{\mathrm{LPC}}$ (MPa) | 0.25 |

${T}_{\mathrm{HP},1}^{\mathrm{OUT}}$ (K) | 245.15 | ${T}_{\mathrm{HP},2}^{\mathrm{OUT}}$ (K) | 120.15 |

${T}_{\mathrm{LP},1}^{\mathrm{OUT}}$ (K) | 290.15 | ${T}_{\mathrm{LP},2}^{\mathrm{OUT}}$ (K) | 240.15 |

Composition (mol %): | |||

Ethane | 47.83 | Nitrogen | 10.00 |

Propane | 34.17 | Methane | 43.80 |

n-Butane | 18.00 | Ethane | 35.20 |

Propane | 11.00 |

**Table 2.**MHEX and refrigerant stream data for Example 2. For unknown variables, the value listed is an initial guess.

Property | Value | Property | Value |
---|---|---|---|

$\eta $ | 1.0 | $\Delta {T}_{\mathrm{min},1}$ (K) | 4.0 |

$U{A}_{3}$ (MW/K) | 0.3 | $\Delta {T}_{\mathrm{min},2}$ (K) | 11.0 |

$\Delta {T}_{\mathrm{min},3}$ (K) | 4.0 | ||

${F}_{\mathrm{W}}$ (kmol/s) | 1.55 | ${F}_{\mathrm{C}}$ (kmol/s) | 1.45 |

${P}_{\mathrm{HPW}}$ (MPa) | 1.67 | ${P}_{\mathrm{HPC}}$ (MPa) | 4.85 |

${P}_{\mathrm{LPW}}$ (MPa) | 0.50 | ${P}_{\mathrm{LPC}}$ (MPa) | 0.25 |

${T}_{\mathrm{HP},1}^{\mathrm{OUT}}$ (K) | 240.15 | ${T}_{\mathrm{HP},2}^{\mathrm{OUT}}$ (K) | 170.15 |

${T}_{\mathrm{HP},3}^{\mathrm{OUT}}$ (K) | 120.15 | ${T}_{\mathrm{LP},1}^{\mathrm{OUT}}$ (K) | 280.15 |

${T}_{\mathrm{LP},2}^{\mathrm{OUT}}$ (K) | 230.15 | ${T}_{\mathrm{LP},3}^{\mathrm{OUT}}$ (K) | 145.15 |

Composition (mol %): | |||

Ethane | 47.83 | Nitrogen | 7.00 |

Propane | 34.17 | Methane | 41.80 |

n-Butane | 18.00 | Ethane | 33.20 |

Propane | 18.00 |

Compostion I: | Composition II: | Composition III: | |
---|---|---|---|

Nitrogen (mol %) | 2.00 | 2.00 | 2.00 |

Methane (mol %) | 85.60 | 87.60 | 89.60 |

Ethane (mol %) | 6.93 | 5.93 | 4.93 |

Propane (mol %) | 3.71 | 2.71 | 1.71 |

n-Butane (mol %) | 1.35 | 1.35 | 1.35 |

i-Butane (mol %) | 0.40 | 0.40 | 0.40 |

i-Pentane (mol %) | 0.01 | 0.01 | 0.01 |

Composition I: | Composition II: | Composition III: | |
---|---|---|---|

Total work (MW) | 14.99 | 15.11 | 15.13 |

${W}_{\mathrm{C}}$ (MW) | 10.26 | 10.40 | 10.43 |

${W}_{\mathrm{H}}$ (MW) | 4.73 | 4.71 | 4.70 |

$U{A}_{1}$ (MW/K) | 2.07 | 2.05 | 2.03 |

$U{A}_{2}$ (MW/K) | 2.63 | 2.87 | 3.41 |

${P}_{\mathrm{LPW}}$ (MPa) | 0.43 | 0.43 | 0.43 |

${P}_{\mathrm{HPW}}$ (MPa) | 1.66 | 1.66 | 1.65 |

${P}_{\mathrm{LPC}}$ (MPa) | 0.26 | 0.25 | 0.25 |

${T}_{\mathrm{HP},2}^{\mathrm{OUT}}$ (K) | 158.22 | 157.95 | 157.50 |

${T}_{\mathrm{LP},3}^{\mathrm{OUT}}$ (K) | 154.22 | 153.95 | 153.50 |

${F}_{\mathrm{C}}$ (kmol/s) | 1.46 | 1.47 | 1.48 |

$\Delta {T}_{\mathrm{min},2}$ (K) | 3.69 | 3.14 | 2.20 |

LNG composition (mol %): | |||

Nitrogen | 2.08 | 2.05 | 2.03 |

Methane | 88.04 | 89.24 | 90.61 |

Ethane | 6.50 | 5.68 | 4.81 |

Propane | 2.67 | 2.15 | 1.48 |

n-Butane | 0.52 | 0.65 | 0.81 |

i-Butane | 0.19 | 0.23 | 0.27 |

i-Pentane | 0.00 | 0.00 | 0.00 |

LNG flowrate (kmol/s) | 0.96 | 0.97 | 0.98 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Vikse, M.; Watson, H.A.J.; Gundersen, T.; Barton, P.I.
Simulation of Dual Mixed Refrigerant Natural Gas Liquefaction Processes Using a Nonsmooth Framework. *Processes* **2018**, *6*, 193.
https://doi.org/10.3390/pr6100193

**AMA Style**

Vikse M, Watson HAJ, Gundersen T, Barton PI.
Simulation of Dual Mixed Refrigerant Natural Gas Liquefaction Processes Using a Nonsmooth Framework. *Processes*. 2018; 6(10):193.
https://doi.org/10.3390/pr6100193

**Chicago/Turabian Style**

Vikse, Matias, Harry A. J. Watson, Truls Gundersen, and Paul I. Barton.
2018. "Simulation of Dual Mixed Refrigerant Natural Gas Liquefaction Processes Using a Nonsmooth Framework" *Processes* 6, no. 10: 193.
https://doi.org/10.3390/pr6100193