# Numerical Evaluation of the Hydrothermal Process in a Water-Surrounded Heater of Natural Gas Pressure Reduction Plants

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{4}, 8 × 10

^{4}, 1 × 10

^{5}, and 12 × 10

^{5}standard cubic meters per hour (or 16.67, 22.22, 27.78, and 33.33 m

^{3}/s). The results indicate that the natural gas outlet temperature achieved to a temperature higher than required. By installing a regulator on the burner, the gas consumption can be reduced, resulting in station cost savings, and also reducing the environmental impacts. The outcomes depict that the maximum possible reductions in monthly gas consumption and economic savings in the proposed system are 67,500 m

^{3}and IRR 25 million at a gas mass flow rate of 60,000 SCMH.

## 1. Introduction

_{2}emissions.

## 2. Materials and Methods

#### 2.1. Geometrical Parameters

^{3}/s; it can absorb 819,500 kcal/h (0.953 kW) with 4 coils. It has eight gas pipes. Coil diameter and length are 4 in (0.1016 m) and 236.22 in (6 m), respectively. Additionally, the operational temperature and pressure of the heater under investigation are 40 °C and 1050 psi (7239.49 kPa), respectively. Moreover, the maximum and minimum burner capacity are 150,000 kCal/h (174.45 kW) and 750,000 kCal/h (827.25 kW), respectively. Furthermore, the fire tube diameter and length are 4 in (0.6 m) and 267.72 in (6.8), respectively.

#### 2.2. Governing Equations and Parameters

**Momentum Conservation Equations [18,19,20,21]:**

_{Mi}, for the amount of momentum in the direction i per unit volume and per unit time, where i includes x, y, or z directions. If the body forces only include gravity, which is the case in the present problem, then S

_{Mx}= S

_{Mz}= 0 and S

_{My}= −ρg.

_{k}is the production of turbulence due to viscous forces, which is defined as follows:

^{+}distribution on the surface of the tube is shown in Figure 2, which shows the acceptable values of y

^{+}in the presented model.

**Mass Conservation Equation [18,19,20,21]:**

**Turbulent Energy Equation [18,19,20,21]:**

#### 2.3. Boundary Conditions

_{S}− T

_{∞}) D

^{3}/ν

^{2}) is used to determine the flow regime in free convection heat transfer. This number indicates whether the flow is laminar or turbulent. The Grashof number is obtained from the ratio of the buoyancy force to the viscous force. In this correlation, the parameters g, β, T

_{S}, T

_{∞}, D, and υ express the gravitational acceleration, volumetric expansion coefficient, hot surface temperature, cold surface temperature, length characteristics, and kinematic viscosity, respectively. If the Grashof number is greater than 10 + 8, the flow is turbulent. According to the specifications of this issue, the Grashof number is about 6 × 10 + 6, so the flow regime is laminar. On the other hand, due to the high liquid flow rate inside the fire tube and gas line, the Reynolds number of the flow is much higher than 2300, so the liquid flow is completely turbulent.

^{3}/s). The gas inlet temperature in the heater was assumed to be 10 °C according to the ambient conditions. An inlet velocity of 5 m/sec and a temperature of 800 K were assumed for the inlet boundary of the fire tube assuming an additional fuel-to-air ratio of 1.8, an air inlet temperature of 30 °C, and a methane flame temperature of 2400 K at a pressure of 1 bar. The volumetric expansion coefficient of water was assumed to be 0.0005 K

^{−1}to model the effects of natural convection. The gas entering the heater consists of various components with different ratios. Table 1 shows the components of the gas and the volume fraction of each component. As can be seen, about 90% of the gas consists of methane gas, so for simplicity’s sake, only methane gas was considered as a component of the city gas in further modeling processes.

## 3. Results and Discussion

^{3}/s). The results include the outlet temperature of methane and combustion gas, the temperature and velocity distribution in the heater, and the thermal efficiency of the heater.

#### 3.1. The Mesh-Independent and Validation Analyses

^{3}/s). The numerical results obtained for these networks are shown in Table 4. It can be concluded that the grid with 4,777,825 cells is suitable for use in the following sections of this work. Images showing grid generated for the heater under consideration from different perspectives are shown in Figure 4. It can be seen that to increase the accuracy of the numerical simulation, the boundary layer grid was used in both the gas tube and the fire tube.

#### 3.2. Investigating the Performance of the Gas Heater at 120,000 SCMH

^{2}.

^{2}.

#### 3.3. Investigating the Impact of Gas Mass Flow Rate

^{3}/s). The parameters studied in this section include the outlet temperature of the coil and the fire tube.

^{3}/s) to 120,000 (33.33 m

^{3}/s) SCHM (100% increase).

^{3}/s), the average temperature of the hot water was 337 K, and with the increase in the mass flow rate to 120,000 SCMH (33.33 m

^{3}/s), the average temperature of the hot water decreased to 325 K. The temperature contours on a slice (X = 0) at different mass flow rates are shown in Figure 14. As can be seen, the water temperature inside the shell dropped significantly when the flow rate was increased.

^{3}/s) to 120,000 SCMH (33.33 m

^{3}/s), the exit temperature of the fire tube increased from about 416 to 409 K.

#### 3.4. Investigating the Fuel Consumption Reduction Using the Considered Heater

_{P}is the specific heat capacity of the water, and (T

_{2}− T

_{1}) is the difference between the primary and secondary temperatures of the tank water.

^{3}. The initial temperature of the fluid, T

_{1}, is obtained according to numerical calculations employing ANSYS Fluent software and is the average temperature of the hot water bath. The secondary fluid temperature, T

_{2}, is assumed to be 300 K. Therefore, using the relationships and assumptions provided, the amount of energy stored in the hot water tank can be determined for different mass flow rates as we know the hot water bath temperature from numerical calculations. The amount of time it takes for the energy to be transferred to the fluid or, in other words, the time it takes for the temperature of the hot water bath to go from T

_{1}to T

_{2}, can be calculated as follows:

_{P}is the heat capacity of the gas, and T

_{1}and T

_{2}are the initial and secondary temperatures of the gas, respectively. Finally, the time needed to transfer energy between the hot water bath and the coils, indicated as burner off time, is determined as follows:

^{3}/s −100% growth), the burner off time declined by about 65.87%.

_{Coil}indicates the time required to heat the gas input to the heater, which, considering that the temperature of the output gas should not be less than 20 degrees, is continuously being heated and has no time delay. Additionally, t

_{Water}, which represents the time required to heat the water to the target temperature before the burner is turned off, is calculated as follows, considering the volume of the bath water and the difference between the desired temperature and the power of the burner:

^{3}and IRR 25 million at a gas mass flow rate of 60,000 SCMH.

## 4. Conclusions

^{3}/s) to 120,000 SCMH (33.33 m

^{3}/s), and by installing a regulator on the burner, gas consumption can be reduced.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**The thermophysical properties of the exhaust gas flow in the fire tube as a function of gas temperature: (

**a**) density, (

**b**) viscosity, (

**c**) heat capacity, and (

**d**) thermal conductivity [25].

**Figure 4.**Various views of the generated grid for the heater under study: (

**a**) shell, (

**b**) fire tube and gas tubes, (

**c**) close-up of gas tube, and (

**d**) different view of gas tubes.

**Figure 8.**The distribution of temperature in the various slices inside the shell: (

**a**) Slice 1, (

**b**) Slice 2, and (

**c**) Slice 3.

**Figure 9.**The distribution of velocity magnitude in the various slices inside the shell: (

**a**) Slice 1, (

**b**) Slice 2, (

**c**) and Slice 3.

**Figure 14.**The temperature distribution across the middle (X = 0) at various inlet mass flow rates: (

**a**) $\dot{\mathrm{m}}$ = 60,000 SCMH (16.67 m

^{3}/s), (

**b**) $\dot{\mathrm{m}}$ = 80,000 SCMH (22.22 m

^{3}/s), (

**c**) $\dot{\mathrm{m}}$ = 100,000 SCMH (27.78 m

^{3}/s), and (

**d**) $\dot{\mathrm{m}}$ = 120,000 SCMH (33.33 m

^{3}/s).

**Figure 16.**The streamline with the contour of velocity magnitude inside the water tank of the heater under study.

**Figure 17.**The iso-surfaces of velocity magnitude with various values inside the water tank of the heater under consideration.

**Figure 19.**The burner off time versus the gas mass flow rate needed to maintain a temperature of 20 degrees for the gas coil output.

**Figure 20.**The burner operation time elapsed before turning it off, after restarting it, and the duration of the burner operation at various gas mass flow rates.

**Figure 21.**(

**a**) The monthly reduction in gas consumption, and (

**b**) the economic savings at different gas mass flow rates in one month.

**Table 1.**Volumetric fraction of natural gas composition [24].

Name | Chemical Formula | Volume Percentage | ||
---|---|---|---|---|

Gas Analysis | Lower Limit | Higher Limit | ||

Methane | CH_{4} | 88.332 | 85 | 95 |

Ethan | C_{2}H_{6} | 4.672 | 2 | 9 |

Propane | C_{3}H_{8} | 4.137 | 0.5 | 3 |

Isobutene | C_{4}H_{10} | 0.484 | 0.2 | 0.3 |

Normal Butane | C_{4}H_{10} | 0.484 | 0.25 | 0.5 |

Isopentane | C_{5}H_{12} | 0.181 | 0.1 | 0.15 |

Normal Pentane | C_{5}H_{12} | 0.181 | 0.06 | 0.1 |

Carbon Dioxide | CO_{2} | 0.694 | 0.1 | 0.4 |

Nitrogen | N_{2} | 4.5 | 2 | 5.7 |

Sulfide | H_{2}S | 0.849 ppm | 1.25 | 6.25 |

Heavy/compound | - | 0 | 0.02 | 0.2 |

**Table 2.**The thermophysical properties of methane at T = 20 °C and P = 700 psi (4826.33 kPa) [25].

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

Density (kg.m^{−3}) | $\rho $ | 34.76 |

Specific Heat Capacity (kJ/(kg.K)) | C_{P} | 2.57 |

Dynamic Viscosity (Pa.s) | μ | 11.96 × 10^{−6} |

Static Viscosity (m^{2}/s) | υ | 0.344 × 10^{−6} |

**Table 3.**Composition of combustion exhaust gases [24].

Fuel Flow Rate (m^{3}/hr) | Carbon Monoxide (ppm) | Carbon Dioxide (ppm) | Nitrogen Oxides (ppm) | Oxygen (%) | Stack Temperature at Input Gate (°C) | Ambient Temperature (°C) | Combustion Efficiency (%) |
---|---|---|---|---|---|---|---|

102 | 81 | 4.14 | 22 | 13.69 | 274 | 8.4 | 73.35 |

111 | 284 | 5.63 | 25 | 11.60 | 314 | 9.7 | 76.55 |

180 | 202 | 7.92 | 39 | 7.20 | 412 | 9.7 | 76.54 |

186 | 301 | 8.14 | 37 | 6.64 | 407 | 9.7 | 77.33 |

192 | 159 | 7.52 | 33 | 7.73 | 427 | 9.5 | 74.56 |

204 | 111 | 8.41 | 42 | 6.16 | 437 | 1.1 | 76.31 |

228 | 44 | 8.36 | 47 | 6.25 | 455 | 0.8 | 75.11 |

252 | 32 | 8.89 | 57 | 5.31 | 488 | 9.8 | 74.61 |

Number | Grid Cell | The Outlet Temperature of the Methane (K) | Error (%) |
---|---|---|---|

1 | 3,708,213 | 313.2 | 0.45 |

2 | 4,777,825 | 314.68 | 0.022 |

3 | 6,210,401 | 314.61 | - |

Number | Mass Flow Rate (SCMH (m^{3}/s)) | Experimental Heater Outlet Temperature (°C) | Numerical Heater Outlet Temperature (°C) | Error (%) |
---|---|---|---|---|

1 | 80,000 (22.22) | 34.5 | 33.85 | 1.88 |

2 | 100,000 (27.78) | 30.1 | 29.15 | 3.15 |

3 | 120,000 (33.33) | 27 | 26.05 | 3.52 |

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**MDPI and ACS Style**

Kazemi Moghadam, H.; Mousavi Ajarostaghi, S.S.; Saffari Pour, M.; Akbary, M.
Numerical Evaluation of the Hydrothermal Process in a Water-Surrounded Heater of Natural Gas Pressure Reduction Plants. *Water* **2023**, *15*, 1469.
https://doi.org/10.3390/w15081469

**AMA Style**

Kazemi Moghadam H, Mousavi Ajarostaghi SS, Saffari Pour M, Akbary M.
Numerical Evaluation of the Hydrothermal Process in a Water-Surrounded Heater of Natural Gas Pressure Reduction Plants. *Water*. 2023; 15(8):1469.
https://doi.org/10.3390/w15081469

**Chicago/Turabian Style**

Kazemi Moghadam, Hamid, Seyed Soheil Mousavi Ajarostaghi, Mohsen Saffari Pour, and Mohsen Akbary.
2023. "Numerical Evaluation of the Hydrothermal Process in a Water-Surrounded Heater of Natural Gas Pressure Reduction Plants" *Water* 15, no. 8: 1469.
https://doi.org/10.3390/w15081469