Introduction

Town border stations (TBS) reduce the high pressure due to gas movement from the refinery to the consumption points inside the town. One of the most important parts of city gate station (CGS) is their preheating system. Hence, an indirect heating was used to supply the needed energy from high-quality refined gas. Heaters in natural gas gate stations as energy equipment in gas delivery industry are used in many countries including Iran. One of the main problems of these preheating systems is the low efficiency that causes high energy waste.

Therefore, improving the efficiency of these indirect heaters will have considerable implications for the consumption of natural gas. Owing to the high pressure of natural gas at the consumption points, the pressure should be reduced before consumption. This pressure reduction occurs at the CGSs. Pressure at CGSs is usually reduced to 1.5–2 MPa [1]. For positive Joule–Thomson effect on natural gas, pressure reduction leads to a drop in the natural gas temperature; the value of natural gas temperature should not be less than the minimum allowed value.

This temperature, called the temperature of hydrate formation, depends on the pressure and composition of natural gas. In fact, freezing water droplets suspended in natural gas occur in the hydrate formation area, blocking the pipeline transmission, especially in cold seasons. To prevent hydrate formation, natural gas flow should be heated up to a specific level before pressure reduction.

In general, line heaters in CGSs are used for preheating the natural gas flow with a lot of fuel consumption to supply the required heat. For this reason, the efficiency of CGSs is not at a satisfactory level. Not many studies have been carried out on the efficiency improvement in CGSs using combined cogeneration of heat, electricity, and expander turbines [2, 3]. One of such studies presents a new configuration, namely nanotechnology, to reduce fuel consumption at CGSs.

Nanofluid was used for the first time by Choi [4]. Subsequently, a lot of research was done to show nanofluids have a good potential for heat transfer applications [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Xuan and Li [21] experimentally investigated the convention heat transfer coefficient of nanofluid containing copper nanoparticles in laminar and turbulent flow in the tube. According to the their results, the heat transfer coefficient of nanofluid is greater than base fluid and the heat transfer process of nanofluid increases drastically with enhanced composition of nanoparticles. The dispersion of nanoparticles and the method for preparing fluids are important parameters for improving the efficiency of nanoparticles. Li and Xuan [22] observed higher Reynolds number and consequently a significant growth in the convention heat transfer coefficient of nanofluid than water at a volume concentration of 2% of water and copper oxide nanofluid. Base nanofluid ethylene glycol has been enhanced up to 35% with addition of 2% volume of copper oxide.

Farzaneh Gord et al. [23] conducted the first study on the effects of flat solar collectors on the supply of the required heat at CGSs. Farzaneh Gord et al. [24] attempted to install solar systems in Sari City, Iran, and presented a solar system to store the required heat by the solar collector and hot water storage during the day and use it overnight. The system consists of an array of 450 solar collectors, and the storage tank has a capacity of 45 cubic meters, which can store fuel consumption up to 11.3%. They changed the above system by including a further storage tank in the second study. Storage tanks in this configuration would collect the sun’s heat during the day and return to the heater at night, when more heat is needed. As a result, fuel consumption has been decreased by 14%, while in the first system only 11% reduction was observed. In the third study, Farzaneh Gord et al. [25] replaced the conventional linear heater at CGSs with an automatic controllable heater and compared the thermal behavior in this system with the mentioned systems. The result of this comparison shows the superiority of the last system in the two previous cases. In a new study conducted by Behseresht et al. [26], the migration effects of nanoparticles addressed by other researchers were discussed and the improper selection of dimensionless number range in previous studies was revealed. Regarding the proper range of dimensionless number, heat transfer is negligible due to the migration of nanoparticles. In another study, Noghreh Abadi et al. [27] showed that, although heat transfer caused by the migration of nanoparticles is negligible, nanoparticle slip in base fluid causes heterogeneity in the nanofluid. This heterogeneity changed the structural characteristics of Nanofluid, thereby affecting the convention heat transfer in nanofluids. Hossein et al. [28], in a numerical study on heat transfer and friction in an elliptical tube, with the addition of 0.25 and 1% volume of nano-titanium oxide with a diameter of 27–50 nm of particles, found an increase in heat transfer at a rate of 9% and friction coefficient at a rate of 6% compared to circular tubes. According to a study by Mahmoud et al. [29], the surface tension and heat transfer in static ethylene glycol fluid using iron oxide nanoparticles possess greater Nusselt number than water-based fluid. Despite sophisticated developments in the field of nanotechnology, the application of copper oxide nanoparticles in indirect heaters at CGSs has not been studied. This is the first research on the enhancement of heat transfer in indirect heaters at a CGS and the shortening of heater size and reduction in fuel consumption.

Indirect heaters at city gate stations

In winter, gas freezing occurs at CGSs due to pressure drop, blocking the gas passage. To prevent this, heaters are necessary to supply the required gas before gas pressure reduction [30].

During heating, direct heat transfer should not occur in the exchangers for reasons of safety. Water as a medium fluid should transfer the heat from the heating source to the gas pipe, and ethylene glycol is added to the water to prevent freezing in winter.

The reason for pressure reduction in the entrance pipe in cities is that after extraction gas is transmitted to the urban consumer with pressure of 1000 psi. This pressure is very high to be used by the consumer. Therefore, the gas pressure is reduced from 1000 psi to 250 psi at CGSs with the valve of a pressure regulator. Gas in the pipelines is exposed to pressure drop, which reduces the temperature. Owing to pressure reduction and reaching of the gas temperature to the dew point, the gas condensate comprising heavy hydrocarbons changes from the gas state to the liquid state, which turns it into ice in the cold season.

Heaters at CGSs are similar to shell and tube converters, as they are in the form of a horizontal cylindrical source with high volume and the volume is proportional to the thermal capacity of the heater. Pipe size is designed according to the volume of gas passing through the pipes. Gas is passed through these pipes and heated. In the shell part of the heater, there are water, i.e., ethylene glycol solution and fire tube. Water–ethylene glycol solution in the converter is an intermediate to transfer thermal energy from the warm fluid to cold fluid, and heat transfer mechanisms in these converters follow convection heat transfer [31].

There is no external factor in convention heat transfer and fluid motion only due to the influence of density. In convention heat transfer, fluid surrounds the heat source and receives heat. Thus, its density is lowered and replaced with cold fluid, and it is then heated and the cycle continues. This process transfers thermal energy from the hot fluid to the gas-passing pipe. Convection is a mechanism or a type of heat transfer where the fluid motion is transferred by the density difference in the fluid that is provided by the temperature gradient. In convection heat transfer, fluid velocity is very low, so the value of heat transfer is also very low [32].

The components of indirect heaters in a gas company (Fig. 1) are as follows:

Fig. 1
figure 1

Total scheme of indirect heater at a city gate station

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  • Cylindrical shell as the converter container

  • Spiral pipes of gas passing into the converter

  • Storage or expansion of water source

  • Burners

  • Chimney

  • Fire tube (fire warehouse)

  • Controlling systems for conducting the fuel to burners

Description of device testing

The laboratory device made (Fig. 2) for the heater test which is actually a closed-circuit system comprises a compressor, a pressure drop regulator valve, a cooling tank for returned water, accurate instruments such as a barometer, a flow meter, thermocouples, water–ethylene glycol solution, and copper oxide nanoparticles. Air compressor is used to create the necessary pressure instead of gas, and valve regulates the pressure drop. The cooling tank removes the heat of the hot water returned from the heater and transports it to the desired temperature. The flow meter sends the intended rate for testing with regulating the existing valve. In the shell part of the device, there are water–ethylene glycol and nanoparticles. The ratio of water to ethylene glycol is 50:50 at ambient temperature. However, in conducting the test, air is replaced by cold gas and necessary changes are applied regarding the rules of similarity and dimensional analysis [33, 34]. Thermocouples are located for measuring the inlet and outlet temperatures. The nanofluid’s motion due to embedded pump prevents the deposition of nanoparticles. In this test, CuO nanofluid is poured in the indirect heaters with fixed water–ethylene glycol base fluid in various concentrations.

Fig. 2
figure 2

a Scheme of laboratory system. b Laboratory-developed indirect heater

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Different parts of a laboratory-developed indirect heater are:

  • Converter shell

  • Converter tube (U-shaped) and inlet and outlet valves

  • Pump

  • Inlet and outlet pipes of the pump

  • Inlet and outlet valves of the pump

  • Device discharge valve

  • Heating element

  • Visiting gate

  • Accurate instruments such as a speedometer, barometer, and thermometer

A converter shell is a 15-L cylinder made of steel sheet with a diameter of 300 mm and a length of 80 cm. Complete specifications of the laboratory-made device are given in Table 1.

Table 1 Specifications of the laboratory-made device
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On the inlet and outlet surfaces of the pipe in the device, two 0.25-inch valves have been installed to change the amount of airflow at the exit and entrance of the device. The inlet air pressure and outlet air pressure of the device are 1.5 and 1 bar, respectively, and the device is adjusted using installed valves on the input and output surfaces of the pipe. It is noteworthy that the required air that is used as a gas substitute has been provided in the laboratory through a compressor with the pressure of 10 bar. One of the main tasks for the non-settling of the nanoparticles is performed by a pump having the capacity of 0.5 horsepower (SQ660 model), which gets the fluid from the bottom part of the shell and again pumps back to the shell. As seen in the figures, in the input and output parts of the pump, two 1-inch valves are installed. When the pump is not needed, we can close the valves and discharge the nanofluids from the heater tank.

Stabilizing the nanofluids

In this study, copper oxide particles with physical and thermophysical properties have been used as nanoparticles with a diameter of 40 nm and water–ethylene glycol at a ratio of 50:50 has been used as the base fluid (Table 2), while sodium dodecyl sulfate has been used as active surfactant (Table 3) for preparing the nanofluids.

Table 2 Physical properties of base fluid, air, and nanoparticles at ambient temperature
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Table 3 Specification of surfactant
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The size of the copper oxide nanofluids was evaluated using SEM and TEM images. As shown in Fig. 3, the copper oxide nanoparticles have a relatively spherical shape and a number of them have an agglomerate shape with an uneven surface. Both images show that the average diameter of particles is less than 100 nm. In order to ensure the stability of the nanofluids and the existence of the functional groups, copper oxide nanofluids have been evaluated using the FTIR spectrum of infrared spectroscopy, as Fig. 4 shows.

Fig. 3
figure 3

SEM and TEM images of copper oxide nanofluids

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Fig. 4
figure 4

FTIR spectrum of copper oxide nanofluids

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The concentration change in the surfactant and its effect on nanofluid sustainability, as well as the concentration of surfactant, sodium dodecyl sulfate used in nanofluids, and optimal weight conditions of 0.1% by PH = 7.8 have been selected. According to Fig. 5, the optimum conditions of the nanofluids are kept stable for at least 27 days; however, in the indirect heater system, they are circulated by a nanofluid pump and nanoparticle sedimentation is minimized.

Fig. 5
figure 5

Stability of nanoparticles in the base fluid. 1. After 7 days, 2. after 15 days, and 3. after 27 days

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Equations and calculations

To develop laboratory equipment, dimensionless quantity needs to be calculated [17, 18] using

$${\text{Dimensionless}}\; {\text{length}} = \frac{L}{D},\quad {\text{Dimensionless}}\;{\text{pressure}} = \frac{\Delta P}{{\rho v^{2} }} ,\quad Re = \frac{\rho vD}{\mu }.$$
(1)

dimensional and similarity analysis in the following manner.

In the above equations, L represents the length of the tube, D is the diameter of the inlet and outlet of the gas pipe, V is airflow velocity, μ is the viscosity of air, ρ is the density of air, and ΔP represents the air pressure difference. Convection heat transfer coefficient is defined using Eq. (2)

$$H = {\text{ }}\frac{{m\;cp\left( {\mathop T\limits^{.} - T_{1} } \right)}}{{A(T_{\text{W}} - T_{\text{m}} )}},$$
(2)

In this equation, m is the mass rate of the entered air and CP is specific heat, T0 and Ti are inlet and outlet air temperatures, respectively, and A is the lateral surface of the pipe. In order to calculate the properties of the base fluid in the indirect heater tank, the equations of density, viscosity, specific heat, and base fluid conductivity coefficient, i.e., the identical mixture of water and ethylene glycol (50:50) at different temperatures derived by Eqs. (3)–(6), have been used [35, 36].

$$\rho_{\text{bf}} = - 0.002475T^{2} + 0.9998T + 1002.5,$$
(3)
$$\mu_{\text{bf}} = 0.001 \times \exp \left( {3135.6 \times \frac{1}{T} - 8.9367} \right),$$
(4)
$$C_{\text{Pbf}} = 4.248T + 1882.4,$$
(5)
$$K_{\text{bf}} = - 0.1054 + 0.0025T - 3.196 \times 10^{ - 6} \times T^{2} .$$
(6)

Equations (7)–(9) show how the properties of the copper oxide nanofluid have been calculated. The density and specific heat capacity are calculated using Pak and Cho equations [37]:

Nanofluid viscosity is calculated using the Brinkman equation [38] as follows:

$$\rho_{\text{nf}} = \left( {1 - \varphi } \right)\rho_{\text{bf}} + \varphi \rho_{\text{p}} ,$$
(7)
$$c_{\text{p,nf}} = \frac{{\left( {1 - \varphi } \right)\rho_{\text{bf}} C_{\text{p,bf}} + \varphi \rho_{\text{p}} C_{\text{p,p}} }}{{\rho_{\text{nf}} }},$$
(8)
$$\mu_{\text{nf}} = \mu_{\text{bf}} \frac{{ \mu_{\text{bf}} }}{{ \left( {1 - \varphi } \right)^{2.5} }},$$
(9)

Nanofluid thermal conductivity coefficient is obtained using the Yu and Choi equation derived by modified Maxwell’s equation [39]:

$$K_{\text{nf}} = K_{\text{bf}} \left[ {\frac{{K_{\text{p}} + 2K_{\text{bf}} - 2\varphi \left( {K_{\text{bf}} - K_{\text{P}} } \right)}}{{K_{\text{p}} + 2K_{\text{bf}} - \varphi \left( {K_{\text{bf}} - K_{\text{p}} } \right)}}} \right].$$
(10)

To calculate Nusselt theory, the Dittos-Bolter Eq. (11) has been used [40].

$$N_{\text{u}} = 0.0243Re^{0.8} Pr^{0.4} .$$
(11)

Results and discussion

In this section, the data obtained from the tests are presented in tables and diagrams. First, Table 4 presents the obtained values of indirect heaters in the absence of nanoparticles in water–ethylene glycol base fluid (W/EG) with equal ratio (50:50). In the next steps, copper oxide nanoparticles are added to the base fluid in volume fractions of 0.025, 0.05, 0.1, 0.2, and 0.3, and some changes are created in the nanofluid and air. Consequently, based on these changes, the amount of heat transfer is recorded.

Table 4 Obtained values for base fluid and air temperature in the laboratory-developed heater
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In Figs. 6 and 7, the viscosity of the nanofluid at different temperatures and volume fractions is presented. Comparisons in the diagrams show that the higher the temperature of the nanofluid, the less the viscosity; however, with increasing volume fraction of nanoparticles, the nanofluid’s viscosity increases as well. The highest nanofluid viscosity is reached in the highest volume fraction and the lowest temperature in the indirect heater tank.

Fig. 6
figure 6

Viscosity of nanofluids at different temperatures and volume fractions

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Fig. 7
figure 7

Ratio of the viscosity of nanofluid to the viscosity of base fluid at different volume fractions of nanoparticles

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Figure 8 shows the density of the nanofluid at different temperatures and volume fractions. Comparisons of diagrams show that, with increasing temperature, the density has not changed, but with increasing volume of the nanoparticles, the nanofluid’s density has increased. The maximum density in the highest volume fraction and at maximum temperature does not affect the nanofluid’s density.

Fig. 8
figure 8

Density of nanofluids at different temperatures and volume fractions

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Figure 9 shows the specific thermal capacity of the nanofluid at different temperatures and volume fractions. The comparisons of diagrams show that higher temperature of the nanofluid does not affect the specific thermal capacity and that with, increasing volume fraction of the nanoparticles, the nanofluid’s specific thermal capacity has decreased. Therefore, the maximum specific thermal capacity is observed in the lowest volume fraction.

Fig. 9
figure 9

Specific thermal capacity of nanofluids at different temperatures and volume fractions

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In Figs. 10 and 11, the temperature difference has been initially increased for the increased volume fraction of the copper oxide nanoparticles at different temperatures of the heater tank. After that, this difference will be higher at the volume fraction of 0.2 and 0.3% with an increase in temperature. At 35 °C above, the highest temperature difference is observed in 0.2% volume fraction, and the results of the present study are consistent with the study of Li and Xuan [22].

Fig. 10
figure 10

Difference between inlet and outlet temperatures of air at different temperatures and volume fractions of nanofluids

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Fig. 11
figure 11

Obtained air temperature differences at different volume fractions of nanofluids

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As shown in Figs. 12 and 13, increased conductivity coefficient of the nanofluid as a factor in increasing air (gas) transfer in the indirect heater is one of the objectives of this study. This factor increases to 0.2% with a higher volume fraction of the nanoparticles and reaches 33%, leading to increased air temperature or outlet gas in the pipe.

Fig. 12
figure 12

Thermal conductivity coefficient ratio to copper oxide nanoparticle volume fraction

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Fig. 13
figure 13

Nanofluid temperature difference in different volume fractions with increasing temperature in the heater tank

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The highest temperature difference in volume fraction of 0.2 and tank’s temperature of 70 °C was 43 °C, while, the obtained highest temperature difference is equal to 25 °C in the absence of nanoparticles. In other words, the temperature difference has been increasing at a rate of 43% with the addition of 0.2% volume fraction of copper oxide nanoparticles in indirect heater in this experimental study.

$$\left( {\frac{{\Delta T_{\text{O}} - \Delta T_{\text{i}} }}{{\Delta T_{\text{i}} }}} \right) \times 100 \approx 36\%$$
(12)

The pump used in the laboratory system for recirculation of the fluid flow causes the non-settling of the nanoparticles in addition to chaotic and random movement of the nanoparticles within the fluid flow. Hence, the conduction heat transfer coefficient is increased and greater convection coefficient is obtained. This result been obtained by several research groups such as Ding et al. [41] and Hay et al. [42] in their attempt to justify the increased heat transfer in the presence of nanoparticles.

In general, with the addition of nanoparticles to the base fluid, the flow structure is changed in a way that, besides increasing the thermal conductivity such as chaotic and random movements, dispersion of suspended nanoparticles leads to turbulence in the nanoparticles, and consequently the rate of energy exchange, heat transfer of the fluid and the pipe wall, and the temperature of the gas inside the pipe are increased [43, 44]. Increasing the volume concentration of nanoparticles increases the interactions and collisions between the nanoparticles.

Moreover, the pump causes relative motion in the tank and the permeability of nanoparticles near the wall, leading to faster heat transfer from the nanoparticles to the wall of the pipe and air (gas) compressible fluid inside the pipe. In the other words, increasing the volume concentration of the nanoparticles intensifies the mechanisms associated with increased heat transfer in air or gas.

To calculate the convection heat coefficient, passing air or gas in laboratory devices from sweep pipes within tank, physical and thermodynamic properties and the average inlet and outlet temperatures of the laboratory indirect heater and relocation convection coefficient relations in theory and experimentally can be obtained. With increasing temperature in gases, density decreases, the viscosity coefficient increases, and the air convection coefficient increases, while with an increase in the Nusselt number, the convection coefficient increases as well. As has been shown, with an increase in the convection coefficient, the Nusselt number is also increased. According to Fig. 14 that is drawn for \(\frac{Nu}{Pr^{0.4}}\) to Reynolds number Re in linear equation and with Dittos-Bolter [40] equation for the larger width of the Reynolds numbers can be used for air with Pr = 0.72 that with difference of 25–30% error for each of the equations and with practical Nusselt is comparable.

Fig. 14
figure 14

\(\frac{Nu}{Pr^{0.4}}\) to the Reynolds number for heating and cooling of passing air through the heat pipe

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Experimental error

The uncertainties of the tests in the process of heat transfer are defined by experimental error, calculation error, and precision of measuring devices in line with Kolmogorov and the uncertainty standards [45, 46]. The resulting maximum error by the flow meter is ± 0.000016 m3/s, and temperature sensors are ± 0.1 °C. The measurement temperature error, flow rate, and the measurement related to the diameter of the pipe in the heat transfer coefficient were calculated on the basis of the Kline–McClintock error theory [47], and its maximum value was 3.22%. Regarding the random errors, errors of measurement device, and errors of heat loss from the tank to the ambience, the maximum error in the calculation of the heat transfer coefficient was equal to 19.24%.

Conclusions

In this study, temperature difference improvement in the presence of nano-copper oxide and water–ethylene glycol (50:50) has been investigated empirically in a laboratory-developed indirect heater for increasing the heat transfer and heating of cold gas (air) in the indirect heater at CGSs, thus increasing the overall heat transfer coefficients of base fluids. All these properties shrink the volume of the heater, which will be very cost-effective in the future.

On the whole, increasing nanofluids’ thermal conductivity coefficient depends on the volume of the particles, size, and shape of the nanoparticles, the type of the base fluid, and the nanoparticles. Conduction and convection heat transfer coefficients can be increased significantly with the addition of small amounts of copper oxide nanoparticles to water–ethylene glycol base fluid. In the present study, as the experimental data show, the following results have been obtained at volume fractions of 0.025, 0.05, 0.1, 0.2 and 0.3, and diameter of 40 nm in temperatures of 40, 50, 60 and 70 °C:

  1. 1.

    We observed 36% growth as the highest temperature difference of the air outlet (gas), which is considered one of the most important parameters in volume fraction of 0.2 and temperature of 70 °C.

  2. 2.

    The nanofluid thermal conductivity coefficient increased to the base fluid (knf/kbf) with increasing temperature and volume fraction, and in volume fraction of 0.2% and at a temperature of 70 °C, 36% more increase in air temperature (gas) output was observed in the indirect heater.

  3. 3.

    The ratio of theoretical Nusselt to experimental had a difference less than 30%, which was due to the absence of any effect of some physical properties on the convection heat transfer coefficient.

  4. 4.

    The results showed that due to prevailing operating conditions in the indirect heater system at CGSs, the use of copper oxide nanoparticles in the base fluid to create the temperature difference of 15–20 °C in the output of pipe for gas compressible fluid is very appropriate and has relatively good and satisfactory consistency with the theoretical discussions.