Studies of methyldiethanolamine process simulation and parameters optimization for high-sulfur gas sweetening

Journal of Natural Gas Science and Engineering 21 (2014) 379e385

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Studies of methyldiethanolamine process simulation and parameters optimization for high-sulfur gas sweetening K. Qiu a, *, J.F. Shang b, M. Ozturk c, T.F. Li a, S.K. Chen a, L.Y. Zhang a, X.H. Gu a a

School of Chemistry and Chemical Engineering, Chongqing University of Science and Technology, Chongqing, China Puguang Branch of Zhongyuan Oilfield Company, SINOPEC, Dazhou, Sichuan, China c School of Chemical, Biological and Materials Engineering, The University of Oklahoma, Norman, USA b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 4 May 2014 Received in revised form 28 August 2014 Accepted 30 August 2014 Available online

The energy consumption of high-sulfur gas sweetening was significantly higher than conventional gas, in order to save energy, a novel Methyldiethanolamine (MDEA) modified process is discussed in this paper. The law of operating conditions' impact on gas sweetening efficiency and economic benefits has been obtained by using process simulation and optimization. The results showed that the maximization of the treated gas yield should be selected as the optimization objective of gas sweetening rather than the minimization of the operating costs. This will enable improvement of the economic efficiency of the gas processing. © 2014 Elsevier B.V. All rights reserved.

Keywords: Gas sweetening Simulation Optimization Amine solution Energy

1. Introduction Sour gas typically contains H2S and CO2, which are toxic, corrosive and prone to cause environmental pollution after burning. Therefore, these acid components must be removed. When H2S and CO2 exist in natural gas simultaneously, H2S can be selectively removed from the gas with a maximum retention of CO2 by Methyldiethanolamine (MDEA). This feature meets the development trends of saving energy in gas processing. MDEA is not only used in general gas sweetening but also in high-sulfur gas (HSG). Although some processes have been applied in HSG sweetening such as mixed amines (Sohbi et al., 2007), DEA (Total Company, 2007), Sulfinol (Palla et al., 1998) and MDEA (Qiu et al., 2013), more and more cases (Amiri et al., 2008; Sourisseau et al., 2007) have indicated the MDEA process is rather favored in this field. The concentration of acid species in HSG is several times higher than in general gas, which leads to a dramatic increase of operating costs and energy in process (Bae et al., 2011; Banat et al., 2014). Moreover, the quantity of treated gas significantly decreases compared to feed gas. The operating conditions are obviously the main factors affecting inherent economic benefits with regard to an existing sweetening unit (Lunsford, 1996).

* Corresponding author. Tel.: þ86 2365023762. E-mail addresses: [email protected], [email protected] (K. Qiu). http://dx.doi.org/10.1016/j.jngse.2014.08.023 1875-5100/© 2014 Elsevier B.V. All rights reserved.

Many authors have concluded that selective amines absorb H2S more than CO2 due to the differences in solubility, rates of reaction, or a combination of the two (Huttenhuis et al., 2007; Pacheco and Rochelle, 1998). The reaction between H2S and MDEA is an instantaneous proton transfer reaction, but the reaction between CO2 and MDEA is a pseudo-first-order reaction. The differences in reaction rates lead to selective absorption. Huttenhuis et al. (2009) studied the solubility of CO2 and H2S in aqueous MDEA, and concluded that the H2S partial pressure increased significantly with increasing CO2 liquid loading. The type of inert gas (N2 or CH4) did influence the H2S solubility rather than CO2. Calculations with the E-EOS model showed that the fugacity coefficient of H2S is more sensitive to an increase in CH4 partial pressure than the fugacity coefficient of CO2. Denny (1994) found that additional trays may actually increase H2S concentration in the sweetened gas due to CO2 absorption. Apparently, adding more trays allows more CO2 to be absorbed which tends to displace the H2S. MaxwelleStefan and enhancement factor theories were utilized by Pacheco and Rochelle (1998) to prove that trayed columns are more selective than packed columns for H2S removal, primarily because of the greater number of liquid-film mass transfer units. By increasing the pressure, the driving forces for the H2S and CO2 absorption become larger, whereas the mass transfer coefficients and interfacial areas decrease because of the lower volumetric gas throughout. Moreover, the gas phase diffusivities

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decrease and hence the gas phase mass transfer coefficients also decrease (Blauwhoff et al., 1985). The acid gas loadings of lean and rich amine solvents and the total amine concentration significantly impact selectivity and circulation rates. Energy in sweetening units is generally made up of a steam reboiler, electricity, and cooling water. Bae et al. (2011) reported reboiler productivity will increase with the increased concentration of H2S and CO2. Very few of these recent studies mention process simulators in amine units' optimization. An optimization analysis may include looking at alternative amines, the number of trays in the absorber, or the regenerator reboiler duty (Abry and Dupart, 1995). Unfortunately, obtaining plant information for other amines, or more equilibrium stages is next to impossible in an operating facility. However, these conditions can be studied easily via process simulation. An optimization study have concluded that if the objective is to slip as much CO2 as possible, we should consider using the most selective amine at the lowest concentration and circulation rates with the fewest number of equilibrium stages in the absorber to achieve the H2S specification. Cold absorption temperatures tend to increase the CO2 slip and enhance H2S pickup. Increasing the lean amine temperature increases CO2 pickup for the selective amines up to a point. The maximum temperature depends on amine concentration, inlet gas composition, and loading (Lunsford, 1996). The goal of sweetening is to produce cost-effective gas. Operating costs or energy usually are taken as optimization goals in process analysis (Hatcher et al., 2012; Ahmad et al., 2012). Patil et al. (2006) used the simulated annealing approach to study process optimization, and operating costs were the optimization objective in that study. The result is the generated design which is costeffective and practical. In recent years there have been few reported studies on the optimization of operating conditions in HSG sweetening. Therefore, research on the effects of operating conditions on sweetening performance will improve the economic benefits of gas sweetening. Aspen Plus is used in this study for process simulation and optimization. 2. Simulation and optimization depiction 2.1. Process simulation The composition of feed gas is (mol%): CH4 74.29, C2H6 0.02, H2S 16.93, CO2 8.26, COS 0.0129, He 0.01, N2 0.4771. The quality of the treated gas meets the specification of: total S  100 mg/m3, H2S  6 mg/m3 and CO2  3 (mol%). The flowsheet model of MDEA process is described in Fig. 1. Feed gas flow into the first absorber T-1, most of the H2S and CO2 is absorbed by MDEA solution. The gas enters the hydrolysis reactor R-1 after heating by exchangers HX-5 and HX-6, COS is catalytically converted into H2S. Then gas flows into the second absorber T-2 after cooling, all the H2S and most of the CO2 is removed in this tower, the treated gas is obtained at the top of T-2. All the H2S and some of the CO2 is removed through the absorption of lean amine solution in T-2, the resulting semi-rich solution flows into T-1 to remove a large number of H2S and CO2 from gas. Some dissolved hydrocarbon gas will be flashed off from the amine when rich solution flows into flash drum via reducing pressure. The rich solution enters the stripper T-3 after heating, a lot of acid gas obtained from above the stripper flows to the sulfur recovery unit. Lean solution obtained from the bottom of the stripper is re-circulated back to T-2 after cooling and increasing pressure. The main operating parameters are absorption pressure (8 MPa), absorption temperature (40  C), feed gas flow rate (5202 kmol/h),

amine circulation rate (21,000 kmol/h), tray number of absorber (18) (tray numbers can be adjusted from 10~18 by selecting different inlet), tray number of stripper (20), regeneration temperature 128  C, MDEA concentration 50 wt%, liquid loading 0.55 mol/mol. KMDEA data packet of the Aspen Plus V7.1 is employed in the studies. The Electrolyte-NRTL model is applied in the calculation of the non-ideal solution, and the PengeRobinson equation is applied in the calculation of the PVT properties of gas. Removal of acid gases from feed gas is typically accomplished by physico-chemical absorption into MDEA solutions. Huttenhuis et al. (2009) listed the reactions. The effects of operating conditions on important economic and technical indicators such as purification efficiency, sweetening selectivity, and energy can be analyzed by using this process model, which will provide a reference for the process optimization.

2.2. Optimization methods 2.2.1. Objective functions The purpose of optimization in HSG sweetening is not only to maximize the output of gas but also to minimize energy as well as operating costs, resulting in the best economic benefits. Decreasing absorption pressure and the number of trays will significantly reduce the absorption of CO2 into the MDEA solution and the dissolution of hydrocarbons. Not only does the selective absorption improve, but the output of gas increases as well (Pacheco and Rochelle, 1998). Based on the analysis of energy in gas sweetening, Blauwhoff et al. (1985) indicated the reboiler energy of the stripper accounts for a significant proportion in the amine unit. The lower the circulation rate, the lower the reboiler energy. The usual practice of decreasing the circulation rate is to improve the concentration of the amine solution and absorption pressure, or increase the number of trays. The operating costs of process depend largely on utilities such as steam, electricity, and circulating water. As the circulation rate increases, the energy of utilities increases, and operating costs will likewise increase (Bullin et al., 1981). As seen from the above analysis, it's always contradictory to maximize the output of gas and simultaneously minimize energy and operating costs, thereby annual profits (AP) is selected as the optimization goal for the process, and the expressions are as follows:

Object :

max AP ¼ Is  Zs  Co

(1)

hðx; yÞ ¼ 0

(2)

l  gðx; yÞ  u

(3)

with Is, Zc, and Co the costs of gas sales, fixed investment and annual operating costs respectively; h(x, y) the series of equations of equality constraints; g(x, y) the equations of inequality constraints; l and u are the boundary conditions of decision variables.

Is ¼ 330Fpro Cpro

(4)

Zc ¼ Z1 þ Z2 þ Z3

(5)

Co ¼

X

CP;i þ

X

CE;i þ

X

CH;i

(6)

With Fpro the output of gas, Cpro the price of gas; Z1, Z2 and Z3 the fixed-asset investment, costs for equipment maintenance, labor costs respectively; operating costs Co is mainly embodied in the utilities costs of the process. In equation (6), Co consists of three

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381

Treated gas Acid gas

Feed gas

Fig. 1. Flowsheet model for MDEA process. 1 Hydrolysis reactor inlet separator; 2 Hydrolysis reactor preheater; 3 Hydrolysis reactor; 4 Hydrolysis feed/Effluent exchanger; 5 Hydrolysis reactor after cooler; 6 Second absorber; 7 First absorber; 8 Lean amine pump; 9 Interstage pump; 10 Interstage cooler; 11 Amine trim cooler; 12 Stripper; 13 Stripper condenser; 14 Stripper reflux drum; 15 Stripper reflux pump; 16 Lean amine booster pump; 17 Lean/rich exchanger; 18 Lean amine cooler; 19 Amine flash drum.

costs: operating costs for pumps and fans CP, coolers CE and steam heaters CH. Each item is calculated as follows:

X

CP;i ¼ CP;5 þ CP;8 þ CP;9 þ CP;13 þ CP;15 þ CP;16 þ CP;18

 CP;i ¼ 9000  24  330bi EP;i 1000 X

CE;i ¼ CE;10 þ CE;11

 CE;i ¼ 9000  24  330bi EE;i ½1000ai ðtout  tin Þ X

CH;i ¼CH;2 þ CH;12

 CH;i ¼ 9000  24  330bi EH;i ð1000ai hÞ

(7) (8) (9) (10) (11) (12)

where EP,i, EE,i and EH,i are energy of pumps and fans, coolers and steam heaters respectively; the values of ai, bi are shown in Table 1. These energy data can be obtained directly from the simulation results. h is set from 0.75 to 0.80. From formula (1), the AP of process depends on three variables: Is, Co, and Zc. Zc are usually regarded as a fixed value during a long period of time. Is depends on the price and quantity of treated gas. Setting the gas price as a fixed value, gas output will affect the AP. The concentration of acid species in HSG is much higher than general gas, and the output of treated gas is significantly less than the feed gas after treatment. Therefore, obtaining treated gas as much as possible is one of the most important means to improve the AP. However, this will be affected by operating conditions. In the case of determining Zc, Fpro, and Cpro, Co is closely related to the operating conditions, which is the main factor affecting AP in amine units.

2.2.2. Parameters and economic data settings In order to conveniently convert various energy transfer mediums into the operating costs, the equivalent coefficient of energy transfer medium for conversion is adopted (Sinopec, 2007), and shown in Table 1.

Economic data in the optimization have made the following assumptions: a plant operates 330 days a year, average fixed assets investment is 8.40  106 RMB/a; equipment maintenance cost is 6.30  106 RMB/a; labor cost is 7.0  105 RMB/a; product gas is 1.40 RMB/m3; circulating water (tout  tin) is 7  C; gasoline is 9000 RMB/t. The price of standard oil can be calculated on the basis of the price of gasoline releasing the same calorific value. 2.2.3. Manipulated variables selection Through a preliminary simulation, we found that the most important key factors are absorption temperature, pressure, number of trays, and circulation rates that affect the purification efficiency, energy, and operating costs (Blauwhoff et al., 1985; Qiu et al., 2012; Qiu et al., 2013). 2.2.4. Initial value of manipulated variables The initial value of manipulated variables is set as follows: absorption temperature is 40  C, pressure is 8 MPa, circulation rate is 21,000 kmol/h, the number of trays is 18, and the reboiler energy is 1.31  105 MJ/h. 2.2.5. Constraint conditions MESH equation is employed to describe the material and energy balance in the process (Xiao et al., 1989). Inequality constraints include H2S  6 mg/m3, CO2  3% (mol%). The range of manipulated variables are absorption temperatures 30e45  C, absorption Table 1 Equivalent coefficient of energy transfer medium. Energy transfer medium

Units

Equivalent coefficient of energy conversion (ai), MJ

Equivalent coefficient of energy consumption (bi), kga

Power Circulating water 0.45 MPa steam 3.5 MPa steam Standard oil Gasoline

kW h t t t t t

10.89 4.19 2857 3684 41,848 43,124

0.26 0.10 68 88 1000 1030

a

Standard oil.

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pressures 5e9 MPa, tray numbers of absorber 10e18, circulation rates 14,000e30,000 kmol/h. 3. Results and discussion The calculation is not easy to converge whenever four manipulated variables are simultaneously optimized. Therefore, reducing the manipulated variables appropriately will improve the speed of convergence. From the analysis of the simulation, we found that the absorption temperature has little impact on the purification efficiency and selectivity. Therefore, the absorption temperature is set at 40  C and the optimization of other operating conditions is analyzed at this temperature. 3.1. The effects of tray number and pressure on circulation rate Energy is the main factor affecting AP in the process. However, the circulation rate has the greatest influence on this process. If we treat the quality of treated gas as a constraint condition, and adjust the absorption pressure and tray number, the variation of circulation rates can be observed in Fig. 2. As Fig. 2 shows, the higher the absorption pressure, the lower the circulation rate. The reason is that the acid gas loading of the MDEA solution will increase as the absorption pressure increases. Therefore, the required circulation rate will decrease accordingly as the purification efficiency is achieved, which is conducive to reducing the energy of the process. With fewer trays, the acid gas loading of the solution is lower due to fewer chances of gaseliquid contact. To meet the strict specification of H2S in treated gas, a greater circulation rate for sweetening is necessary, especially absorption below 7 MPa. Therefore, in order to save operating costs, the process should run at lower circulation rates and use more trays. 3.2. The effects of tray number and pressure on the output of treated gas For HSG, the output of treated gas is significantly lower than the flow rate of feed gas, the operating conditions tend to have a great impact on the output of treated gas. By adjusting the tray number and pressure of absorption, the variation in the output of treated gas can be perceived in Fig. 3. The higher the absorption pressure, the lower the output of treated gas compared to the same tray number. The reason for this

Fig. 2. Effects of tray number and pressure on circulation rate.

Fig. 3. Effects of tray number and pressure on flow rate of treated gas.

is the solubility characteristic of CO2 and hydrocarbon in MDEA solution is a physical dissolution (Huttenhuis et al., 2009). Therefore, it is beneficial to reduce the absorption of CO2 and hydrocarbons into MDEA at low pressure so that the sweetening selectivity improves and the output of treated gas also rises. When the tray number is no more than 12, to meet the specifications of H2S, a greater circulation rate is needed. Therefore, a large amount of CO2 and hydrocarbon dissolved in the MDEA solution, which decreases the output of treated gas. Once the tray number increases, the gaseliquid contact becomes more adequate, and the purification efficiency is also improved. The gas specifications can still be satisfied in the case of a sharp decrease in circulation rate. Meanwhile, the total quantity of CO2 and hydrocarbon absorbed in the MDEA decreases as well. As mentioned above, we should obtain more treated gas at low pressure in sweetening. In addition, as long as the tray number is more than 13, adding trays will have little impact on the output of treated gas.

3.3. The effects of tray number and pressure on energy The variation of energy in the process can be observed by changing the absorption pressure and tray number. The results are shown in Fig. 4.

Fig. 4. Effects of tray number and pressure on energy.

K. Qiu et al. / Journal of Natural Gas Science and Engineering 21 (2014) 379e385

383

Table 3 Comparison of field data and theoretical optimization results. CO2 in H2S in Selectivity Flash gas Treated gas Circulation outlet outlet (%) (%) (kmol/h) (kmol/h) rate (mg/m3) (kmol/h)

Items

Field data 3.68 Theoretical 5.94 optimal

1.28 0.96

70.81 69.87

72.33 185.93

3884.40 3753.88

21,000 19,073

Further calculation shows the energy of the reboiler accounts for 70.90% of the total energy in the process, which coincides with the result of Blauwhoff et al. (1985). Therefore, circulation rate is the key factor affecting the process energy.

3.4. The effects of tray number and pressure on AP Fig. 5. Composition of energy in sweetening units.

Fig. 6. The effects of operating conditions on the AP.

As Fig. 4 shows, the energy of sweetening in high pressure is less than that of low pressure. It is mainly because the former increases the acid gas loading of MDEA solution, which is conducive to reducing the circulation rate, thereby reducing the energy of process. As the tray number increases, the purification efficiency of gas improves. Circulation rate and energy of sweetening can be reduced accordingly under a certain absorption pressure. The energy is rather high when using no more than 12 trays in absorption, which is due to a greater circulation rate. With more than 12 trays, the circulation rate will decline slowly with the increasing number of trays, and energy slowly decreases as well. According to the analysis of energy in Fig. 5, steam accounts for 73.26% of the total energy, while cool water accounts for 20.30%.

According to simulation data obtained from Aspen, the law of operating conditions' impact on AP can be calculated and drawn by using the formulas (1)e(12). Results are as shown in Fig. 6. Fig. 6 shows that under the same pressure, the AP increases with an increase in tray number. This is because adding more trays leads to an improvement in the purification efficiency. Moreover, the circulation rate and operating costs decrease, energy likewise declines, thus the AP can be improved. The greater the pressure, the higher the AP. Therefore, to maximize the AP of the process, it is preferable to operate the sweetening process at high pressure, meanwhile more trays should be adopted in the operation. The operating conditions and economic data of the process correspond to the maximum AP which is shown in Table 2. Because the operating costs account for nearly 40% of the income sales, reducing those costs is an important way to improve AP, and is therefore an essential practice for chemical plants. Based on the analysis of the above data, it can also be found that when the AP of the process reaches its maximum, sweetening selectivity (Blauwhoff et al., 1985) is only 69.87%. As previously mentioned, the amount of CO2 and hydrocarbons dissolved in the solution will increase if the absorption is at high pressure, which will not enable the output of treated gas to reach its maximum. However, this is an inevitable choice in order to maximize the AP.

3.5. Comparison of field data and theoretical optimization results The comparison of field data and theoretical optimization results are shown in Table 3. Obviously, it can be seen that the field data is better than the theoretical optimization data. Because increasing the tray number and pressure to reduce the circulation rate can reduce the operating costs and improve the AP. Taking the above optimization strategy will decrease the sweetening selectivity and output of treated gas. However, because of the high pressure in absorption, the flow rate of flash gas is larger than usual. Therefore, it is necessary to reexamine the optimization strategy in the actual production.

Table 2 Operating conditions and economic data corresponding to maximum AP. Operating conditions

Absorber temperature ( C)

Absorber pressure (MPa)

Number of trays (blocks)

Circulation rate (kmol/h)

Reboiler energy (MJ/h)

e

Data

40

8

18

19,073

130,200

e

Economic indicators

Treated gas (kmol/h)

Selectivity (%)

Operating costs (108RMB/a)

Sales income (108RMB/a)

Fixed investment (108RMB/a)

Annual profits (108RMB/a)

Data

3753.88

69.87

3.99

10.03

0.154

5.88

384

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Table 4 Optimal operating conditions and economic data based on the maximized output of treated gas. Operating conditions

Absorber temperature ( C)

Absorber pressure (MPa)

Absorber trays (block)

Circulation rate (kmol/h)

Reboiler energy (MJ/h)

e

Data

40

7

14

27,803

187,260

e

Economic data

Treated gas (kmol/h)

Selectivity (%)

Operating costs (108RMB/a)

Sales income (108RMB/a)

Fixed investment (108RMB/a)

Annual profits (108RMB/a)

Data

3961.36

71.98

1.54

10.48

0.154

8.79

Table 5 Comparison of actual operating data and optimal data by simulation. Items

H2S in outlet (mg/m3)

CO2 in outlet (%)

Selectivity (%)

Flash gas (kmol/h)

Treated gas (kmol/h)

Circulation rate (kmol/h)

Actual data Simulated data

4.92 5.98

1.52 1.67

71.53 71.98

29.13 17.06

3936.41 3961.36

26,749 27,803

The output of acid gas desorbed from the stripper in HSG sweetening units is significantly higher than that of general gas. The acid gas flows into sulfur recovery units and reacts with O2. This exothermic reaction will produce a considerably large byproductd3.5 MPa and 0.5 MPa steam. Besides, SCOT tail gas units and utilities produce a certain amount of steam. Total steam approaches 100 t/h. However, the steam consumption of the reboiler is 52 t/h and the hydrolysis reactor preheater is 1.52 t/h. In conclusion, steam used by the purification plant mainly relies on the steam byproduct derived from the process device. So, the steam consumed by sweetening units can be approximately considered as zero cost, and there is some surplus steam that can be used. 3.6. The optimization strategy for sweetening process As can be seen from Fig. 3, although lowering pressure and the number of trays will appropriately increase circulation rate, sweetening selectivity and output of treated gas will rise. The increased circulation rate brings an increase in the heating load of the reboiler which doesn't lead to a significant improvement in operating costs. Based on this, optimization goals can be modified to maximize the output of treated gas. According to the calculation of AP, it should merely set the operating costs of steam for the reboiler and hydrolysis reactor preheater at approximately zero. The optimal operating conditions corresponding to the largest output of treated gas can be achieved. According to Fig. 3, optimal conditions should ensure the largest output of treated gas and a relatively low circulation rate. The optimal data for process simulation is seen in Table 4. The HSG purification plant has adjusted the process parameters according to the optimization strategydmaximized output of treated gas. The comparison of actual operating data and optimal data by simulation is shown in Table 5. Tables 4 and 5 show that the sweetening selectivity and output of treated gas were further improved, the flow rate of flash gas decreased when purification plants adopted the optimization strategy. The increased energy caused by the increase of circulation rate comes mainly from the steam energy, which increases about 40%. While surplus steam is available in plants, the increased energy is acceptable. The output growth of treated gas will eventually result in an increase of AP. 4. Conclusions To guarantee a rigorous purification target, a greater circulation rate must be achieved in a high-sulfur gas sweetening, which obviously causes energy to surpass that of general gas sweetening.

By setting AP as the optimization goal, we found that improving absorption pressure and tray number will significantly reduce circulation rate. Energy and operating costs reach their minimum value, while the AP simultaneously reach maximum value. The reasons for this phenomenon are that the operating costs of process account for a large proportion of income sales of treated gas; by lowering the operating costs, the best AP can be achieved. When sweetening under conditions of high pressure and many trays, CO2 and hydrocarbons will be absorbed excessively by MDEA solutions, and the output of treated gas will decrease significantly. Considering that there is surplus steam which can be used in purification plants, increasing the circulation rate appropriately can reduce both the absorption pressure and tray numbers while still meeting the gas specifications. Thus, the cost of increased energy is acceptable. Such operating conditions can reduce the absorption of CO2 and hydrocarbons by MDEA solution, and the output of treated gas will increase significantly. Therefore, the economic benefits of gas processing will be improved. Acknowledgement This project is supported by National Science and Technology Major Project of the Ministry of Science and Technology of China (Grant No. 2011ZX05017-005). Symbols used ai [MJ] Equivalent coefficient of energy conversion AP [RMB/a] Annual profits bi [kg] Equivalent coefficient of energy consumption CE,i [RMB/a] Cooler operating costs CH,i [RMB/a] Steam heater operating costs Co [RMB/a] Operating costs of sweetening unit CP,i [RMB/a] Pump and fan operating costs Cpro [RMB/m3] Price of natural gas EE,i [MJ/h] Energy of the cooler EH,i [MJ/h] Energy of the steam heater EP,i [MJ/h] Electric energy of pumps and fans Fpro [m3/d] Output of natural gas Is [RMB/a] Natural gas sales tin [ C] Cooler inlet temperature tout [ C] Cooler outlet temperature Z1 [RMB/a] Fixed-asset investment per year Z2 [RMB/a] Costs for equipment maintenance per year Z3 [RMB/a] Labor costs per year Zc [RMB/a] Fixed investment per year h [%] Thermal efficiency of steam

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