Integrated Optimization for the Coupling Network of Refinery and Synthetic Plant of Chemicals

Abstract

Synthetic plant of chemicals (SPC) consumes large amounts of hydrogen and carbon-oxides while refineries require high-purity hydrogen. Coal gasification (CG) and steam methane reforming (SMR) are common industrial hydrogen production technologies. Their gas products are essentially a mixture of H₂, CO, and CO₂. Therefore, such gas products can provide both syngas for SPC and concentrated hydrogen for refinery through appropriate allocation. Based on the composition complementation of gas products from CG and SMR for their efficient utilization, this paper proposed an integration methodology for refinery and SPC coupling networks to conserve both fossil fuel resources and carbon emissions. A superstructure is established as a problem illustration and a nonlinear programming model (NLP) is formulated as a mathematical solution. A case study is performed, and the results show that the coupling network integration can save 19.1% and 20.2% of coal and natural gas consumption, as well as corresponding carbon emission and operation costs.

1. Introduction

The huge consumption of fossil fuels including oil, natural gas, and coal affects climate change and causes a series of environmental problems [1]; thus, there is increasing widespread interest in the efficient usage of energy resources and the reduction in carbon dioxide emission for sustainable development. According to the BP Statistical Review of World Energy [2] for 2021, primary energy consumption will be reduced by 4.5%, indicating that energy efficiency and emission reduction are becoming a major trend.

Coal is a non-renewable fossil fuel and has been used as the main source of energy for human production activities for several centuries. Jin et al. [3] proposed a coal-based natural gas-electricity co-generation process in which the syngas is delivered directly to the methanation unit without adjusting the hydrogen-to-carbon ratio to a suitable level. Thus, the CO₂ concentration leaving the reactor is increased to reduce CO₂ capture. Huang et al. [4] directly recycled the hydrogen-rich syngas exiting the conversion unit back to the low-temperature methanol wash unit to remove acid gas, so that the total process investment cost can be reduced by 13.2% and energy efficiency can be increased by 16.5%. Qin et al. [5] analyzed the effects of the steam-to-coal ratio, oxygen-to-coal ratio, and carbon dioxide charge on system performance, the results indicate that the carbon capture process saves 40.6% energy consumption compared to the coal-to-methanol process, 22.2% energy consumption compared to the coal to the hydrogen power process.

Natural gas is also an important part of the world’s energy supply and is one of the cleanest and safest sources of energy [6]. Oil has been the most important energy source for so many years but on a declining trend. Natural gas has risen to 24.2% and it is foreseen that at some point in the future, it will overtake oil and coal as the dominant global energy source [7]. Natural gas is playing an increasingly important role as a raw material for chemicals, and as a branch of the chemical industry, natural gas is used as the main raw material for the production of various chemical products through direct and indirect pathways. The direct conversion method uses the alkane component of natural gas to produce hydrogen [8], alkynes [9], olefins [10], aromatics [11], etc. The indirect conversion method first converts natural gas into synthesis gas (CO, H₂) [12], which is then further converted into various chemical products such as clean oil, methanol, low carbon olefins, ammonia, and urea.

In addition to using coal and natural gas as feedstock, respectively, researchers have also conducted research on processes by combining the two energy sources as co-feedstocks. Zhou et al. [13] developed a dual co-production system using coal and natural gas as feedstock to produce dimethyl ether and electricity. The system was found to be highly efficient and economically effective in terms of hydrazine efficiency and a significant reduction in CO₂ emission. In recent years, research on co-production processes for multiple chemicals has also received increasing attention. Yu et al. [14] conducted a study on the steady-state design and economic evaluation of a coal-based synthetic natural gas-ammonia gas co-production process. The results showed that when 20–40% percentage of syngas used for ammonia production can obviously reduce energy consumption and operation cost. Gu et al. [15] proposed fixed-bed coal gasification for the methanol process by partially reusing the carbon dioxide for methanol synthesis. The methane product is obtained through a deep cooling separation unit. This process can greatly improve carbon utilization and energy efficiency compared to the counterpart coal-to-gas process using the same amount of coal feedstock. Through the appropriate combination of coal gasification and steam methane reforming, the process is able to achieve a stepwise utilization of energy and a high-value production process, with the advantages of clean production and energy saving effect.

Hydrogen is a basic industrial raw material and occupies an important position in chemical industries, especially in refineries and SPC. China is the largest hydrogen manufacturer in the world. The productivity is 20 million tons of hydrogen in 2019, 62% of which comes from coal-to-hydrogen processes and 19% from natural gas reforming processes [16]. Both coal gasification and steam methane reforming consume large amounts of energy and are accompanied by CO₂ emissions. With the “carbon neutralization” target, the conservation of hydrogen in chemical processes is becoming crucial. The concept of “hydrogen surplus” was first introduced by Alves [17] to determine the minimum flow of fresh hydrogen. El-Halwagi et al. [18] proposed a rigorous graphical solution to determine the minimum hydrogen utility based on the study of mass exchange networks. Zhao et al. [19] proposed the hydrogen load-flow diagram to obtain the minimum hydrogen utility. Foo et al. [20] proposed the gas cascade analysis by improving the water network optimization method. Zhang et al. [21] introduced contaminant load and hydrogen load as relative concentration constraints to perform pinch analysis for further hydrogen utility reduction. Yang et al. [22] developed relative concentration to describe individual hydrogen sources and hydrogen traps based on the basic concept of pinch points, which can determine the minimum fresh hydrogen consumption and pinch point locations. Li et al. [23] to reduce fresh hydrogen consumption through hydrogen storage. In addition to graphical methods, mathematical planning methods are also widely used. Hallale et al. [24] first established a mathematical model for the optimization of hydrogen systems. Zhang et al. [25] developed an NLP model containing all the necessary constraints for the synthesis of a multi-impurity hydrogen network based on relative concentration. Jia et al. [26] constructed a mixed integer non-linear programming (MINLP) model and identified the optimal impurity removal scenario to obtain the hydrogen network with the lowest annual cost. Liao et al. [27] proposed a superstructure hydrogen network optimization model considering a compressor and extended this approach to consider purification reuse.

Compared to refineries, the synthetic plant of chemicals (SPC) involves complex parameters, numerous equipment, and diverse processes, which also offer great potential for energy savings. Lin et al. [28] analyzed a coal-based methanol production system and demonstrated the advantages of coal to methanol in the power scenario. Bose et al. [29] proposed a coal-based system for power generation and CO₂ for urea production. The results showed that the utilization of CO₂ had a direct impact on economic performance and carbon emissions. Zhang et al. [30] proposed an integrated coal utilization through gasification, pyrolysis, and combustion for hydrogen to carbon ratio of coal syngas, natural gas, and/or biomass were introduced as co-feedstock to improve the hydrogen-to-carbon ratio of syngas and reduce carbon emissions. Chen and Barton [31] established a coal and biomass hybrid poly-generation system to synthesize methanol and naphtha, and simultaneously generate electricity and steam. Later, Adams and Barton [32] proposed a coal and natural gas system to synthesize methanol and F-T oil. Yang et al. [33] used natural gas and CO₂ dry reforming to improve the hydrogen-to-carbon ratio of coal syngas to make ethylene more efficiently and reduce carbon emissions. Yang et al. [34] used hybrid CG, SMR, and graded conversion to produce methanol, oil, and electricity. In response to the low CH₄-CO₂ reforming syngas generation technologies to improve the performance of ethylene glycol synthesis system. For SPC, if an optimal hydrogen-to-carbon ratio feed gas can be produced at the syngas stage by trade-offs with refinery hydrogen, there will be a significant reduction in coal or natural gas consumption, as well as energy consumption and emission. The potential for coupled optimization of the refinery network and SPC is therefore enormous.

At the same time, the hydrogen-to-carbon ratio of the syngas produced by CG and SMR are complementary. Specifically, the hydrogen-to-carbon ratio of the syngas from SMR is higher than that of the syngas from CG. Therefore, the use of a combined CG and SMR supply to the coupled SPC-refinery system can have a high resource utilization efficiency. Studies have been carried out to address the impact of multiple resources on the system. For the coupling network of refinery hydrogen and SPC, Zhang et al. [35] have made a theoretical exploration and quasi-established an LP model for this problem. However, the reaction and separation of syngas are not considered. In this paper, the coupling integration of refinery-SPC through reaction and separation is carried out. A proxy model is established for the improvement of resource utilization and emission reduction. This work is great progress in refinery-SPC coupling network integration for resource conservation, energy efficient utilization, and emission reduction.

2. Problem Description

Syngas is a hinge source for many chemical production processes. On one hand, different reaction routes (SMR, GC) and different feed ratios (water to gas ratio, coal to oxygen ratio) significantly influence specific compositions in the production of syngas; on the other hand, various chemical scenarios such as refinery hydrogen systems, ammonia, and methanol synthesis require different compositions of hydrogen, carbon dioxide, and carbon monoxide in syngas. In order to improve the raw material utilization in the syngas production process and the waste of hydrogen and carbon monoxide, as well as carbon dioxide emissions in the syngas consumption scenarios, a coupling integration of the syngas production and consumption network is considered. Therefore, the aim of this study is to develop a mathematical methodology based on a proxy model for the optimal design of refinery and SPC.

The refinery-SPC network contains the generation and consumption of syngas, and all possible connections among these processes form the refinery-SPC coupling network. The superstructure constructed in this paper consists of two syngas production unit processes, a syngas network, and a hydrogen network, as shown in Figure 1. In the actual process, there are two sources of syngas, one is SMR and the other is CG. The generated syngas goes through separation to obtain pure carbon monoxide, carbon dioxide, hydrogen, and syngas for SPC and refinery. The SPC includes three synthesis units of methanol, glycol, and urea. The gas mixture is generated by coal gasification (CG) and methane steam reforming (SMR). Afterwards, the gas mixture is separated to successively obtain pure H₂, CO_2, and CO, and the remaining syngas is supplied to methanol, ethylene glycol, and urea in SPC while refinery hydrogen processing for product oils. Specifically, pure hydrogen can be supplied to methanol, ethylene glycol, urea ammonia and refinery; pure CO₂ and CO can only be supplied to urea and methanol; pure CO can be supplied to methanol and ethylene glycol; H₂ can be delivered to both SPC and refinery. This paper presents an optimization methodology to obtain the optimal gas allocation network.

In order to reduce the complexity of the model, the following assumptions are made previously to simplify the refinery-SPC network superstructure:

(1) The SPC network only considers the feed requirements of each synthesis unit and does not include a rigorous mechanistic model for reaction.

(2) The separation process only considers the mass balance of the gas mixture without a detailed simulation.

3. Optimization Model and Solution Method

The integration of the refinery-SPC coupling network is performed to reduce the consumption of coal and natural gas to efficiently use hydrogen, carbon monoxide, and carbon dioxide. Therefore, a modeling framework based on the syngas reaction mechanism is proposed in this paper, as shown in Figure 2. The complete optimization model consists of two parts: a high-precision proxy model for GC and SMR, and a refinery-SPC network optimization model.

Firstly, based on the simulation results of CG and SMR by ASPEN-PLUSV12, a proxy model is established to describe the functional relationship between the feed flow rate, feed composition, and the syngas productivity and composition. Secondly, the proxy model is obtained. This chapter will formulate the two models in detail.

3.1. Proxy Model

Specifically, there are five main steps for the construction of proxy model:

Step 1: Input and output variables are determined according to the problem, the input and output variables selected for this study are specified in Figure 3 and Figure 4.

Step 2: The polynomial regression method is selected to model the general expression as shown in Equation (1), where x_N denotes the input variables; y denotes the output variables; $f_{n{n}^{\prime }}(x_n,x_{n^{\prime }})$ and $f_{12\cdot \cdot \cdot N}(x_1,x_2,\cdot \cdot \cdot ,x_N)$ denote the second-order terms and the N-order terms.

$$y=f(x)=f_0+{\displaystyle \sum _{n=1}^N{f}_n(x_n)+{\displaystyle \sum _{n=1}^N{\displaystyle \sum _{n^{\prime }=n+1}^N{f}_{n{n}^{\prime }}(x_n,x_{n^{\prime }})+\cdot \cdot \cdot +f_{12\cdot \cdot \cdot N}(x_1,x_2,\cdot \cdot \cdot ,x_N)}}}$$

(1)

Step 3: Sampling the input data points within the model fit. In this study, the Sobol random sequence sampling method is chosen due to its advantages of efficient sampling and uniform distribution in both high and low-dimensional space. The sampling process starts from sampling in the [0,1] space and then transforming the corresponding values in the model input range through the inverse normalization formula.

Step 4: After completing the sample points selection, simulation is then performed through Aspen plus as shown in Figure 5 and Figure 6. The output results corresponding to the input conditions under the strict mechanism model are obtained.

Step 5: The input conditions and output results are employed to construct the proxy model. The coefficient of determination (R²), the root mean square error (RMSE), and the residual plot are chosen to assess its accuracy and reliability, and they are formulated in Equations (2)–(4).

$$R^2=1-\frac{{\displaystyle \sum _{i=1}^m{\left(y_i-\widehat{y}\right)}^2}}{{\displaystyle \sum _{i=1}^m{\left(y_i-\overline{y}\right)}^2}}$$

(2)

$$RMSE=\sqrt{\frac{{\displaystyle \sum _{i=1}^m{\left(y_i-\widehat{y}\right)}^2}}{m}}$$

(3)

$${\epsilon }_i=y_i-\widehat{y}$$

(4)

3.2. Refinery-SPC Network Model

3.2.1. SPC Network

There are two kinds of syngas generation: SMR and CG. Specifically, the SMR is influenced by the CH₄ and H₂O ratio and temperature, while the CG is influenced by the coal–oxygen ratio, coal–water ratio, and temperature. In this paper, the flow rate and composition of SMR and CG products are represented by proxy models. The proxy model in the form of a higher-order polynomial will be demonstrated in Section 4.2. The constrained expressions are shown in Equations (5) and (6):

$$F_{react,out}(i)=g_i{(F_{material}(i),F_{O_2}(i),F_{H_{2}O}(i),T)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(5)

$$y_{react,out}(i,j)=f_i{(F_{material}(i),F_{O_2}(i),F_{H_{2}O}(i),T)}^{}\hspace{1em}\hspace{1em}\forall i\in I,\forall j\in J$$

(6)

where i denotes different syngas routes, including two feedstocks, and one is coal and the other is natural gas; j denotes the components of the syngas, including CO₂, H₂, CO, H₂O, and CH₄.

In the separation process of syngas, the first step is to remove the water. It is assumed that the water is completely removed from syngas using the unit operation of flash evaporation. Equations (7)–(10) represent the mass balance of such a process.

$$F_{H_{2}O,out}(i)=F_{react,out}(i)-F_{H_{2}O,Sep}{(i)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(7)

$$y_{H_{2}O,out}(i,j)={\frac{F_{react,out}(i)\times y_{react,out}(i,j)-F_{H_{2}O,Sep}(i)\times y_{H_{2}O,Sep}(i,j)}{F_{H_{2}O,out}(i)}}^{}\hspace{1em}\hspace{1em}\forall i\in I,\forall j\in J$$

(8)

$$\frac{F_{H_{2}O,Sep}(i)\times y_{H_{2}O,Sep}(i,H_{2}O)}{F_{H_{2}O,out}(i)\times y_{H_{2}O,out}(i,H_{2}O)}=Rat{e}_{H_{2}O,Sep}{(i)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(9)

$$\frac{y_{H_{2}O,Sep}(i)}{{\displaystyle \sum _{i\ne H_{2}O}{y}_{H_{2}O,Sep}(i)}}={\frac{y_{react,out}(i)}{{\displaystyle \sum _{i\ne H_{2}O}{y}_{react,out}(i)}}}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(10)

where F denotes the flow rate, y denotes the component concentration, and Rate denotes the water removal rate.

After the removal of water from the syngas, gas components are purified successively. CO₂ was separated by MEA chemical absorption, and its conservation of substance is represented by Equations (11)–(13). In this model, it is assumed that only CO₂ is absorbed during the MEA process and that the amounts of the other gas components do not change. At the same time, the amount of CO₂ in the gas obtained by separation does not fall below 0.9999, as in Equation (14); the relative amounts of the other gases remain the same as before separation, as in Equation (15).

$$F_{C{O}_2,out}(i)=F_{H_{2}O,out}(i)-F_{C{O}_2,Sep}{(i)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(11)

$$y_{C{O}_2,out}(i,j)={\frac{F_{H_{2}O,out}(i)\times y_{H_{2}O,out}(i,j)-F_{C{O}_2,Sep}(i)\times y_{C{O}_2,Sep}(i,j)}{F_{C{O}_2,out}(i)}}^{}\hspace{1em}\hspace{1em}\forall i\in I,\forall j\in J$$

(12)

$$\frac{F_{C{O}_{2}Sep}(i)\times y_{CO,Sep}(i,C{O}_2)}{F_{C{O}_2,out}(i)\times y_{CO,out}(i,C{O}_2)}=Rat{e}_{C{O}_2,Sep}{(i)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(13)

$$y_{C{O}_2,Sep}(i,C{O}_2)\ge {0.9999}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(14)

$$\frac{y_{C{O}_2,Sep}(i)}{{\displaystyle \sum _{i\ne C{O}_2}{y}_{C{O}_2,Sep}(i)}}={\frac{y_{H_{2}O,out}(i)}{{\displaystyle \sum _{i\ne CO}{y}_{H_{2}O,out}(i)}}}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(15)

H₂ was separated by pressure swing adsorption (PSA). Its conservation of substance is represented by Equations (16)–(18). In this model, it is assumed that during the PSA process, mainly H₂ is separated by adsorption and the amounts of the other gas components are recalculated according to mass balance. In this case, the amount of H₂ in the separated gas is not less than 0.9999, as in Equation (19); the relative amounts of other gases remain the same as before separation, as in Equation (20).

$$F_{H_2,out}(i)=F_{C{O}_2,out}(i)-F_{H_2,Sep}{(i)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(16)

$$y_{H_2,out}(i,j)={\frac{F_{C{O}_2,out}(i)\times y_{C{O}_2,out}(i,j)-F_{H_2,Sep}(i)\times y_{H_2,Sep}(i,j)}{F_{H_2,out}(i)}}^{}\hspace{1em}\hspace{1em}\forall i\in I,\forall j\in J$$

(17)

$$\frac{F_{H_2,Sep}(i)\times y_{H_2,Sep}(i,H_2)}{F_{H_2,out}(i)\times y_{H_2,out}(i,H_2)}=Rat{e}_{H_2,Sep}{(i)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(18)

$$y_{H_2,Sep}(i,H_2)\ge {0.9999}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(19)

$$\frac{y_{H_2,Sep}(i)}{{\displaystyle \sum _{i\ne H_2}{y}_{H_2,Sep}(i)}}={\frac{y_{C{O}_2,out}(i)}{{\displaystyle \sum _{i\ne H_2}{y}_{CO}{}_{{}_2,out}(i)}}}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(20)

cryogenic separation is further employed to obtain high purity CO. The mass balance of the CO separation process is formulated by Equations (21)–(23). According to the assumptions of the model, in the CO separation process, mainly CO is separated and purified, and the amounts of the other gas components are recalculated according to mass balance. Thus, the amount of CO in the separated gas is not less than 0.9999, as in Equation (24); the relative amounts of other gases remain the same as the composition of the gas obtained after PSA separation of H₂, as in Equation (25).

$$F_{CO,out}(i)=F_{H_2,out}(i)-F_{CO,Sep}{(i)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(21)

$$y_{CO,out}(i,j)={\frac{F_{H_2,out}(i)\times y_{H_2,out}(i,j)-F_{CO,Sep}(i)\times y_{CO,Sep}(i,j)}{F_{CO,out}(i)}}^{}\hspace{1em}\hspace{1em}\forall i\in I,\forall j\in J$$

(22)

$$\frac{F_{CO,Sep}(i)\times y_{CO,Sep}(i,CO)}{F_{CO,out}(i)\times y_{CO,out}(i,CO)}=Rat{e}_{CO,Sep}{(i)}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(23)

$$y_{H_2,Sep}(i,CO)\ge {0.9999}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(24)

$$\frac{y_{CO,Sep}(i)}{{\displaystyle \sum _{i\ne CO}{y}_{CO,Sep}(i)}}={\frac{y_{H_2,out}(i)}{{\displaystyle \sum _{i\ne CO}{y}_{H_2,out}(i)}}}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(25)

After the syngas separation process, high-purity CO, CO_2, and H₂ and a mixture of the three gases are obtained and distributed according to the demand for methanol, urea, and ethylene glycol synthesis and fresh hydrogen for the refinery.

Equations (26) and (27) represent the mass balance of hydrogen in the coupling network. They show that all the hydrogen required by the refinery and SPC comes from the reaction and separation and that the refinery and SPC networks are coupled in the allocation of the hydrogen. The constraint stipulates that part of the hydrogen from the CG and SMR goes to the SPC gas network to participate in the gas distribution process, another part goes to the refinery hydrogen network as fresh hydrogen, and the last part is discharged as waste gas.

$$y_{H_2,Sep}(i,H_2)={\frac{H_i+{\displaystyle \sum _{s=1}^{S}H(i,s)\times y_{H_2,Sep}(i,H_2)}+F_{CO,out}(i)\times y_{CO,out}(i,H_2)}{F_{H_2,Sep}(i)}}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(26)

$${\displaystyle \sum _{b=1}^B{H}_{1,b}}={{\displaystyle \sum _{i=1}^I{H}_i}}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(27)

where (17) denotes the demand of fresh hydrogen for the refinery hydrogen network and s denotes the three synthesis processes of methanol, urea, and ethylene glycol.

$$y_{CO,Sep}(i,CO)={\frac{{\displaystyle \sum _{s=1}^{S}FCOLin{k}_{i,s}}+F_{CO,out}(i)\times y_{CO,out}(i,CO)}{F_{CO,Sep}(i)}}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(28)

$$y_{C{O}_2,Sep}(i,C{O}_2)={\frac{{\displaystyle \sum _{s=1}^{S}FC{O}_{2}Lin{k}_{i,s}}+F_{C{O}_2,out}(i)\times y_{C{O}_2,out}(i,C{O}_2)}{F_{C{O}_2,Sep}(i)}}^{}\hspace{1em}\hspace{1em}\forall i\in I$$

(29)

Equations (28) and (29) represent the CO and CO₂ mass balance of the network. In those constraints, it is indicated that the CO₂ and CO from the CG and MSR have two destinations after separation. One is into the route of the synthesis process, where they participate in the synthesis reactions of methanol, ethylene glycol, and urea; the other is discharged as waste gas.

3.2.2. Hydrogen Network

Equations (30)–(34) describe the hydrogen network purification reuse. Specifically, H denotes the hydrogen flow rate, RC denotes the relative concentration of contaminants, a is the subscript for hydrogen sources, b is that for hydrogen sinks and k is that for contaminants. Renew denotes the purified hydrogen product.

Equation (30) stipulates that the flow rate of hydrogen supplied by sources should be no less than the demand of each hydrogen sink. Equation (31) specifies that the contaminant concentration of each hydrogen sink cannot exceed the prescribed upper limit. Equation (32) imposes a constraint that the allocated hydrogen flow rate from any source, including purified product, should not exceed its available flow rate.

$$H_{SK,b}\le {\displaystyle \sum _{a=1}^A{H}_{a,b}}+H_{Renew,b}\hspace{1em}\hspace{1em}\forall b\in B$$

(30)

$${\displaystyle \sum _{a=1}^A{H}_{a,b}\cdot R{C}_{sr,a,k}}+H_{Renew,b}\cdot R{C}_{Renew,k}\le R{C}_{sk,b,k}^{\max }\cdot {({\displaystyle \sum _{a=1}^A{H}_{a,b}}+H_{Renew,b})}^{}\hspace{1em}\hspace{1em}\forall b\in B$$

(31)

$$H_{SR,a}\ge {\displaystyle \sum _{b=1}^B{H}_{a,b}}+H_{Renew,a}\hspace{1em}\hspace{1em}\forall a\in A$$

(32)

Equations (33) and (34) describe the mass balance of hydrogen and contaminants in purification process, respectively.

$${\displaystyle \sum _{a=1}^A{H}_{Renew,a}}={\displaystyle \sum _{b=1}^B{H}_{Renew,b}}+H_{Renew,out}$$

(33)

$${\displaystyle \sum _{a=1}^A{H}_{Renew,a}\cdot R{C}_{sr,a,k}}={\displaystyle \sum _{b=1}^B{H}_{Renew,b}\cdot R{C}_{Renew,k}}+H_{Renew,out}\cdot R{C}_{Renew,out,k}$$

(34)

3.2.3. Objective Function

$$\begin{array}{c}Min\hspace{1em}Objective={\displaystyle \sum _{i=1}^I{\lambda }_i\cdot F_{material}(i)}+{\displaystyle \sum _{i=1}^I{\lambda }_{CO}\cdot F_{CO,Sep}(i)\cdot y_{CO,Sep}(i,CO)}\hfill \\ +{\displaystyle \sum _{i=1}^I{\lambda }_{H_2}\cdot F_{H_2,Sep}(i)\cdot y_{H_2,Sep}(i,H_2)}+{\displaystyle \sum _{i=1}^I{\lambda }_{C{O}_2}\cdot F_{C{O}_2,Sep}(i)\cdot y_{C{O}_2,Sep}(i,C{O}_2)}\hfill \\ +{\displaystyle \sum _{i=1}^I{\lambda }_{\mathrm{Cos}t,C{O}_2}\cdot F_{CO,out}(i)\cdot (y_{CO,out}(i,CO)+y_{CO,out}(i,C{O}_2))}+{\displaystyle \sum _{b=1}^B{\lambda }_{H_2}\cdot H_{Renew,b}}\hfill \end{array}$$

(35)

Equation (35) represents the objective function aiming to minimize the operation cost. λ denotes the cost factor, which includes the price of natural gas and coal, as well as the gas separation cost and the carbon trading cost. The model has a large number of bi-linear terms in gas separation and hydrogen network constraints, so it is a nonlinear programming (NLP) model.

4. Case Study

4.1. Case Data

Table 1. Data for synthetic plant of chemicals.

Reaction	Output t/h	Feed Gas Flow Rate kmol·h−1
		CO	CO2	H2
Ethylene glycol	36.94	1578	0	2981
Methanol	73.49	0	1242	4271
Urea	73.02	2664	91.9	5603

is an SPC case from literature illustrating the demand for CO, CO₂, and H₂ for methanol, ethylene glycol, and methane synthesis reactions. The methanol synthesis requires pure CO₂ and pure H₂ or their mixture; the ethylene glycol requires pure CO and H₂; the urea requires pure CO₂, pure H_2, and pure CO. The ratios of the feed gases for these three synthesis reactions must also meet the requirements shown in Table 1.

Table 2. Hydrogen source data.

Hydrogen Source	Molar Flow kmol·h−1	Relative Concentration of Impurities
		S	N	C
sr1	2901.79	0.0000	0.0000	0.0001
sr2	892.53	0.0115	0.0264	0.1089
sr3	1205.98	0.0147	0.0170	0.0995
sr4	1189.67	0.0180	0.0159	0.0276
sr5	883.43	0.0067	0.0552	0.0112
sr6	999.40	0.0271	0.0627	0.1092

and

Table 3. Hydrogen sink data.

Hydrogen Sink	Molar Flow kmol·h−1	Relative Concentration of Impurities
		S	N	C
sk1	785.71	0.0226	0.0769	0.0769
sk2	457.14	0.0131	0.0559	0.0559
sk3	687.14	0.0154	0.0162	0.0162
sk4	1002.56	0.0075	0.0085	0.0085
sk5	1134.38	0.0354	0.1311	0.1311
sk6	1409.38	0.0132	0.0518	0.0518

showcase data from the literature containing the hydrogen sources of the refinery hydrogen network, the hydrogen flow rate of the hydrogen sinks, and the relative concentration of contaminants.

4.2. Syngas Generation

The input and output data from the syngas reaction unit were fitted and the polynomial model was selected as an approximation to the strict light hydrocarbon recovery process model by comparing the model accuracy and complexity aspects. The results of the validation of the light hydrocarbon recovery unit model are presented in

Table 4. Results of the syngas reaction unit model.

Device	Output Variables	RMSE	R2	Device	Output Variables	RMSE	R2
SMR	$F^{SMR}$	101.8	0.9999	CG	$F^{CG}$	5.619	0.9999
	$y_{H_2}^{SMR}$	0.001444	0.9999		$y_{H_2}^{CG}$	0.0000461	0.9999
	$y_{CO}^{SMR}$	0.000835	0.9995		$y_{CO}^{CG}$	0.0000131	0.9999
	$y_{C{O}_2}^{SMR}$	0.000251	0.9989		$y_{C{O}_2}^{CG}$	0.0000095	0.9999
	$y_{H_{2}O}^{SMR}$	0.001319	0.9999		$y_{H_{2}O}^{CG}$	0.0000235	0.9999
	$y_{C{H}_4}^{SMR}$	0.000734	0.9912

, where the obtained polynomial proxy model has an R² value of 0.99 or more, the RMSE values of each component output variable are below 0.002 and the RMSE values of the flow rates are below 200. The residuals of the model were randomly distributed around “0”, indicating that there is no intrinsic relationship between the residuals and the regression prediction. The results of the proxy model for the syngas reaction unit provide a good approximation of the syngas reaction unit.

4.3. Refinery-SPC Network Integration

In order to verify the advantages of the model for resource conservation and carbon emission reduction, two scenarios were designed to make a comparison. The first scenario is termed the ‘original situation’, in which the three synthesis processes—ethylene glycol, methanol, and urea—have a single source of feed gas. Specifically, the gas required by urea, methanol synthesis, and refinery comes from three different SMR units, while the gas required by ethylene glycol synthesis is supplied by one CG unit, as shown in

Table 5. Original network resource consumption and emission.

Items	Raw Material Consumption		H2 Discharge kmol/h	CO2 Discharge kmol/h	CO Discharge kmol/h	Cost 104 ¥/y
Coal to ethylene glycol	48.8 t/h		0	1006.0	0	80,359
Natural gas to urea	1264.0 kmol/h		804.0	0	35.3	117,391
Natural gas to methanol	2836.6 kmol/h		2914.6	29.7	11.9	193,251
Natural Gas to Hydrogen (Refinery)	315.4 kmol/h		0	325.9	9.4	30,398
Total	Coal Natural gas	48.8 t/h 4415.9 kmol/h	3718.6	1361.6	103.6	421,184

. In the second scenario, the refinery-SPC coupling network, whose gas is supplied by one set of CG units and one set of SMR units. In this case, the specific feedstock consumption and gas distribution are obtained by solving the mathematical model described in Section 3.

To ensure that the solution obtained is globally optimal, Gurobi was chosen as the solver for this case. Computer hardware information is as follows: Intel(R) Core(TM) i7-10870H CPU@ 2.20 GHz, Gurobi software version 9.5.1, and solution time is 26.4 s.

The results are listed in

Table 6. Resource consumption and emission of the optimized network.

Items	Raw Material Consumption		H2 Discharge kmol/h	CO2 Discharge kmol/h	CO Discharge kmol/h	Cost 104 ¥/y
Original situation	Coal Methane	48.8 t/h 4415.9 kmol/h	3718.6	1361.576	103.62	421,184
Optimization results	Coal Methane	39.5 t/h 3479.4 kmol/h	0	0	0	322,547
Reduction	Coal Methane	19.1% 21.2%	100%	100%	100%	23.46%

and illustrated in Figure 7. In Figure 7, blue lines, red lines, green lines and gray lines represent hydrogen streams, CO₂ streams, CO streams and mixed streams of the gas network, respectively. The analysis shows that the refinery-SPC network integration can save 19.1% and 21.2% of coal and natural gas consumption. and simultaneously pure gas H₂, CO, and CO₂ waste can be completely avoided. Consequently, 23.5% of operation cost can be reduced. Such results demonstrate that modeling the coupling integration can obtain an obvious economic and environmental effect.

5. Conclusions

Refinery and synthetic plant of chemicals (SPC) are complementary in hydrogen and carbon oxides utilization, and thus, their coupling integration is prospective in resource conservation and emission reduction. In this work, a non-linear programming (NLP) model is developed for SPC-refinery gas networks, based on the constraints of reaction-separation simulation results. A practical coupling network case is employed to demonstrate its superiority over traditional individual integration. Quantitatively, pure gas H₂, CO, and CO₂ separated from the mixture can be completely utilized with zero waste, and thus, 19.1% and 21.2% of coal and natural gas can be conserved. The integrated refinery-SPC coupling network can effectively improve the efficiency of coal and natural gas utilization and reduce CO₂ emission. The integrated approach presented in this paper offers suggestions for future applications in the chemical industry.