Integration of flare gas with fuel gas network in refineries

Integration of flare gas with fuel gas network in refineries

Nassim Tahouni*, Majid Gholami, M. Hassan Panjeshahi

School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Iran

Abstract

The high price of crude oil, strict environmental regulations and ever-increasing demand for energy have made refineries adopt a more holistic approach to integrating energy, economics and environment in their design and operation. Gas flaring is a major factor for the wastage of energy in oil and gas industries that could be better utilized and even generates revenue. Integration and use of wasted and flared gases with fuel gas network (FGN) is an effective approach for reducing GHG emissions as well as conserving energy in refineries. In this paper, current FGN model introduced by Hassan et al. was modified and also a novel methodology was presented for grass-root and retrofit design of FGNs using integration of flare gas streams. GHG emission concept is added to the base model as new constraint to control and minimize the flaring. A FGN proposed for a refinery case study with integration of flare gas streams indicated a $12 \%$ reduction in natural gas consumption compared to the non-integrated flare gas stream case and a $27.7 \%$ reduction compared to the base case with no FGN. In the retrofit case, results suggested that the maximum utilization of flare gas streams can be the most profitable solution.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Flaring of waste and unwanted gases to the atmosphere is a major concern in whole petroleum industry. According to the recent data, 139 billion cubic meters of gas are flared annually [1], which is equal to $4.6 \%$ of world natural gas consumption of total 3011 billion cubic meters in 2008 [2]. This results in about 281 millions of tons of $\mathrm{CO}_{2}$ emissions per year [3]. Flaring emissions also lead to warming of the earth and intensify the natural greenhouse effect on atmosphere and hence to climate changes over the coming century [4]. Many developing oil producing countries flare and ventilate large amounts of unwanted, waste or purge hydrocarbon gases with high heating value and make huge losses to energy and economic resources [5].

Global energy demand due to high economic growth has continuously reached new peaks and is predicted to increase by $57 \%$ from 2004 to $2030[6,7]$. This concern in addition to successive reduction of hydrocarbon fuel reserves has provided new advanced concepts for energy management in oil and gas industries [8]. Different approaches to increasing energy efficiencies by reducing unnecessary wasting, purging, and energy recovering from waste streams were reported in many researches. These can be reached by

^[1]investing on improving equipment efficiencies and applying research on new energy resources to replace the fossil fuels and hence reduce fuel consumption and pollution emissions [9]. Alsalem presented the main sources of flaring in Kuwait’s petroleum refineries. Better utilization of recovered heat through units and carbon capture projects were suggested [10]. Voldsund et al. analyzed the exergy destruction for on four North Sea offshore platforms and indicated that exergy losses with gas flaring can be significant. A survey was conducted to investigate the installation of flare gas recovery systems for supplying heat demand by waste heat recovery from the exhaust gases and by heat integration with other process streams. Gas filed and gas injection was used as recovery strategies [11]. Morrow III et al. developed energy-usage reduction curves for the United States petroleum refining. The results can estimate the potentials for energy savings and $\mathrm{CO}_{2}$ emission reductions for refining technologies like refinery gas processing and flare systems [12]. Jou et al. indicated that recovering and reusing waste tail gas emitted from petrochemical industries is a great method for saving energy and reducing the environmental impacts [13]. Liu et al. investigated the key energysaving technologies in Chinese refineries. They implemented flare gas recovery for fluid catalytic cracking and coker processes, as large values of hot flare gas are generated in these units. Also, the liquid fuel replacing with natural gas was suggested to reduce energy consumptions [14]. Ptasinski et al. applied the Extended Exergy Accounting (EEA) indicator to performance analysis of

Dutch chemical and energy transformations [15]. Persson et al. considered the influence of seasonal variations on energy-saving opportunities in a kraft process using process integration techniques [16]. Worrell et al. identified the energy savings and $\mathrm{CO}_{2}$ abatement potentials in the United State iron and steel industry by examining several specific energy efficiency technologies [17].

Over $40 \%$ of the operating cost of a chemical plant is contributed from energy [18], which is a main component of daily operating costs in plants such as refineries. Thus, a systematic network utilizing waste and flare gases as the fuel to be consumed in the fuel gas sinks such as turbines, furnaces, and boilers, is an efficient tool to save energy and reduce GHG emissions. A FGN collects various waste gases, flare gases, and fuel gases as source streams and passes them through pipelines, valves, heaters, coolers, and compressors to mix them in an efficient manner and supply them to various fuel sinks [19].

A new management and control strategy to improve the performance of FGN without changing the existing superstructure in a petroleum refinery has already been studied [20]. Wicaksono et al. proposed a mixed-integer nonlinear programming (MINLP) model in an LNG plant for integration of various fuel gas sources [21]. Wicaksono et al. further extended this practice by integrating jetty boil-off gas as an additional source [22]. Afterwards, Hasan et al. addressed the optimal synthesis of a FGN with different practical features such as auxiliary equipment (pipelines, valves, heaters, coolers, compressors, etc), non-isothermal and non-isobaric operation, non-linear mixing, non-isothermal mixing, non-linear fuel quality specifications, treatment costs, and fuel and utility costs. They proposed a FGN superstructure that installs possible alternatives for moving, mixing, heating, cooling, and splitting and also developed a non-linear programming (NLP) model.

However, Hasan et al. did not consider the environmental issues on their proposed model. In this study, the model proposed by him is used as a base model, and new constraints for flaring emissionsmostly for $\mathrm{CO}_{2}$ emissions-are then developed. Also, their approach is only valid for grass-root design of FGNs, which is extended here to propose our novel profit-based retrofit NLP model.

2. Problem statement

A typical FGN superstructure introduced by Hasan et al. consists of three main nodes (Fig. 1). The first node consists of all available fuel gas sources $(i=1,2, \ldots, l)$. A source is a kind of gas stream which has a non-zero heating value and potential for mass balance. The waste/purge gas streams from different units in refineries (such as crude distillation unit, amine unit, or visbreaker unit), feed/ byproduct/product gas streams (such as LPG in refineries), and external fuel gasses (such as natural gas which are purchased), are some examples of source streams [23].

The second node consists of $J$ pools that are used as mixing headers $(j=1,2, \ldots, J)$. These pools are used to receive and mix fuel gas streams from different sources and send them to different sinks to satisfy their requirements. Although different source streams that enter into these pools can have different temperatures; however, they should be of the same pressure.

The third node consists of $K$ sinks where fuel gas streams are used $(k=1,2, \ldots, K)$. A sink is any equipment or plant which needs fuel gas stream to produce heat or work. There are different kinds of sinks such as turbines, furnaces, boilers, and flares. Some sinks such as gas turbine drivers are defined as fixed sinks, since they need a constant value of energy. By contrast, sinks that can consume fuel gas more than their energy need for producing power/heat are defined as flexible sinks such as steam generating boilers [23].

As illustrated in Fig. 1, source stream $i$ entering into the network will be divided by splitters. Each sub-stream passes through

Fig. 1. Schematic superstructure of a fuel gas network [23].
auxiliary equipment (cooler, heater, compressor, and valve) and connects to header $k$. Each header transmits the mixture of substreams to the sink $k$.

The problem is formulated with the following data:
(1) A set of source streams with known characteristics such as compositions, temperatures, pressures, etc,
(2) A set of fuel sinks with known energy requirements and acceptable ranges for different specifications such as flows, compositions, pressures, temperatures, lower heating value (LHV), Wobbe Index (WI).
(3) Operating and capital cost parameters for equipment used in the FGN.

We make the following assumptions:
(1) Plant operates in the steady state condition with no chemical reaction;
(2) No temperature dependency for lower heating value of fuel gases is considered;
(3) Only valves are used for expansions and all expansions comply with Joule-Thompson expansion theory;
(4) Gas compressions are adiabatic and single stage;
(5) No pressure drop in equipment and pipes are assumed;
(6) There is unlimited utility operation at any temperature;
(7) Reference temperature and pressure are $68{ }^{\circ} \mathrm{F}$ and 14.7 Psia.

It is desirable to design a network distributing fuel gas source streams to fuel gas sinks with known characteristics through auxiliary equipment with known duties. All stream specifications such as pressure, temperature, and flow must be calculated. The objective function of total annualized cost (TAC) of FGN should be minimized. The capital costs of the network equipment, operating costs of the fuels and environmental costs due to flaring are included in TAC.

3. Model formulation

Now we can formulate the FGN model with the following

Table 1
Data and parameters for sources in grass-root case.

constraints on the flow rates, energy requirements of sinks, limits of temperature, pressure and fuel quality, and environmental regulation limitations [19], [23].

Fuel gas flow in sub-stream $S S_{i k}$ is $F_{i k}$. Where $F_{i}$ is the available flow of source stream $i$ that can be used.
$\sum_{k=1}^{K} F_{i k}=F_{i}$
Source flow of valuable fuel gas streams is limited by the following constraint, where $F_{i}^{L}$ and $F_{i}^{U}$ are the minimum and maximum flow rate of source i.
$F_{i}^{L} \leq F_{i} \leq F_{i}^{U}$
Constraint (2) will change for the valuable fuel gases as Equation (3) to ensure that all amounts of waste/purge gases are consumed.
$F_{i}^{L}=F_{i}=F_{i}^{U}$
Flow limits of sink $k\left(F_{k}^{L}, F_{k}^{U}\right)$ restricts the flow received by itself.
$F_{k}^{L} \leq \sum_{i=1}^{I} F_{i k} \leq F_{k}^{U}$
The following constraints will be used for energy needs $\left(D_{k}\right)$ of fixed and flexible sinks.
$\sum_{i=1}^{I} F_{i k} L H V_{i}=D_{k} \quad$ (for fixed sinks)
$\sum_{i=1}^{I} F_{i k} L H V_{i} \geq D_{k} \quad$ (for flexible sinks)
As the operation in the FGN is non-isothermal and non-isobaric, energy balance through the network is expressed in enthalpy change terms. $h_{i k}$ is the heat content of the fuel gas stream passing from source $i$ to sink k . It is calculated as the initial enthalpy of source gas stream $\left(C p_{i} T_{i} F_{i k}\right)$ plus enthalpy change through compressor $\left(\Delta h_{i k}^{B}\right)$, valve $\left(\Delta h_{i k}^{V}\right)$, heater $\left(\Delta h_{i k}^{H}\right)$, and cooler $\left(\Delta h_{i k}^{C}\right)$.
$h_{i k}=C p_{i} T_{i} f_{i k}+\Delta h_{i k}^{B}-\Delta h_{i k}^{V}+\Delta h_{i k}^{H}-\Delta h_{i k}^{C}$
The enthalpy change across the valve is calculated as below, where $\mu_{i}, P_{i}$, and $P_{k}$ are joule-Thomson coefficient, pressure of source stream $i$, and pressure of sink $k$
$\Delta h_{i k}^{V} \geq \mu_{i} C p_{i} F_{i k}\left(P_{i}-P_{k}\right)$

The enthalpy change across the compressor, where $\eta_{i}$ is adiabatic compression efficiency and $n_{i}$ is adiabatic compression coefficient $\left(\frac{P}{P_{k}}\right)$ is
$\Delta h_{i k}^{B} \geq \frac{\left(C p_{i} T_{i} F_{i k}-\Delta h_{i k}^{C}\right)}{\eta_{i}}\left(\left(\frac{P_{k}}{P_{i}}\right)^{\eta_{i}}-1\right)$
Constraint (9) limits the pressure of sink $k$ within the acceptable range of $\left(P_{k}^{L}, P_{k}^{U}\right)$
$P_{k}^{L} \leq P_{k} \leq P_{k}^{U}$
Acceptable Enthalpy range of source $i$ is limited by (10) and (11), where $T_{i}^{L}$ and $T_{i}^{U}$ are the lower and upper allowable source $i$ temperature.
$h_{i k} \leq C p_{i} T_{i}^{U} F_{i k}$
$C p_{i} T_{i} F_{i k}-\Delta h_{i k}^{V}-\Delta h_{i k}^{C} \geq C p_{i} T_{i}^{L} F_{i k} \Delta h_{i k}^{V}$
For the mixing header $k$, the enthalpy balance is defined by Equation (12), where $T_{k}$ is the sink $k$ temperature and $T_{k}^{L}, T_{k}^{U}$ are the allowable bounds of sink $k$ temperature.
$T_{k} \sum_{i=1}^{I} C p_{i} F_{i k}=\sum_{i=1}^{I} h_{i k}$
$T_{k}^{L} \leq T_{k} \leq T_{k}^{U}$
Enthalpy changes are the non-negative variables. In case of existence of equipment, the enthalpy changes are positive, otherwise they are zero.
$\Delta h_{i k}^{B} \geq 0, \Delta h_{i k}^{V} \geq 0, \Delta h_{i k}^{H} \geq 0, \Delta h_{i k}^{C} \geq 0$
There are some fuel quality specifications to be considered for sinks. Specific gravity (SG) which is the ratio of the density of a gas to the air is controlled by Equation (15). For an ideal gas, specific gravity is the ratio of the gas molecular weight to the air molecular weight.
$\sum_{i=1}^{I} F_{i k} S G_{i}=S G_{k} \sum_{i=1}^{I} F_{i k}$
Constraint (16) restricts the specific gravity limits of sink k.

Table 2
Data and parameters for sinks in grass-root case.

$S G_{k}^{L} \leq S G_{k} \leq S G_{k}^{U}$
Lower heating value showing the energy content of a fuel gas is an important fuel quality specification for sinks [24]. Equation (17) calculates the LHV of the sink $k$ and Equation (18) controls it between allowable ranges of LHV for sink $k$.
$\sum_{i=1}^{I} F_{i k} L H V_{i} \geq L H V_{k} \sum_{i=1}^{I} F_{i k}$
$L H V_{k}^{L} \leq L H V_{k} \leq L H V_{k}^{U}$
While LHV measures the heat content of a fuel gas, Wobbe Index (WI) shows the interchangeability and energy flow of a fuel gas. Constraint (20) keeps WI between its allowable limits [25].
$W I=\frac{L H V}{\sqrt{S G}}$
$\left(W I_{k}^{L}\right)^{2} S G_{k} \leq\left(L H V_{k}\right)^{2} \leq\left(W I_{k}^{U}\right)^{2} S G_{k}$
The methane number (MN) usually used for gas turbines, measures the knock resistance of a fuel gas [23]. $q_{i}$ is the mole fraction of alkane composition in the fuel gas source stream i.

$$\begin{aligned} 0.242 \sum_{i=1}^{I} F_{i k} q_{i, C_{i} H_{4}} \geq 1.516 \sum_{i=1}^{I} F_{i k} q_{i, C_{i} H_{6}} \\ & +3.274 \sum_{i=1}^{I} F_{i k} q_{i, C_{4} H_{8}} \\ & +5.032 \sum_{i=1}^{I} F_{i k} q_{i, C_{4} H_{10}} \\ & +6.79 \sum_{i=1}^{I} F_{i k} q_{i, C_{i} H_{12}} \\ & +8.548 \sum_{i=1}^{I} F_{i k} q_{i, C^{5}} \end{aligned}$$

Constraints (22) and (23) set the temperature of network over the moisture dew point (MDP) and hydrocarbon dew point (HDP) for restraining condensation [19], [26].

Table 3
Capital and operating cost parameters for equipment [23].

$$\begin{aligned} & \left(M D P_{k}+\frac{5}{9}\left(5.15\left(\frac{P_{k}}{100}\right)-312\right)\right) \leq T_{k} \\ & \left(H D P_{k}+\frac{5}{9}\left(2.33\left(\frac{P_{k}}{100}\right)^{2}-2.8\left(\frac{P_{k}}{100}\right)-305\right)\right) \leq T_{k} \end{aligned}$$

$\mathrm{CO}_{2}$ emission from petrochemical plants and refineries can be calculated from the below relation extracted from Title-40 of Code of Federal Regulations (CFR-40) [27].
$C O_{2}=0.98 \times 0.001 \times\left(\sum_{i}^{n}\left[\frac{44}{12} \times(\text { Flare })_{i} \times \frac{M W_{i}}{M V C} \times C C_{i}\right]\right)$
where:
$\mathrm{CO}_{2}: \mathrm{CO}_{2}$ emissions (t/y)
Flare: volume of source gas $i$ flared $\left(\mathrm{m}^{3} / \mathrm{y}\right)$
$C C_{i}$ : carbon content of flare gas ( kg of carbon $/ \mathrm{kg}$ of fuel)
$M W_{i}$ : molecular weight of flare gas
MVC: molar volume conversion factor ( $849.5 \mathrm{scf} / \mathrm{kgmole}$ for STP of $20^{\circ} \mathrm{C}$ and 1 atm , or $24.06 \mathrm{~m}^{3} / \mathrm{kgmole}$ for STP of $20^{\circ} \mathrm{C}$ and 1 atm )
44/12: ratio of molecular weights, $\mathrm{CO}_{2}$ to carbon
0.001: conversion factor, kg to t

Constraint (25) calculates the total $\mathrm{CO}_{2}$ emissions from different fuel gas sources in the flare sink.
$h c_{k} \geq 0.98 \times \sum_{i=1}^{I} \frac{44}{12} \times C C_{i} \times F_{i k} \times \frac{M W_{i}}{M V C}$
Note that emission fee for $h c_{k}$ will be considered in the objective function to precise the current model (Hasan’s model).

3.1. Objective function for grass-root case

Finally, the objective function for grass-root case (TAC) is written by Equation (26):

ParseError: KaTeX parse error: Expected & or \\ or \cr or \end at position 355: …lta h_{i k}^{C}\̲r̲i̲g̲h̲t̲) \\ & +O P H^{…

where the first five terms are related to capital cost for pipes, valves, compressors, heaters, and coolers. The other terms are the operating costs including cost of fuel gases, treatment cost, $\mathrm{CO}_{2}$ emission penalty, revenue from flexible sinks and equipment operating costs. The cost parameters are as follows: $a f$ is the annualization factor, $C C_{i k}$ is the equipment capital cost, $O P H$ is the operating hours per year, $\alpha_{i}$ is the fuel gas cost, $\varepsilon_{k}$ is the treatment factor for sink k , $t c_{i}$ is the treatment cost for source $i, \gamma_{k}$ is the $\mathrm{CO}_{2}$ emission penalty by flaring, $\beta_{k}$ is the revenue from flexible sink, and $O C_{i k}$ is the equipment operating cost.

3.2. Objective function for retrofit case

Here, a new methodology for retrofit design of FGNs by integration of flare gas streams is developed. As there is a non-optimum FGN network in most refineries, new constraints should be defined and added in case of retrofit design. Binary variables Y are used to determine the existence of new connections and auxiliary equipments. When connections and auxiliary equipment on that connection exist, the binary variables are set to one and the respective capital cost is set to zero. It is clear that constraints (27) to (31) will be applied to model for the binary variables of one.
$F_{i k} \leq F_{i k}^{\max } * Y_{i k}^{p}$
$\Delta h_{i k}^{V} \leq \Delta h_{i k}^{V \max } * Y_{i k}^{V}$
$\Delta h_{i k}^{R} \leq \Delta h_{i k}^{R \max } * Y_{i k}^{B}$
$\Delta h_{i k}^{C} \leq \Delta h_{i k}^{C \max } * Y_{i k}^{C}$
$\Delta h_{i k}^{H} \leq \Delta h_{i k}^{H \max } * Y_{i k}^{H}$
where $Y_{i k}^{p}, Y_{i k}^{V}, Y_{i k}^{B}, Y_{i k}^{C}$, and $Y_{i k}^{H}$ are binary variables for existence of pipes, valves, compressors, coolers, and heaters between source stream i and sink k , respectively. Also, $F_{i k}^{\max }, \Delta h_{i k}^{\max }, \Delta h_{i k}^{\text {Rmax }}, \Delta h_{i k}^{\text {Cmax }}$, and $\Delta h_{i k}^{\text {Hmax }}$ are maximum allowable flowrate in pipes, maximum allowable enthalpy change across valve, compressor, cooler, and heater between source stream i to sink k .

While in the grass-root design, the objective function of TAC is
minimized to obtain the optimum network, savings and payback period after retrofitting of a current network are considered as objective functions for retrofit design. Equation (32) represents the relation between saving, payback, and investment.
payback $=\frac{\text { Investment }}{\text { Saving }}$
Investment is the capital cost of new pipes or any auxiliary equipment which is installed in retrofit design of network. To achieve the best FGN in retrofit design, the maximum saving at minimum investment on that change are considered. Therefore, net saving would be used as objective function to be maximized:

$$\begin{aligned} & \text { Net Saving }=\left(\sum_{m=1}^{M}\left(N G_{m}^{\text {old }}-\sum_{k=1}^{K} F_{m k}\right) * \alpha_{m}+\sum_{n=1}^{N}\left(T G_{n}^{\text {old }}-\sum_{k=1}^{K} F_{n k}\right)\right. \\ & * t c_{n}+\sum_{k=1}^{K}\left(h c_{k}^{\text {old }}-h c_{k}\right) * \gamma_{k}+\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{p} F_{i k}^{\text {old }} \\ & -\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{p} F_{i k}+\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{V} \Delta h_{i k}^{V, \text { old }} \\ & -\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{V} \Delta h_{i k}^{V}+\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{R} \Delta h_{i k}^{R, \text { old }} \\ & -\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{R} \Delta h_{i k}^{R}+\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{H} \Delta h_{i k}^{H, \text { old }} \\ & -\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{H} \Delta h_{i k}^{H}+\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{C} \Delta h_{i k}^{C, \text { old }} \\ & \left.-\sum_{i=1}^{I} \sum_{k=1}^{K} O C_{i k}^{C} \Delta h_{i k}^{V}\right) * O P H-I C^{*} A F \end{aligned}$$

The first three terms of the Equation (33) are savings obtained from natural gas consumption, total treated fuel gases, and gas flaring in the retrofit design compared to current design. In this expression, $N G_{m}^{\text {old }}, T G_{m}^{\text {old }}$, and $h c_{k}^{\text {old }}$ are natural gas consumption from $m$ sources, amount of fuel gases that should be treated from $n$ sources, and amount of fuel gases flared in the current design. Each next two terms are savings obtained by difference of operating costs between current and retrofit design for pipes and auxiliary equipment. Where $F_{i k}^{\text {old }}, \Delta h_{i k}^{V, \text { old }}, \Delta h_{i k}^{R, \text { old }}, \Delta h_{i k}^{H, \text { old }}$, and $\Delta h_{i k}^{C, \text { old }}$ are flow from source i to sink k , enthalpy change across valve, compressor, heater, and cooler in the current design. The last term is annualized capital cost of new installed equipment invested in the retrofit design. The investment cost is calculated as follows:

$$\begin{aligned} \text { Investment } & =\sum_{i=1}^{I} \sum_{k=1}^{K}\left(Y_{i k}^{p}+1\right) C C_{i k}^{p} F_{i k}+\sum_{i=1}^{I} \\ & =\sum_{k=1}^{K}\left(Y_{i k}^{B}+1\right) C C_{i k}^{B} \Delta h_{i k}^{B}+\sum_{i=1}^{I} \\ & =\sum_{k=1}^{K}\left(Y_{i k}^{V}+1\right) C C_{i k}^{V} \Delta h_{i k}^{V}+\sum_{i=1}^{I} \\ & =\sum_{k=1}^{K}\left(Y_{i k}^{H}+1\right) C C_{i k}^{H} \Delta h_{i k}^{H}+\sum_{i=1}^{I} \\ & =\sum_{k=1}^{K}\left(Y_{i k}^{c}+1\right) C C_{i k}^{c} \Delta h_{i k}^{c} \end{aligned}$$

Table 4
Flow distribution from sources to sinks in grass-root case $\left(\mathrm{m}^{3} / \mathrm{h}\right)$.

Table 5
Variable values in sinks in grass-root case.

In Equation (34), the first term represents capital cost of new pipes invested in the retrofit design. The next four terms corresponds to capital cost of new auxiliary equipment invested in the retrofit network. As mentioned, $\mathrm{Y}_{\mathrm{ib}}$ and $\mathrm{CC}_{\mathrm{ib}}$ for each pipe and auxiliary equipment is a ( $\mathrm{i} \times \mathrm{k}$ ) matrix. If any pipe or auxiliary equipment exists in the sub-stream from source i to sink k then the binary variable Y would set to one and the respective capital cost would set to zero.

Thus with three equations of net saving, investment, and payback and all constraints from grass-root design as well as constraints (27) to (31), we have formulated the integration of flare gas streams to FGN for retrofit design.

4. Solution methodology

The methodology includes maximizing Equation (33) with constraints (1) to (31) and then calculating investment and payback from Equations (32) and (34). The first part of the Equation (33) defines saving and the second part defines the investment cost for each feasible natural consumption in the network. By maximizing Equation (33) the saving is maximized and the investment

Table 8
Variable values in sinks in grass-root case with integration.

cost is minimized for that specified natural gas consumption. The feasible ranges of natural gas consumption is the key variable in the FGN model, which is defined as the range from minimum to current natural gas consumption without utilizing flare gas streams.

Subsequently, when net saving (Equation 33) is maximized for defined natural gas consumption, model variables will be determined and thus investment cost and payback are calculated from Equations (32) and (34). When plotting these results (saving, investment, payback vs. natural gas consumption), each point represents a different network with different flare gas stream utilization. As it is obvious less natural gas consumption means more utilization of flare gas.

Now we have completed our NLP models formulation for both grass-root and retrofit design for FGNs. These models are solved using commercial software.

5. Case study

Now, our modified model is applied to a live refinery as case study for both grass-root and retrofit design. In the grass-root case,

Table 6
Variable values in sinks in grass-root case.

Table 7
Flow distribution from sources to sinks in grass-root case with integration $\left(\mathrm{m}^{3} / \mathrm{h}\right)$.

Table 9
Economic data of comparison between 3 scenarios.

Fig. 2. Current network of refinery case study.
a FGN of the refinery is designed considering available waste and fuel gas source streams. Then, the flare gas stream is integrated with the FGN to find the optimum network. At the second level, the retrofit design of the refinery current fuel gas system is considered.

5.1. Grass-root case

The refinery has five waste fuel gas source streams and a flare stream which is aimed to integrate with other source streams to make an optimum FGN. S1-S4 are waste gas streams from Visbreaker, Amine, Naphta hydrotreating, Catalytic reforming, Hydrogen, Hydrocracking units in the refinery, S5 is natural gas which is an external fuel gas and we wish to consume it as low as possible and FS is the stream which is normally flared. It should be noted that waste gas streams from visbreaker, naphta hydrotreating, and hydrocracking are converted to one main stream after being treated.

Our case study has nine fuel sinks. C1-C7 are furnaces in different units, C8 is sum of all boilers within the units and C9 is flare sink. Tables 1 and 2 show the data and parameters of source and sink streams, which has been extracted from process flow diagram of refinery fuel gas system. Table 3 represents the cost parameters for different equipments. The annualization factor and working hours for plant are considered $10 \%$ and 8000 h .

5.1.1. Impact of FGN model

Our model is now solved to obtain an optimal network. Note that flare stream (FS) is not entered to the model in this stage. Tables 4 and 5 show the flow distribution from sources to sinks and calculated variables for sinks. From Table 5, we can see that all model variables are in the allowable ranges of sinks.

Table 6 compares the natural gas consumption and TAC of base scenario with the designed optimum FGN. We consider a base scenario with no FGN, which natural gas is the only source stream and other waste gases are normally sent to flare. Hence, the optimal FGN for this case indicates $89 \%$ reduction in flaring amount and $90.6 \%$ reduction in flaring emission penalty.

5.1.2. Impact of integration of flare gas stream in FGN

Again, our model is solved to obtain an optimal network with flare gas stream integrating to the network. Data and parameters

Table 10
Data and parameters for sources in retrofit case.

Table 11
Summary of results in retrofit case.

Fig. 3. Optimal fuel gas network for retrofit case.
for sources and sinks are depicted in Tables 1 and 2. Note that flare stream (FS) in Table 1 is entered to the model as a source stream. Tables 7 and 8 show the flow distribution from sources to sinks and variable values in sinks. Table 8 illustrates that model variables are in the allowable ranges of sinks.

Note that our optimal FGN uses valves and other equipment which is not required in this case. TAC for this case is $\$ 79,802,440$ including $\$ 79,198,420$ for operating costs and $\$ 604,020$ for capital costs. Natural gas fuel cost includes a significant part of operating costs. We consider a base scenario with no FGN, to calculate savings from the optimal FGN, which natural gas is the only source stream and other waste gases are normally sent to flare.

Table 9 shows the results of economic comparison between three cases of base scenario, designed FGN without flare gas stream and integration of flare gas stream with FGN. Integration of flare gas stream to FGN saves $\$ 30,637,014$ compared to the base scenario (27.7%). Also, natural gas consumption has been reduced to $51,786 \mathrm{~m}^{3} / \mathrm{h}$ showing $31.6 \%$ reduction compared to the base

Table 13
Variable values in sinks for retrofit case.

scenario. TAC shows 6,473,570 $/y reduction (8%) due to integrating flare gas stream with FGN compared to the second case. This is owing to high impact of operating cost rather than capital cost in TAC. Cost of supplying natural gas in addition to other waste fuel gas streams for satisfying network sinks is an important factor in the network operating cost. Natural gas consumption shows 12% reduction as the flare gas stream integrates with the FGN. As indicated in Table 9, our proposed FGN shows $89 \%$ reduction in flaring amount and $90.6 \%$ reduction in flaring emission penalty due to utilization of waste and flare streams though it remains at its minimum limit in both two last scenarios.

5.2. Retrofit case

For the retrofit case, a live existing FGN with no flare gas integration is considered (Fig. 2). As illustrated in Fig. 2 three gas streams from VISB, NHT, HCR units after treatment are mixed with gas streams from Amine, CCR, Hydrogen units and finally natural gas is added to form a unit fuel gas stream to supply different sinks.

To retrofit, the natural gas stream from the final fuel gas mixture is omitted and considered as a single source stream. Also, flare gas stream is entered to the network as another source stream. Hence, there will be three fuel gas source streams consisting of a mixture of waste streams from units, natural gas, and flare gas. Table 10 gives the flows, pressures, temperatures, and specifications for the three source streams for the retrofit case. Fuel gas sinks and the cost data parameters previously presented are used in retrofit case. However, the capital costs of existing pipe connection are set to zero.

Table 12
Flow distribution from sources to sinks in retrofit case $\left(\mathrm{m}^{3} / \mathrm{h}\right)$.

The feasible range of natural gas consumption for the current FGN is between $51,786 \mathrm{~m}^{3} / \mathrm{h}$ (minimum flowrate using the whole flare gas recovery) and $58,828 \mathrm{~m}^{3} / \mathrm{h}$ (flowrate of the current network). The summary of results for selected amounts of natural gas consumptions are shown in Table 11, where each network is an economically optimal solution (maximum net saving in Equation (33)).

One can conclude that if there is no limitation in investment cost, maximum utilizing of flare gas stream can be the most profitable solution.

Fig. 3 shows the retrofit network for complete use of flare gas stream in the FGN. Tables 12 and 13 represent the flow distribution from sources to sinks and variable values in sinks.

Fig. 3 depicts the network configuration is set to satisfy all sinks quality demands. For instance, due to lower heating value of TFG stream that is $29.82 \mathrm{MJ} / \mathrm{m}^{3}$, which is lower than lower heating value limits of all sinks ( $30 \mathrm{MJ} / \mathrm{m}^{3}$ ), the model has to use other source streams (NG, FS) in order to increase the quality of heating value in each sink. This can be obviously illustrated in sink C4. However, for sink C9 which its lower heating value limit is 12, TFG source stream easily satisfies its demand. Also, another reason that model uses this source stream in the flare sink, is due to its carbon content which is lower than two other source streams. It results lower flaring penalty based on constraint (25) in the retrofit network.

Note that considering network configuration in retrofit and current networks (Figs. 2 and 3), no investment cost is calculated between fuel gas drum and different sinks for piping owing to reusing fuel gas drum in retrofit network. This is due to defining parameter Y in constraints (27) to (31).

6. Conclusions

In this work, flared gas stream is integrated to FGN including waste and fuel gas streams. The base FGN model proposed by Hasan et al. in grass-root design is modified through adding some constraints in $\mathrm{CO}_{2}$ emissions by flaring. This term in TAC can help reduce GHG emissions and flaring penalties as much as possible. Also, a profit-based retrofit model is proposed for integration of flare gas streams in FGNs. The refinery case study proved that by utilizing flared gas stream to the network, our optimal FGN can reduce energy costs and flaring emissions.

Nomenclature

Indices

i fuel source
j pools
k fuel sinks

Parameters

$D_{k}$
energy demand of sink $k$
$F_{i}$
available flow of source stream $i$
$F_{i}^{L}$
minimum flow rate of source $i$
maximum flow rate of source $i$
maximum allowable flowrate in pipes
minimum allowable flow to sink $k$
maximum allowable flow to sink $k$
amount of fuel gases flared in the current design
hydrocarbon dew point of sink $k$
lower heating value of source stream $i$
minimum allowable lower heating value of sink $k$
maximum allowable lower heating value of sink $k$
moisture dew point of sink $k$
molar volume conversion factor
molecular weight of flare gas
adiabatic compression coefficient
sum of natural gas consumption from $m$ sources
operating cost of compressor from source $i$ to sink $k$
operating cost of cooler from source $i$ to sink $k$
operating cost of heater from source $i$ to sink $k$
operating cost of pipe from source $i$ to sink $k$
operating cost of valve from source $i$ to sink $k$
pressure of source $i$
pressure of source $k$
minimum allowable pressure of sink $k$
maximum allowable pressure of sink $k$
mole fraction of alkane composition in the fuel gas source stream $i$
gas constant
specific gravity of source $i$
minimum allowable specific gravity of sink $k$
maximum allowable specific gravity of sink $k$
temperature of source $i$
minimum allowable temperature of source $i$
maximum allowable temperature of source $i$
minimum allowable temperature of sink $k$
maximum allowable temperature of sink $k$
treatment cost for source $i$
amount of fuel gases treated from $n$ sources
minimum allowable Wobbe Index of sink $k$
maximum allowable Wobbe Index of sink $k$
binary variable for existence of compressor from source $i$
to sink $k$
binary variable for existence of cooler from source $i$ to
sink $k$
binary variable for existence of heater from source $i$ to
sink $k$
binary variable for existence of pipe from source $i$ to sink $k$
binary variable for existence of valve from source $i$ to sink $k$
maximum allowable enthalpy change across compressor
maximum allowable enthalpy change across cooler
maximum allowable enthalpy change across heater
maximum allowable enthalpy change across valve
enthalpy change across compressor in current design
enthalpy change across cooler in current design
enthalpy change across heater in current design
Variables
$\mathrm{CO}_{2} \quad \mathrm{CO}_{2}$ emissions
flow from source $i$
Fuel gas flow in sub-stream $S S_{ik}$
heat content of fuel gas stream from source $i$ to sink $k$
total $\mathrm{CO}_{2}$ emissions in flare sink

$L H V_{k} \quad$ lower heating value of sink $k$ pressure of sink $k$ specific gravity of sink $k$ temperature of sink $k$ enthalpy change through compressor enthalpy change through cooler enthalpy change through heater enthalpy change through valve

References

[1] Elvidge CD, Ziskin D, Baugh KE, Tuttle BT, Ghosh T, Pack DW, et al. A fifteen year record of global natural gas staring derived from satellite data. Energies 2009;2:595-622.
[2] BP. BP statistical review of world energy June 2010. 2010. Available at: www. bp.com/statisticalreview.
[3] Johnson MR, Coderre AR. An analysis of staring and venting activity in the Alberta upstream oil and gas industry. J Air & Waste Manag Assoc 2011;61(2): 190-200.
[4] Rahimpour MR, Jamshidnejad Z, Jokar SM, Karimi G. A comparative study of three different methods for stare gas recovery of Asalooye gas refinery. J Nat Gas Sci Eng 2012;4:17-28.
[5] The World Bank Group. Kyoto mechanisms for staring reductions. Report no. 2. Washington, DC: World Bank. See also: www.wds.worldbank.org/external/ default/main?pagePK–64193027&piPK–64187937&theSitePK–523679& menuPK–64187510&searchMenuPK–64187283&siteName–WDS& entityID–000160016_20031231101644, (Accessed 08.11.15).
[6] International Energy Outlook. Washington, DC: U.S. Energy information administration; 2008.
[7] Hu JL, Kao CH. Efficient energy-saving targets for APEC economies. Energy Policy 2007;35(1):373-82.
[8] Lunghi P, Burzacca R. Energy recovery from industrial waste of a confectionery plant by means of BIGFC plant. Energy 2004;29(12-15):2601-17.
[9] Mani M, Nagarajan G. Influence of injection timing on performance, emission and combustion characteristics of a DI diesel engine running on waste plastic oil. Energy 2009;34(10):1617-23.
[10] Al-Salem SM. Carbon dioxide $\left(\mathrm{CO}_{2}\right)$ emission sources in Kuwait from the downstream industry: critical analysis with a current and futuristic view. Energy 2015;81:575-87.
[11] Volshund M, Nguyen T, Elmegaard B, Ertesvag IS, Rosjorde A, Jossang K, et al. Exergy destruction and losses on four North Sea offshore platforms: a comparative study of the oil and gas processing plants. Energy 2014;74: $45-58$.
[12] Morrow III WR, Marano J, Hasanbeigi A, Masanet E, Sathaye J. Efficiency improvement and $\mathrm{CO}_{2}$ emission reduction potentials in the United States petroleum refining industry. Energy 2015;93:95-105.
[13] Jou CG, Wu C, Lee C. Reduction of energy cost and $\mathrm{CO}_{2}$ emission for the furnace using energy recovered from waste tail-gas. Energy 2010;35(3): $1232-6$.
[14] Liu X, Chen D, Zhang W, Qin W, Zhou W, Qiu T, et al. An assessment of the energy-saving potential in China’s petroleum refining industry from a technical perspective. Energy 2013;59:38-49.
[15] Ptasinski KJ, Koymans MN, Verspagen HHG. Performance of the Dutch energy sector based on energy, exergy and extended exergy accounting. Energy 2006;31(15):3135-44.
[16] Persson J, Berntsson T. Influence of seasonal variations on energy-saving opportunities in a pulp mill. Energy 2009;34(10):1705-14.
[17] Worrell E, Price L, Martin N. Energy efficiency and carbon dioxide emissions reduction opportunities in the US iron and steel sector. Energy 2001;26(5): $513-36$.
[18] Zargarzadeh M, Karimi IA, Alfadala H. A tool for online exergy analysis. In: Presented at the 17th European symposium on computer aided process engineering (ESCAPE 17), Bucharest, Romania, May 27-30; 2007.
[19] Hasan MMF, Karimi IA, Avison CM. Preliminary synthesis of fuel gas networks to conserve energy & preserve the environment. Ind. Eng Chem Res 2011;50: $7414-27$.
[20] De Carli A, Falzini S, Liberatore R, Tomei D. Intelligent management and control of fuel gas network. In: IEEE; 2002. p. 2921-6.
[21] Wicaksono DS, Karimi IA, Alfadala HE, Al-Hatou OI. Optimization of fuel gas network in an LNG plant. In: 689 g (10A06), presented at the AIChE annual meeting, san Francisco, CA, Nov 12 - 17; 2006.
[22] Wicaksono DS, Karimi IA, Alfadala HE, Al-Hatou OI. Integrating recovered jetty boil-off gas as a fuel in an LNG plant. In: TS-201, presented at the 17th European symposium on computer aided process engineering, Bucharest, Romania, May 27 - 30; 2007.
[23] Jagannath A, Hasan MMF, Al-Fadhli FM, Karimi IA, Allen DT. Minimize flaring through integration with fuel gas networks. Ind. Eng Chem Res 2012;51: $12630-41$.
[24] Kovacs VB, Meggyes A. Investigation of utilization of low heating value gaseous fuels in gas engine. In: PS17, presented at the European combustion meeting, Vienna, Austria, Apr 14-17; 2009.
[25] Elliot FG, Kurz R, Etheridge C, O’Connell JP. Fuel system suitability considerations for industrial gas turbines. J Eng Gas Turbines Power 2004;126:119-26.
[26] Report GEI 41040G- Specification for fuel gases for combustion in heavy-duty gas turbines. Atlanta, GA: GE Power Systems; Revised 2002.
[27] 40 CFR 98.253-Calculating GHG Emissions. Cornell university law school. Legal Information Institute. Available at: www.law.cornell.edu/cfr/text/40/98. 253 (accessed 08.11.15).