Optimisation of gas mixture injection for enhanced coalbed methane recovery using a parallel genetic algorithm

Journal of Natural Gas Science and Engineering 33 (2016) 942e953

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Optimisation of gas mixture injection for enhanced coalbed methane recovery using a parallel genetic algorithm Mohammad Sayyafzadeh a, Alireza Keshavarz b, * a b

The University of Adelaide, Australian School of Petroleum, Australia CSIRO, Energy Business Unit, Australia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 February 2016 Received in revised form 25 May 2016 Accepted 13 June 2016 Available online 15 June 2016

Gas injection in coalbed Methane reservoirs is an environmentally friendly and economically viable enhanced recovery technique. Promising results can be obtained by injecting a mixture of CO2 and N2. The optimum composition is a function of geomechanical and sorption characteristics of the coal. In the current study, it is sought to optimise the composition of the injected gas, based on an economic objective function. The decision variables are the composition of the injected gas and the injection rate that can be both subjected to change over a continuous injection. In the formulated objective function, the OPEX costs (e.g., separation, compression for injection and injectant supply) and the income, resulting from, CH4 production and CO2 sequestration are considered. This optimisation problem is nonlinear, and the corresponding search space is high-dimensional. Therefore, a sophisticated optimisation algorithm is required. For this study, a parallel real-value genetic algorithm is coded in MatLab and coupled to a commercial coalbed simulator (ECLIPSE-E300). This interface allows us to measure the goodness of each solution-candidate and also to perform optimisation automatically. The algorithm is used to optimise rates and compositions of a semi-synthetic ECBM case study, and the optimum scenario is compared with the optimum scenario of a constant composition injection. The comparison confirms that a varying-composition strategy results in more revenue from an ECBM project. In this study, also, the optimum solution for different economic conditions are approximated and then the optimum solutions are compared with each other to investigate the effect of carbon credit and Methane price on the injection schedule. In those economic conditions that carbon credit is higher than CO2 supply costs, the optimum scenarios tend to yield a higher amount of sequestrated CO2, and in all of them, the optimum schedules are the ones that start with a very low fraction of CO2 in the injected gas and continue by a gradual increase of CO2 fraction. In other economic conditions, the optimum scenarios move towards the ones that less CO2 is injected. © 2016 Elsevier B.V. All rights reserved.

Keywords: ECBM Varying composition injection Optimisation CO2-sequestration Genetic algorithm Coalbed

1. Introduction Coalbed Methane (CBM) reservoirs are naturally fractured rocks, consisting of cleats and matrix (Gray, 1987; Gamson et al., 1996; Palmer, 2010; Seidle, 2011; Keshavarz et al., 2014, 2015). The micropores of coal matrix are the major sites for the storage and can hold a considerable amount of gas in the adsorbed phase on the walls of the pores (Gamson et al., 1996; Gilman and Beckie, 2000; Xu et al., 2013a,b; Verma and Sirvaiya, 2016). This storage

* Corresponding author. CSIRO, Energy Business Unit, 11 Julius Ave, North Ryde, NSW, 2113, Australia. E-mail address: [email protected] (A. Keshavarz). http://dx.doi.org/10.1016/j.jngse.2016.06.032 1875-5100/© 2016 Elsevier B.V. All rights reserved.

characteristic distinguishes CBM from the conventional reservoirs in which gas is trapped mostly in the free state (Seidle, 2011). Coal matrixes are typically enclosed by a cleat system and the bedding planes, and do not contribute directly into the flow to the wellbore (Seidle, 2011; Palmer, 2010; Clarkson et al., 2010). Gas can only flow to the neighbouring cleats, via diffusion (Staib et al., 2015a,b). In contrast with the matrix, cleats are well-connected through two sets of perpendicular fractures, face and butt cleats (Paul and Chatterjee, 2011a,b), which create a decent connection between the wellbore and the reservoir (Clarkson et al., 2010). The cleats are usually filled with water at the initial condition, and this creates the sufficient pressure (usually equal to hydrostatic pressure) to avoid the discharge of gas from the matrix.

M. Sayyafzadeh, A. Keshavarz / Journal of Natural Gas Science and Engineering 33 (2016) 942e953

At the primary stages of production, (known as dewatering), only water is produced, and meanwhile the reservoir pressure declines. This pressure drawdown leads to the liberation of gas from the matrix, once the reservoir pressure falls below the equilibrium pressure corresponding to the gas content. The desorbed gas diffuses from the matrix to the cleats, and then flows, along with the remaining water, from the cleats to the wellbore (Seidle, 2011). The gas rate increases, by the reduction of water-in-place, and the two-phase flow continues until the water saturation falls below the residual saturation (Seidle, 2011). After that, there will be a single-phase flow of gas, until the reservoir pressure reaches the abandonment pressure. This process is known as the natural depletion and is not expected to result in more than 50% gas recovery (Puri and Yee, 1990). To enhance the recovery and improve the production rate, the reservoir pressure should be maintained and simultaneously the Methane partial pressure gradient, between cleats and matrix, increases. This can be obtained by a continuous injection of a foreign gas into the coal, known as enhanced coalbed Methane (ECBM). The injected gas sweeps Methane in the cleats, resulting in Methane partial pressure drop (which accelerates desorption), while maintains the reservoir pressure, keeping the cleats open. Several laboratory, simulation, pilot and field studies have shown that CO2 (Carbon Dioxide) injection can increase Methane recovery (Fulton et al., 1980; Sinayuç and Gümrah, 2009; Stevens et al., 1998), and has carbon sequestration benefits (Wong et al., 2000). In such a technique, there is a major problem, cleats closure due to matrix swelling (Durucan and Shi, 2009; Durucan et al., 2009). Mazzotti et al. (2009) measured the changes of cleats volume, by exposing coal samples to different gases (CO2, N2, CH4 and He), the results indicated that the coal is swollen more severely by CO2 in comparison with the others, which is because of greater affinity of coal towards CO2 (Fulton et al., 1980; Moore, 2012; Fang et al., 2013). As a result of this fact, the well injectivity might lessen by two orders of magnitude (Durucan and Shi, 2009). Another set of studies have shown that a rapid production rate enhancement can be achieved by N2 (Nitrogen) injection (Reeves and Oudinot, 2004; Perera et al., 2015). However, an early N2 breakthrough was observed, which degrades the quality of the produced gas (Reeves and Oudinot, 2004; Zhou et al., 2013a). The quick increment of production rate is due to the improvement of well injectivity (Shi et al., 2008). Shi and Durucan (2005) conducted a micro-pilot study in the Fenn Big Valley to analyse the effect of CO2/N2 mixture on ECBM performance, and the investigations indicated that flue gas (a mixture of N2 and CO2) injection results in a better performance, compared to pure N2 and CO2. Durucan and Shi (2009) also carried out a simulation analysis on a similar subject, and it was concluded that injecting a mixture of 13% CO2/87% N2 through a continuous injection would result in the highest Methane recovery, while the quality of produced gas is not degraded significantly and well injectivity does not decline sharply. In a recent study (Sayyafzadeh et al., 2015), it has been shown that the performance (recovery and also production rate) of mixture gas injection can be improved by applying a varying composition strategy, throughout a continuous injection of N2/CO2 mixture. A series of sensitivity analyses were performed to find an optimal scenario. The results of the optimum scenario then were compared with the outcomes of the optimum scenario of fixed composition gas injection. The criterion of comparison was the ultimate Methane recovery, and therefore, by executing a few scenarios, an optimum for each strategy could be approximated. To have a better criterion for the comparison, in this study, an economic objective function (net-present-value) is defined to measure the goodness of the ECBM scenarios (fixed composition

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injection and varying composition injection). In the objective function, the following terms are taken into consideration: ultimate Methane recovery, ultimate Carbon sequestration, compression costs, separation costs, injectant supply costs and a discount rate which takes into account the effect of production/injection rates. Because of the number of elements impacting the fitness value of the scenarios and due to the nonlinearity of the function, the optimum scenario cannot be found with a simple sensitivity analysis. Hence, an optimisation algorithm is implemented. For this study, a real-value parallel genetic algorithm is coded in MatLab (Matlab, 2013a) and coupled to a commercial coalbed simulator (ECLIPSEE300) (Schlumberger, 2013), to find the optimum scenario, for a semi-synthetic case study. Genetic algorithm has a long history in oil and gas industry and thus far, different forms of genetic algorithm have been used in research studies (Sayyafzadeh et al., 2012, Salmachi et al., 2013; Sayyafzadeh, 2015b; Romero and Carter, 2001; Velez-Langs, 2005). In the current study, the effect of gas price and carbon sequestration credit on the optimum point (the best injection schedule) is also investigated. In the next section, decision variables, modelling, objective function formulation and optimisation are explained. Model description section presents the details of coal and gas characteristics used for building the simulation-model. In the results and discussion section, the outcomes of the proposed method are presented and analysed. In the last section, some conclusive remarks are given.

2. Methodology In order to find an economically optimal gas injection scenario for an ECBM project, the following steps should be done: i-defining the decision variables and the feasible region of the corresponding search space, ii-integrating a numerical simulation into a programming language, in order to deliver forecasts for each scenario and extract the required data from the simulation output, automatically, iii-formulating an objective (fitness) function to quantitatively distinguish among the scenarios (solution-candidate), based on the extracted data and iv-designing an optimisation algorithm to search the solution space, for the best scenario (i.e., to approximate the global optimum point of the formulated function). For this study, a real-valued genetic algorithm (GA), as a common evolutionary optimisation algorithm, is coded and utilised. These steps are explained, in details, in the following subsections.

2.1. Defining the decision variable In the current work, it is sought to investigate which strategy results in more revenue from an ECBM project, varying the composition of injectant, through a few practically feasible steps (nt), or a constant composition injection. To answer this question, nt decision variables per injector should be defined (as the alterations are step-wise) to represent the percentage of CO2 in the N2/CO2 mixture injection in each step. The minimum and maximum of these variables are zero and one, respectively. In addition to the injectant composition, the injection rate in each of these steps, through controlling well bottomhole pressure, are considered as decision variables, in order to increase injection flexibility. The range of possible values for this set of variables is from the hydrostatic head (i.e., no flow) to a pressure lower than fracing pressure (pf). The decision variables are summarised in Table 1, for a reservoir with a pair of wells. The corresponding search space is a bounded 2nt dimensional continuous space, and X is a point in this space.

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Table 1 Decision variables. X

Decision variables (DV)

min

Max

Variable x1 … xnt Variable x(ntþ1) … x2nt

CO2 composition of injectant Bottomhole pressure of injector

0 patm þ ph

1



’ X ¼ x1 ; …; x2nt

(1)

To simulate ECBM, a compositional simulation is required in which Nc þ 1 continuity equations (each component plus water) are solved, Equation 2 (for each component, i) and 3 (for water) (King et al., 1986). It is assumed that gas does not dissolve in water phase.

V$ rg yi

kkrg

mg

VФg

 v rg yi 4Sg  Mg qi ¼ 0  vt

  kkr v V$ rw w VФw  ðrw 4Sw Þ  Mw qw ¼ 0 vt mw

(2)

(3)

Peng-Robinson model, Equation 4, is applied, as the equation of state, to relate gas properties to pressure and composition (Zhu et al., 2003).

p¼

RT aa  2 Vm  b Vm þ 2bVm  b2 which a ¼

In

0:457235R pC

2

Tc2

(4)

c b ¼ 0:077796RT , a ¼ ð1 þ kð1  Tr0:5 ÞÞ2 Pc

andk ¼ 0:379642 þ 1:48503uj  0:164423u2j þ 0:016666u3j .

For

gas viscosity, Lorentz-Bray-Clark method (Lohrenz et al., 1964) is P used, ½ðm  m0 Þx þ 104  ¼ ð 5i¼1 ai bi1 Þ4 . r To model fluid flow in coal rocks, a dual-porosity model (Warren and Root, 1963) is usually applied (Huy et al., 2010; Cui and Bustin, 2005), in which the following assumptions distinguish it from a regular dual-porosity model: i-gas in the matrix is in adsorbed phase, ii-the gas content in the matrix is defined by concentration, iii-matrix’s permeability is zero, iv-the flow between matrix and cleats is govern by diffusion, and v-water cannot flow into the matrix. In the dual-porosity model, the continuity equations have an additional sink/source term that corresponds to the flow between cleats and matrix, denoted by qmci. In the equilibrium condition, the gas content of each component (Vi) on the coal matrix is a function of partial pressure of that component in cleats (pi ¼ yip) and sorption characteristics of coal, defined by extended Langmuir isotherm, Equation 5 (Zhou et al., 2013a). Coal affinities to different components are described using the Langmuir constants.

Vi ¼ VLi

pyi PLi

1þ

PNc

pyj j¼1 PLj

(5)

aDci ðmsi  Vi rcoal Þ s

Dε ¼

Nc X k¼1

cm

40

ðp  p0 Þ þ

1



40

  K  1 ðDεÞ M

(7)

(6)

The other important characteristic of coal is the change of cleat

Nc X εk bk ak p εk bk ak p0  P c PNc bap 1 þ j¼1 bj aj p k¼1 1 þ N j¼1 j j 0

(8)

As generally agreed, the cleat permeability is proportional to the cube of cleat porosity (van Golf-Racht, 1982; Khanna et al., 2013; Keshavarz et al., 2016)

k ¼ k0



4 40

3 (9)

ECLIPSE-E300 is used as the coalbed simulator, and coupled to MatLab. This integrated interface allows us to evaluate each solution-candidate automatically (i.e., it can generate the ECLIPSE input data file, call the simulator, read the output of and extract the required data), (Sayyafzadeh, 2013). 2.3. Objective function formulation The task of an objective function is to measure the goodness of solution-candidates. In this study, an economic objective function is formulated in which all the typical operational expenditure (OPEX) costs of an ECBM project are included, such as gas compression for injection, injectant supply and separation of Methane from the produced gas, if Methane-cut is below a predefined value. The incomes are from produced Methane and Carbon credit, as a result of CO2 sequestration. To calculate the future cash flow (CF) for each year (j), the following data are required: cumulative produced CO2, N2 and CH4 (Qp), cumulative injected CO2 and N2 (Qi), and average Methane-cut (Zhou et al., 2013b).

   CFj ¼ $CH4 QpCH4j þ $CO2credit QiCO2  QpCO2  $comp QiCO2 þ QiN2 j j    $sep Qptotal  $CO2 QiCO2  $N2 QiN2 j

j

j

(10) Qptotal is the summation of cumulative produced CH4, CO2 and N2. A quicker depletion of the seam(s) is favourable, if having a positive discount rate. Therefore, net-present value is used, as the objective function. Net present value is calculated using Equation 11.

0

Fick’s law, Equation 6, represents the flow between matrix and cleats (qmci), in which the flow rate of each component is proportional to corresponding concentration gradient and the diffusion coefficient (King et al., 1986).

qmci ¼





4 p; y1 ; ::; yNc ¼ 40 1 þ

Dε is total volumetric strain which is calculated using Equation 8.

2.2. Numerical simulation of fluid flow in coal seams

!

porosity with the alteration of effective stress and the amount of adsorbed gas. Palmer-Mansoori model (2010), Equation 7, is a model that can describe this phenomenon, with the assumption that overburden and horizontal stresses are constant. Cleat porosity at pressure p with the composition of y1, …,yNc can be calculated as follow:

NPV ¼ @

( T X j¼1

CFj

ð1 þ DRÞj

)

1  $CAPEX  $OPER A 

( T X j¼1

)

CFj

ð1 þ DRÞj (11)

Capital expenditure (CAPEX) costs and $OPER (e.g., well maintenance and other operational costs) are the same for any solution candidate (injection scenario). CAPEX costs are the same, because it is assumed that the decision for executing an ECBM project is

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already made, and it is going to take place with a specific capital expenditure. With this assumption, the optimisation can be emphasised on the following questions, which of the strategies (varying composition or constant composition) yields to more revenue and which scenario in each strategy is the optimum. $OPER is the same for each scenario, because the number of wells and the production duration are the same. Therefore, $CAPEX and $OPER are constant and do not impact the solution of the optimisation, accordingly they are removed, for simplification. The output is presented in a vector form, as below:

h dcal ¼ QpCH41 ; …; QpCH4T ; QpCO21 ; …; QpCO2T ; QpN21 ; …; QpN2T ; QiCO2 ; …; QiCO2 ; QiN2 ; …; QiN2 ’ A simulation should be 1 T 1 T executed, to obtain dcal vector, for each strategy (X). g represents the simulator and W is the simulation-model, which is assumed known and unique. dcal ¼ gðX; WÞ

(13)

As it can be seen, NPV is a function of X (NPV ¼ NPV(X)). NPV function is expected to be highly nonlinear and multi-modal. For such a function, a stochastic optimiser can deliver better results, as they visit the search space randomly for finding the global optimum. 2.4. Genetic algorithm In this study, a real-value genetic algorithm is applied. The general procedure is explained below, and then the applied operators and the way of parallel implementation are explained in the next paragraph. A genetic algorithm begins with a generation of a set (known as population) of individuals (known as chromosomes) using an initialisation procedure. All the individuals are evaluated based on an objective (fitness) function. After the evaluation of the initial individuals, the main loop of the algorithm starts. In each step (known as generation) of the main loop, a sub-set of the current population is picked using a selection operator, conducted according to the fitness of individuals. A mating operator, called crossover, is applied with probability pc to the selected set of individuals and a new set of individuals is produced. The new set of individuals is recombined with the current population and then the mutation operator is applied with probability pm to the recombined set. The new set generated by the selection, crossover, recombination and mutation creates a new population, with the same number of individuals. All the individuals of the new population are evaluated. In order to keep the best ever found solution(s), the fitting individuals (known as elites) from the previous population are migrated directly to the new population. This loop is repeated until the predefined stopping criteria are met (Sayyafzadeh et al., 2012). In this study, the following operators are used: i-a tournament with size of 2, ii-a heuristic crossover with ratio of 1.2, iii-a uniform mutation (in which two randomly selected genomes of the randomly selected individuals are mutated and replaced by a constrained random number) and iv-a random recombination. The stopping criterion is the number of generations. Table 2 summarises the configurations of the applied GA. Fig. 1 shows the

Fig. 1. Genetic algorithm workflow.

workflow. This algorithm has been validated using a few benchmarking functions (Sayyafzadeh, 2015a). It should be mentioned that each optimisation is executed twice with two different seed

Table 2 GA properties. Population size (Npop)

Stopping criteria

Mutation probability

Crossover probability

Number of elites

Tournament size (Ntour)

80

Nogen < 125

pm ¼ 0.35

pc ¼ 0.95

5

2

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numbers, and the best result of the two runs is used. A relatively large number of generations is used to search the space properly to increase chance of approximation of the global optimum. In genetic algorithms, it is straightforward to execute the optimisations on clusters with parallel evaluation of the individuals, in each generation, on several cores (depending on software and hardware availability), as the individuals do not have interaction and generated independently, in each generation. This can be of great importance, in terms of optimisation-time reduction. For this study, a workstation with dual Xeon CPUs (total 8 cores with 16 threads) is used. Using the parallel toolbox of MatLab, the individuals of each population are evaluated in 10 batches; each batch, 8 simultaneous simulations on 8 cores, Fig. 2. This can reduce the time of optimisation almost 8 times.

3. Model description A synthetic coalbed model was constructed by Law et al., 2002 to study ECBM. A similar simulation-model is used, in this study. A rectangular coal, 200 m  200 m, with a uniform thickness of 5 m is built. The dip angle of the seam is zero degree, and the reservoir depth is 775.5 m. All the boundaries are assumed no-flow, and the seam is assumed thermally isolated and the injection/production does not change the temperature. Cleat permeability is homogenous and isotropic. The compressibility of the coal is assumed to be reversible without hysteresis. Table 3 summarises the coal characteristics taken from different references. The cleats are initially saturated with water. The relative permeability tables used in this study can be found in the following articles (Gash, 1991; Law et al., 2002). As shown in Fig. 3, two vertical wells, injector (‘I’) and producer (‘P’), are located at two corners of the seam (one quarter of a 5-spot pattern). It is assumed the skin factor of wells is zero. There are 21  21  1 gridblocks in x,y and z direction, which are duplicated (dual-porosity). The following economic and operational constrains are applied, in order to assure the comparison study is reliable: i-the minimum gas production rate is 50 Sm3/day, ii-the bottomhole pressure of the injector cannot exceed 125 bars (fracing pressure), iii-the bottomhole pressure of the wells cannot fall below 3 bars (hydrostatic head), and iv-the maximum gas injection rate is 5000 Sm3/day. The injection of a foreign gas in all scenarios starts after almost 90 days and ends after almost 5 years.

Fig. 2. Parallel evaluation.

4. Results and discussions Sayyafzadeh et al. (2015) proposed a new strategy for improving gas production from CBM reservoirs by optimising the composition of injected gas through a continuous injection of N2/CO2 mixture. They showed that: 1. for both constant and varying composition injection strategies there is an optimum composition of injected gas by which the maximum Methane is produced, and 2. the optimum scenario of a varying composition injection strategy produces more Methane, compared to the optimum scenario of a constant composition strategy. The optimum injection scenarios were achieved based on only one objective, Methane recovery, and the rests of economic constrains and the revenue resulting from sequestrated CO2 were not taken into consideration. In order to find a more realistic optimum injection scenario and deliver a better comparison, there is a need to apply an optimisation tool to maximise the revenue by maximising both produced Methane and sequestrated CO2 for a certain economic condition and minimising all the OPEX costs. In this section, the first aim is to find the optimum composition of injected gas in both constant and varying strategies using the developed optimisation tool. Comparing the optimum scenarios in two strategies for a given economic condition helps us to assess the method. The second goal is to find the optimum composition of injected gas, for different economic conditions. Economic conditions are developed, based on the typical values for gas compression cost at injector, N2 separation cost at producer, injectant (CO2 and N2) supply cost, including capturing and transporting cost, and discount rate (Zhou et al., 2013b) and a typical range for both Methane price and carbon credit (Table 4). In all the cases, the operational costs are assumed to be the same (see Section 2.3), while Methane price and carbon credit are different in the ranges provided in Table 4. For each economic condition, the optimisation tool explained in Section 2 is used to find the optimum composition. It should be mentioned that the separation cost is applied when Methane composition in the produced gas falls below 90%. In Subsection 4.1, the optimum scenario of a constant composition injection strategy is found and compared to the optimum scenario of varying composition strategy, in the same economic condition. In Subsection 4.2, several economic conditions are defined to evaluate the effect of carbon credit on gas production, CO2-sequestration, the optimal solution and revenue. Subsection 4.3 studies the effect of Methane price on the same subjects. 4.1. Comparison between the optimum scenarios in constant and varying composition strategies In this section, the optimum scenarios in constant and varying composition strategies are found for the economic condition of 0.0865 ($/m3) Methane price and 82 ($/tonne) carbon credit and compared with each other. For the mentioned economic condition, first, the optimisation tool is adopted to find the best composition of the injected gas and injector bottomhole pressure to maximise the profit in a constant composition strategy. Then, the same tool is applied for a varying composition strategy, in which the composition of injected gas and the injector bottomhole pressure are allowed to change over the project period. Fig. 4 illustrates the optimum composition of injected gas in both strategies. The optimum composition of injected gas in the constant composition strategy is achieved by 7% CO2 and 93% N2, while the composition of the injected gas in the optimum scenario in varying composition strategy is changing and the optimum can be seen in Fig. 4. It should be mentioned that for both strategies, the injector bottomhole pressure during the entire period is kept at the

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Table 3 Coal seam characteristics and initial conditions. Property

Value

Reference

Coal density Initial cleat permeability Initial cleat porosity Desorption time of CO2, N2 and CH4 Langmuir pressure (PL) of CO2, N2 and CH4 Langmuir adsorbed gas content (VL) of CO2, N2 and CH4 Bulk modulus (K) and grain compressibility Axial modulus (M) f Strain at infinite pressure for CO2, N2 and CH4 Initial reservoir pressure Initial gas composition in matrix Temperature

1434 kg/m3 3.65 mD 0.003 2.3, 5 and 3 days 6, 15 and 13.5 bars 0.035, 0.01 and 0.025 Sm3/kg 20,000 bars and 0 bars-1 40,000 bars 0.5 0.015, 0.004 and 0.007 76.5 bars 100% Methane 45

(Law et al., 2002) (Law et al., 2002) (Ross et al., 2009) (Zhou et al., 2011) (Zhou et al., 2011) (Zhou et al., 2011) (Palmer and Mansoori, 1998) (Connell and Detournay, 2009) (Palmer and Mansoori, 1998) (Ross et al., 2009) (Law et al., 2002) (Law et al., 2002) (Law et al., 2002)

Fig. 3. Coal seam simulation model.

maximum. Figs. 5 and 6 demonstrate the ultimate Methane production and CO2-sequestration for the optimum scenario of constant and varying composition gas injection. As shown in Fig. 5, the ultimate Methane production is higher in the optimum scenario of varying strategy, compared to the optimum scenario of constant strategy. However, the ultimate sequestrated CO2 obtained by the optimum of the constant strategy is higher than that of the optimum of the varying strategy (Fig. 6). As shown in Fig. 6 there is a linear increase in the cumulative injected CO2 in a constant composition strategy curve while sequestrated CO2 reaches a plateau after 3.5 years in the varying

Table 4 Economic parameters used in the model. Economic parameters

Values

Methane price Carbon credit Discount rate CO2 supply cost N2 supply cost Cost of compressing CO2/N2 at injector Separation cost at producer

0.0865e0.25 ($/m3) 0.019e1 ($/m3) or 10e545 ($/tonne) 10% 0.11 ($/m3) or 58 ($/tonne) 0.002 ($/m3) 0.011 ($/m3) 0.018 ($/m3) 90%

Minimum allowed average Methane cut ðMcutj Þ

Fig. 4. Average CO2 composition in optimum injection scenarios in both fixed and varying strategies for economic condition 0.0865 ($/m3) Methane price and 82 ($/tonne) carbon credit.

Fig. 5. Cumulative Methane production in optimum injection scenarios in both fixed and varying strategies for economic scenario 0.0865 ($/m3) Methane price and 82 ($/tonne) carbon credit.

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aperture during the production time (Perera et al., 2012). As coal characteristic changes by time during the production/injection period, the optimum composition of injected gas should be modified accordingly. A varying composition gas injection strategy allows us to adapt the composition of the injected gas based on the new coal characteristic. This justifies the superiority of varying composition strategy in comparison with a fixed composition injection strategy. It should be stated that to find the optimum scenario for each strategy, the optimisation was performed twice and the best of the two runs were compared with each other. This can reduce the effect of seed number on the assessment. It should be mentioned that as the concentration of CO2 in produced gas is zero, the amount of injected CO2 is the same as sequestrated CO2.

Fig. 6. Injected (Sequestrated) CO2 in optimum injection scenarios in both fixed and varying strategies for economic scenario 0.0865 ($/m3) Methane price and 82 ($/tonne) carbon credit.

composition strategy. It can be explained by the fact that the injection rate remains constant as long as the bottomhole pressure is below the maximum allowed injection pressure (fracturing pressure). In the optimum scenario of the constant composition injection strategy, the bottomhole pressure never exceed the maximum pressure, that indicates the permeability reduction due to swelling is not too severe even when the equilibrium condition corresponds to 7% CO2 e 93% N2 is achieved. But in the varying composition strategy the swelling effect is significant, due to the increase of CO2 concentration in the injectant over time which cannot be counterbalanced by the bottomhole pressure increase. According to the economic model, which is a better tool of assessment, the revenue achieved in the optimum varying scenario is 13% more than that of the optimum scenario of constant composition strategy. It confirms the superiority of varying composition strategy in comparison with the fixed composition injection. The 13% revenue enhancement is attained just by yearly updating the composition of injected gas, which is quite practical and technically feasible, with no extra cost. The reason of existing an optimum composition for injected gas is that the pure N2 adsorption rate is very slow, and accordingly the N2 front reaches the producer very fast, which degrades the quality of the produced gas; on the other hand, coal has a high affinity to adsorb CO2, which causes matrix swelling and injectivity decline, in the case of CO2 injection. A mixture of CO2 and N2 is expected to yield a better performance. Adding CO2 in the injected gas postpones breakthrough time, because, a less amount of N2 will be injected, and meanwhile the total injected gas can remain the same, which provides enough time for Methane to get desorbed. Consequently, the front of mixed injected gas reach the producer later compared to pure N2 injection. But, a high concentration of CO2 in the injected gas, on the other hand, may cause coal matrix swelling, which results in the cleat permeability reduction and consequently Methane production decline. Therefore, there is an optimum injected gas composition in which the breakthrough time is maximized while the chance of severe matrix swelling is minimized. The optimum composition of the injected gas can be dissimilar in different cases according to the geomechanical and petrophysical properties of coal. As coalbed Methane reservoirs are stress sensitive, the petrophysical properties of coal change due to reservoir pressure variation in the production/injection duration. In addition, matrix shrinkage due to Methane desorption and swelling due to CO2 adsorption cause the variation of permeability and cleat

4.2. Effect of carbon credit on optimal scenario In this section, the effect of carbon credit on Methane production, CO2-sequestration, composition of injected gas and revenue is studied. 5 economic conditions are created and evaluated. In all conditions, Methane price is kept constant at 0.0867 ($/m3), while carbon credit is changing in the range of 10e545 ($/tonne). Although the high values of this range may be unrealistic, these conditions are examined to give a broader view of the effect of carbon credit on the efficiency of N2/CO2-ECBM. Fig. 7 illustrates the cumulative Methane production in five different conditions. In all of them, Methane price is 0.0865 ($/m3), while carbon credits are 10, 82, 100, 272 and 545 ($/Tonne). For each condition, the optimisation algorithm was executed twice (each one 10,000 simulations), and the best optimum scenario of two runs is used for the comparison. As shown in Fig. 7, the higher the carbon credit is, the more the ultimate Methane production will be. It is due to the fact that where the carbon credit is high, the gas injection is economically viable even with a low amount of Methane is produced; therefore, gas injection and production processes continue for a longer period. If the carbon credit is extremely higher than the injection costs and gas supply, gas injection will be independent of Methane production and stop just as soon as the CO2-sequestration is technically impossible or when the project period is over (Fig. 8). However, where the carbon credit is less than the injection costs and gas supply, the gas injection continues as long as the Methane production is economic. As shown in Fig. 7, scenarios with the low carbon credits produce more Methane in the first half of the injection time. However, the less ultimate Methane is resulted in the conditions with the low carbon credits; because, as mentioned before, the injection process stops

Fig. 7. Cumulative Methane production vs. time (Methane price is the same for all cases but carbon credit is different).

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Fig. 8. Cumulative gas injection vs. time (Methane price is the same for all five conditions but carbon credit is different).

Fig. 10. Revenue vs. carbon credit (where Methane price is the same for all five economic conditions).

earlier in the low carbon credit scenarios (Fig. 8). For instance, in economic conditions of 10 ($/tonne) and 82 ($/tonne) carbon credit, gas injection stops at 2.5 and 3.5 years after injection starting date, respectively (Fig. 8); however, in economic conditions of 272 ($/tonne) and 545 ($/tonne) carbon credits, the gas injection continues during the whole period of injection. As shown in Fig. 7, for the selected coal characteristic, increasing carbon credit does not improve the Methane production significantly. For instance, by increasing carbon credit from 10 ($/tonne) to 545 ($/tonne), Methane production rises by only 10%. However, increasing carbon credit increases the sequestrated CO2 quite significantly (Fig. 9). It is due to the fact that increasing carbon credit encourages the optimisation model to move toward solutions which yields more sequestrated CO2. In fact, in high carbon credit cases, where net carbon credit (Carbon credit e CO2 injection cost and supply) is higher than Methane price, the optimisation algorithm gives more weighting to CO2 sequestration than Methane production. Hence, enhancement in Methane production is not as much as expected. Although increasing carbon credit does not improve Methane production considerably (Fig. 7), it enhances the revenue substantially (Fig. 10) by sequestrating more CO2. By comparing Figs. 7 and 9, it can be seen that the increase of carbon credit from 10 ($/tonne) to 545 ($/tonne), not only rises the amount of sequestrated CO2 (about 50,000 Sm3) but also enhances Methane recovery significantly (about 100,000 Sm3). It shows that

Methane recovery is not independent of the volume of sequestrated CO2. Although one of the reasons for enhancement of Methane production through CO2/N2 injection is the replacement of adsorbed Methane by CO2, other phenomena play also important roles on enhancing Methane production, such as sweeping free/released Methane from the cleats and keeping Methane partial pressure gradients between matrix and cleats. The Methane recovery can be technically improved by injecting a mixture of CO2 and N2 rather than their individual injection. The mixture injection results in postponing the breakthrough time and triggering Methane release from matrix to fracture (if compared to the pure N2 injection) and reducing the intensity of matrix swelling (if compared to pure CO2) (Sayyafzadeh et al., 2015). However, in some cases, adding CO2 to the injected gas might be uneconomic, due to CO2 supply cost. As shown in Fig. 9, for the case of 10 ($/tonne) carbon credit, the optimum injection scenario has no CO2 composition in any stage of the injection period. Because the carbon credit is lower than the CO2 supply cost and the benefit earned from Methane production enhancement and CO2 sequestration resulting from the addition of CO2 to the injected gas is less than the profit achieved from injecting pure N2. In the case of 82 ($/tonne), the CO2 injection cost is almost the same as carbon credit. Hence, some CO2 is added to the injected gas in order to maximise the benefit (Fig. 9). The ultimate Methane production and revenue in conditions, 10, 82 and 100 ($/tonne) are almost the same (see Figs. 8 and 10), however, by increasing carbon credit, more CO2 has been sequestrated (Fig. 9) which is important in terms of greenhouse gas mitigation. The reason for having almost the same revenue can be explain by the fact that although the ultimate Methane recovery is almost the same for the three cases, the low carbon credit cases produce more Methane in earlier times (Fig. 5). Therefore, according to the effect of discount rate, more profit is achieved by Methane production in low carbon credit cases. However, this revenue improvement in low carbon credit cases is cancelled out by the additional profit due to sequestrating more CO2 in high carbon credit cases and at the end they reach almost the same net revenue. Fig. 11 illustrates the average of CO2 composition in the injected gas over sequential periods of 6 months. As shown in Fig. 11, in 10 $/ tonne carbon credit condition, the composition of CO2 in injected gas is zero for the whole period of injection. It means that for this value of carbon credit adding CO2 to the injected gas decreases the profit of the project. Therefore, there is no economic justification for CO2 injection. In all other economic conditions, the optimum

Fig. 9. Cumulative Sequestrated (injected) CO2 vs. time (where Methane price is the same for all five economic conditions but carbon credit is different).

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Fig. 11. Average CO2-composition in the injected gas over sequential periods of 6 months vs. time (where methane price is the same for all cases but carbon credit is different).

injection scenario, is the one in which the composition of injected gas is changed over the injection time which confirms that the varying composition of injected gas may result in a better performance in comparison with a constant composition strategy. In addition, in all economic conditions (except for the case of very low carbon credit 10 $/tonne in which CO2 injection is not economic in any circumstances) there is an increasing trend in CO2 composition over the injection time. It means that the optimum composition of injected gas starts by very low fraction of CO2 in the injected gas and continues by a gradual increase of CO2 in the next time steps. This injection schedule makes a better balance between breakthrough time, Nitrogen cut and matrix swelling via prolonging the injection time. Extending the period of injection provides enough time for Methane to be desorbed from coal matrix, diffuses through matrix to the cleat system and be pushed consistently by the injected gas to the production well. In the first half of the injection time, the cases with higher carbon credits display a higher composition of CO2 in the injected gas. However, the trend in the second half of the injection time is almost opposite, in which the higher carbon credits, the lower the CO2 compositions in the injected gas (see Fig. 11). It can be explained by the fact that as in high carbon credit conditions, an earlier sequestration of CO2 increases the profit of the project, the optimisation model tends to add more CO2 to the injected gas in the early stages of injection in order to maximise the revenue. Therefore, when the CO2 credit is higher, the CO2 injection starts earlier (Fig. 11). The rate of adding CO2 to the injected gas declines over time to reduce the negative effects of matrix swelling and permeability reduction. In another word, in high carbon credit conditions, more weight is allocated to the CO2 sequestration rather than improving Methane production. In low carbon credit conditions, the main target is to improve the profit by producing more Methane. Therefore, the amount of CO2 addition to the injected gas should be low enough to only postpone the breakthrough time and somehow trigger the Methane desorption from the matrix to the fracture system while not causing matrix swelling which may result in the permeability reduction.

effect of Methane price on gas production profile, CO2sequestration, the optimum composition of injected gas and revenue. Figs. 12 and 13 compare Methane production and CO2sequestration for two optimum injection scenarios with the same carbon credit (82 $/tonne) and different Methane prices (0.0865 $/m3 and 0.25 $/m3). As illustrated in Figs. 12 and 13, for the higher Methane price (0.25 $/m3) condition, more Methane is produced while less CO2 is sequestrated. It is due to the fact that in this case the main focus of the optimisation tool is to maximise the revenue via improving the Methane production. On the contrary, when the Methane price is low (0.0865 $/m3), the optimisation model gives more weighting to the CO2sequestration, in order to maximise the profit. Hence, CO2 injection starts one year earlier and the ultimate sequestrated CO2 is also higher in the low Methane price scenario (0.0865 $/m3) compared to the high one (0.25 $/m3). Fig. 14 shows the average CO2 composition in the sequential periods of 6 months in the injection time for two optimum injection scenarios with the same carbon credit (82 $/tonne) and different Methane prices (0.0865 $/m3 and 0.25 $/m3). As demonstrated in Fig. 14, CO2 composition has an increasing trend in both cases. However, when the Methane price is low (0.0865 $/m3), CO2 is added earlier and its composition is more at any time, compared to the other case (0.25 $/m3). It confirms that at low Methane price (0.0865 $/m3) condition, the optimisation tool gives more attention to CO2-sequestration, compared to the high Methane price (0.25 $/m3) case. Fig. 15 compares revenues achieved in two optimum injection scenarios with the same carbon credit (82 $/tonne) and different Methane prices (0.0865 $/m3 and 0.25 $/m3). As illustrated in Fig. 15, increasing Methane price from 0.865 to 0.25 ($/m3) improves the revenue by about 4 times. However, as shown in Fig. 10, for a given gas price (0.0865 $/m3), increasing carbon credit from 10 to 545 ($/tonne) improves the revenue only about 1.6 times. It is due to the fact that as the volume of produced gas is much higher than the amount of sequestrated CO2, the revenue is much more sensitive to Methane price rather than carbon credit; however, the degree of sensitivity is affected by coal characteristic. 5. Conclusions In this paper, a study was conducted to analyse the optimisation of an enhanced coalbed Methane recovery (using N2 and CO2 mixture injection) project, for a semi-synthetic case study. The

4.3. Effect of methane price on optimal scenario In this section two economic conditions (0.0865 $/m3 Methane price-82 $/tonne carbon credit and 0.25 $/m3 Methane price-82 $/tonne carbon credit) are evaluated. In both cases, carbon credit is the same while Methane price is different. The aim is to study the

Fig. 12. Cumulative Methane production vs. time (where carbon credit is the same for both cases but Methane price is different).

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which the income, resulting from Methane production and CO2 sequestration, and costs, resulting from compression, separation and injectant supply, were taken into consideration. The decision variables were the composition of the injected gas and injector bottomhole pressure which can be both subjected to change over the injection period. The changes were stepwise, and the intervals were designed in a way to be operationally viable. Due to the complexity of the optimisation in such a problem, a simple sensitivity analysis is not sufficient, and therefore a genetic algorithm was coded and utilised in order to find the optimum scenario. By analysing the outcomes of the optimisation for a specific economic condition, the following conclusion can be made:

Fig. 13. Cumulative CO2 injection vs. time (where carbon credit is the same for both cases but Methane price is different).

1 A varying composition strategy can result in more revenue from an ECBM project, compared to a typical gas injection strategy (a fixed composition). For the case study with a specific economic condition, it was observed that the revenue increases 13% by applying a varying composition. In this study, a sensitivity analysis was also performed on the value of carbon credit on the revenue and the performance of ECBM project. Comparison results indicate that

Fig. 14. Average CO2-composition in the injected gas over sequential periods of 6 months vs. time (where carbon credit is the same for both cases but Methane price is different).

2 In the cases that the ratio of carbon credit to Methane price is low, scenarios with high N2 concentration is preferred, and those can result in more revenue from the project. This is chiefly due to the destructive impact of CO2 on well injectivity. If the carbon credit does not compensate the CO2 supply and injection costs, the composition of CO2 in the injected gas should be minimised. It means that the beneficial influence of CO2 on Methane desorption process vanishes, when the carbon credit is low. 3 In the cases that the ratio of carbon credit to Methane price is high, the optimum scenarios will be the ones with injected CO2. The noteworthy point is that not only in these conditions, the amount of sequestered CO2 was greater, in comparison with low carbon credit condition, but also a higher Methane recovery was obtained. This is because of the fact that the high carbon credit can keep the injection economically viable for a longer period. 4 In the cases that the ratio of carbon credit to Methane price is extremely high, the main governing element is the amount of sequestrated CO2. 5 In the conditions CO2 injection is economically viable, the composition of CO2 in the injectant, at the beginning is minimal and it rises sequentially over the period of injection. By this injection pattern, both well injectivity decline and N2 breakthrough can be postponed. It is fair to mention that the abovementioned conclusions (2e4) are expected to be subjective to the economic condition and coal characteristics. Nomenclature a,b & a

Peng-Robinson parameters

ak

PVNkc

CF cm

cash flow

1 K M Mþf 1

DR Dci dcal g k

discount rate the diffusion coefficient of component i, a column vector consisting of required simulation data reservoir simulation absolute permeability

j¼1

Fig. 15. Revenue comparison (where carbon credit is the same for both cases but Methane price is different).

objective function was formulated, based on an economic model in

Vj

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K bulk modulus krg relative permeability of gas krw relative permeability of water M axial modulus W reservoir simulation-model Mg molecular density of gas Mw molecular density of water msi the surface (matrix) concentration of component i Nc number of components Nogen generation number Ntour tournament size nt number of step alteration p pressure pi partial pressure of component i p0 reference pressure Pc critical pressure pc crossover probability pf fracing pressure ph hydrostatic head pm mutation probability qi sink/source term of component i qmc flow rate between cleat and matrix qw sink/source term of water phase QpCH4 i cumulative produced CH4 in year i QpCO2 i cumulative produced CO2 in year i QpN2 i cumulative produced N2 in year i QiCO2 i cumulative injected CO2 in year i QiN2 i cumulative injected N2 in year i R gas constant Sg gas saturation Sw water saturation T temperature Tc critical temperature Tr reduced temperature Vi gas content of component i Vm molar volume X decision variables xi an element of X yi fraction of component i in gas phase $CH4 methane price $CO2 Credit carbon credit $comp compression cost $Sep separation cost $CO2 CO2 supply cost $N2 N2 supply cost Greek Letters a a constant for unit conversion bk and εk matching parameters Dε volumetric strain rg gas density rw water density rcoal coal density mw water viscosity mg gas viscosity Ф potential energy 40 porosity at the reference pressure 4 porosity u acentric factor g grain compressibility s matrix-cleats interface area References Clarkson, C.R., Pan, Z., Palmer, I.D., Harpalani, S., 2010. Predicting sorption-induced

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