Ziwei Wang ,Yong Qin, *,Teng Li ,Xiaoyang Zhang

a Key Laboratory of Coalbed Methane Resources & Reservoir Formation Process,Ministry of Education,China University of Mining and Technology,Xuzhou 221116,China

b School of Resources and Geosciences,China University of Mining and Technology,Xuzhou 221116,China

c College of Petroleum Engineering,Xi’an Shiyou University,Xi’an 710065,China

d College of Earth Sciences and Engineering,Shandong University of Science and Technology,Qingdao 266590,China

Keywords:Sublayer interlayer interference index Permeability ratio Reservoir pressure difference Interval distance Production contribution

ABSTRACT Multiple-seam gas coproduction is a technology with potential to achieve economic targets.Physical experiments could replicate gas flow dynamics in two seams.In this study,numerical simulation was conducted based on physical experiments.Through calibration,the simulated results agreed with the experimental results.Three findings were obtained.First,the pressure distribution intrinsically depends on the depressurization effectiveness in each coal seam.The gas pressure difference and interval distance influence the pressure distribution by inhibiting depressurization in the top seams and bottom seams,respectively.Second,the production contribution shows a logarithmic relationship with the permeability ratio.The range of the production contribution difference grows from 11.24%to 99.99%when the permeability ratio increases 50 times.By comparison,reservoir pressure has a limited influence,with a maximum of 13.64%.Third,the interlayer interference of the top seams and bottom seams can be intensified by the reservoir pressure difference and the interval distance,respectively.The proposed model has been calibrated and verified and can be directly applied to engineering,serving as a reference for reservoir combination optimization.In summary,coal seams with a permeability ratio within 10,reservoir pressure difference within 1.50 MPa,and interval distances within 50 m are recommended to coproduce together.

1.Introduction

Coalbed methane(CBM)is an important clean energy source for many countries,including the U.S.[1,2],Australia[3],Canada[4,5],China[6],and India[7].Coal is typically found in multiple seams in a basin [8–11].It is increasingly important to extract multiseam gas from a basin for the best economic gains.However,multiseam interactions can complicate gas flow behavior.A solid understanding of multiple coal seam gas coproduction is necessary for the efficient extraction of gas.Multiseam gas coproduction can offer a unique advantage by elongating the stabilizing production duration [12].However,compared with production from a single coal seam,there are many technical and operational challenges for multiseam gas coproduction.Even though the accumulated CBM resources are expected to be high in multiseam coal regions and settings,the nature of seam heterogeneity across the targeted seams can significantly complicate reserve assessments and engineering implementations.The heterogeneous properties include gas content variation,reservoir pressure,seam thickness,underlying and overlying strata sealing capacities,and discontinuities of the seam.These heterogeneities can impede the high productivity of CBM wells[13,14].Currently,only a few basins across the world have successfully achieved commercial gas flows through multiseam gas coproduction,including the Black Warrior Basin in Alabama,U.S.[11,15],the Alberta Basin in Canada [16],and the Surat Basin in Australia [17,18].

For multiseam gas coproduction,cross-seam interactions and interferences are expected to complicate well completion and drawdown management.To address these challenges,a multiparameter optimization approach should be considered for well design and depletion management by comprehensively analyzing sedimentary conditions [19,20],hydrogeological conditions[21,22],tectonics [23,24],and CBM engineering [25].

In practice,for conventional multilayer reservoir hydrocarbon coproduction,physical laboratory studies and analysis of interlayer interference seem to be effective and informative for aiding reservoir development [26,27].In CBM coproduction,physical experiments are proven to be a valid method to characterize the flow interactions [28].However,the investment in physical experiments is relatively high,and these experiments may not fully replicate the in situ conditions for multiseam coal formations.Numerical simulation can serve as an alternative for improving the understanding of multiseam formation interactions because it offers a cost-effective way to analyze full-scale field conditions[29,30].CBM reservoirs are known to have low permeability and porosity,and the gas is mainly absorbed to the surface of micropores [6,31–34].Hydraulic fracturing is widely used to stimulate formations for enhanced production [35–37].

Based on the regular two-phase and dual-porosity threedimensional (3D) model,Zhang and his co-worker [38,39] simulated the process of hydraulic fracturing with IMPES software.Yin et al.[40]mimicked the effects of horizontal stress on hydraulic fracturing with ANSYS 14.0 and found that when the difference between the maximum and the minimum horizontal stresses exceeded 5.00 MPa,hydraulic fractures more easily penetrated the roof and/or the floor.In addition to hydraulic fracturing,N2/CO2enhanced coalbed methane (N2/CO2-ECBM) has also been piloted to enhance recovery.According to the ARI-COMET 3 simulation results,the gas mixture of 40%N2and 60%CO2was found to be the best for injection,as it has the minimum leakage of N2and CO2,achieving the maximum production output [41].Numerical simulation is also used in the optimization of CBM well patterns[42,43] and multiseam fracturing of CBM reservoirs [44–46].

Numerical simulations have not been employed to optimize gas reservoirs for multiseam gas coproduction.One of the challenges of numerical modeling is the selection of reliable input parameters for numerical models.It is always a good practice to couple the experimental results into the proposed numerical model to optimize the field operations.In this study,the authors established a model framework to couple experimental results in the lab to engineering guidance for field operation,maximizing multiseam gas coproduction in western Guizhou and eastern Yunnan,China[28].A geometric model was established that can best replicate the geometry of the physical experiment arrangement.Then,the initial and boundary conditions were set in the simulation to be consistent with the actual physical experiments.After calibration and validation with the experimental results,the proposed simulation model was shown to help accelerate research progress and reduce research expenses.By predicting gas production and interlayer interference under variable exploitation schemes,the simulation results can provide guidance for analyzing gas coproduction behaviors for multiseam coal settings.

2.Physical experiments and numerical simulation of CBM coproduction

2.1.Geological background of multiseam coproduction

From the stratigraphic map(see Fig.1),one of the most obvious geological features is individual multiple coal seams.Up to 32 coal seams are stacked vertically and separated by sandstone,mudstone,and limestone with various thicknesses.

For a well in the Enhong syncline,Yunnan Province,China,constrained by budget and technical challenges,it was not practical to perforate and hydraulically fracture all of the seams.In this well,two coal seam groups were selected.The top group contains coal seams No.16,No.17,No.23,No.25,and sandstone K7,and the bottom group is composed of coal seams No.30 and No.32 and sandstones K11 and K12.

The coal porosity,rock porosity,gas pressure coefficient,and permeability of each seam are plotted in Fig.1.Primarily,coal porosity determines the pore volume containing gas and water,and the rock porosity influences the sealing capacity of the roof and floor.The pressure coefficient is an indicator of the driving force.From top to bottom,the pressure coefficients are in the range of 0.81 and 0.92 under pressurization.Permeability is closely related to the gas production contribution of each seam.It is clear that these parameters are variable vertically,causing seam heterogeneity.

Two coproduction methods can be applied in CBM engineering.The first is fracturing and producing a whole group.In Fig.1,the coal seams and sandstones in top group are perforated,fractured,and produced together.After fracturing,the initial individual coal seams are connected by tiny artificial fractures,through which water and gas flow,so they are regarded as one thick seam with a compound composition.The second method is fracturing separately and producing together.Two baffle plates are placed on the casing before installing and cementing the casing at locations between coal groups that are to be individually fractured.After perforation,the upper baffle in coal seam No.25 passes a smaller ball to the lower baffle in the sandstone K12.The bottom group is fractured first,and then a larger ball is dropped down to block the upper baffle in coal seam No.25.The top group is fractured later.The two coal groups coproduce together.In this manner,the two groups are still isolated because of the interval between coal seams No.25 and No.30.In these physical experiments and numerical simulations,the authors concentrate on the second way of CBM coproduction.

2.2.Background information about physical experiments

Physical experiments are conducted to simulate the scenarios in which two groups are perforated and hydraulically fractured individually and coproduce together.Coal samples used in experiments were collected from the coal seams No.3 and No.9 of the Tianjing coal field,located in Fuyuan County,Yunnan Province,China (104°25′E–104°41′E,25°03′N–25°21′N).Weak aquosity in coal seams results in a low water production rate,ranging from 0.288 to 0.727 m3/d.Based on the results of proximate analysis and vitrinite maximum reflectance tests,the coal samples are classified as anthracite coal.The two cylindrical coal cores placed horizontally represent two coal seams.According to the well test in the study area,the reservoir permeability is mainly distributed in the range of 0.001 and 0.260 mD,and the reservoir pressure varies from 3.71 to 11.27 MPa.These values serve as a reference for the experimental settings.The permeability,inlet pressure and outlet pressure of the top cores remain at 0.500 mD,7.00 MPa,and 0.50 MPa,respectively.The permeability,inlet pressure and outlet pressure of the bottom cores are set with four levels to observe the dynamics of the forward and reversed gas flow rates running through two cores.The details of the physical experiments were fully described in the authors’ previous publication [28].

2.3.Numerical simulation

2.3.1.Model governing equations and their associated assumptions

Coal is known as a dual-porosity medium with pores and fractures.The fractures/cleats provide the gas pathway,and the pores and voids serve as a gas storehouse [47–50].Robertson [51]pointed out that fracture permeability was eight orders higher than matrix permeability in coal seams.When preparing coal samples prior to physical experiments,all coal samples were drilled along the bedding plane.The permeability along the radial direction(xaxis)is much higher than that along the tangential direction(yaxis)and vertical direction(zaxis).The model complies with the following assumptions:(1) the temperature is constant at 25 °C;(2) methane is the only ideal gas flowing through coal cores;and(3) the initial permeability along thexaxis (kx0) is assumed to be 100 times higher than that along theyaxis(ky0)and thezaxis(kz0).

Fig.1.Sketch map of CBM coproduction in the Enhong syncline.

A simplified geometrical model is constructed to conceptualize the dual-porosity system[52],in which three groups of perpendicular fractures exist along thex,y,andzaxis [53,54] (see Fig.2).

The main path for gas flow is along thexaxis.For lab experiments,coal specimens are loaded with a confining stress of 16.00 MPa.For the simulation,as a dual-porosity medium,the flow is governed by the effective stress σe.The change of the coal unit length alongjaxis (Δsjwherejrepresents thex,y,zaxis) is the sum of the change of matrix cell length (Δsm) and the fracture aperture change alongjaxis (Δbj) (see Fig.3).

Eq.(1) is employed.

wherebjis the fracture aperture alongjaxis;Δbjthe fracture aperture change alongjaxis;sthe matrix cell length;Δsjthe change of the coal unit length alongjaxis;Δsmthe change of the matrix cell length;Δσethe effective stress change;Ejthe coal elastic modulus alongjaxis;andEmthe matrix elastic modulus.

The relationship between the fracture aperture and rock porosity in three dimensions is as follows [55].

Fig.2.Dual-porosity model of methane migration.

where φf0is the initial porosity of fractures.

Substituting Eq.(2) into Eq.(1),

whereRjis the loss rate of coal elastic modulus alongjaxis;and Δεjethe strain changes caused by effective stress alongjaxis.

According to Rutqvist’s theory [56],the permeability equations can be described as follows.

wherekx,ky,kzare the permeability alongx,y,zaxis,respectively.

Substituting Eq.(4)into Eq.(5)and Eq.(6)into Eq.(7),the equations of coal permeability dynamics are derived as follows.

When going through the permeable flow domain,the gas flow velocity correlates with the gas viscosity,the permeability of the passing porous medium,and the pressure gradient.Based on Darcy’s law,the velocity of the gas can be estimated as follows.

Fig.3.Schematic of the opening fracture change.

where v is the gas velocity in porous media;kjthe permeability alongjaxis;μ the dynamic viscosity;ρ the gas density;gthe gravitational acceleration;Δhthe water head height difference;and ΔPthe gas pressure difference.

As the inlet and outlet have the same height and only gas flushes through the laminar flow domain,Eq.(11)can be simplified as follows.

During physical experiments,coal samples were saturated with methane prior to gas flushing.According to the principle of material balance,Eq.(13) can be obtained.

whereQdis the gas mass difference between the inlet and outlet of porous media;andQrthe gas mass changes in porous media.

For single-phase gas,the mass conservation equation is defined as follows.

where φ is the porosity in porous media;andtthe time for gas going through the coal unit.

When gas flows in the borehole,it conforms to the principle of mechanical energy conservation.The equation is defined as follows.

wherePis the gas pressure;θ the angle from horizontal line;MEthe mechanical energy;anduzthe gas velocity in laminar flow area alongzaxis.

When gas runs into the borehole,the gas pressure drops because of the position difference,the surface friction,and the gas running acceleration [57].

where(dP/dz)positionis the pressure gradient caused by position difference;(dP/dz)frictionthe pressure gradient caused by friction;and(dP/dz)accelerationthe pressure gradient caused by acceleration.

The pressure gradient caused by position differences can be disregarded because of the low density of methane.Friction and acceleration determine the pressure gradient,and the equations are as follows.

where λ is the flow resistance coefficient;Dthe inner diameter of borehole;Gthe gas mass flow;andAthe cross sectional area of borehole.

In summary,the gas flow equation in the borehole is defined as follows.

From porous media to the borehole,the gas flow follows the continuity equation.For the boundary,the gas velocity continuum equation is applied as follows.

whereuxanduyis the gas velocity in laminar flow area alongxandyaxis,respectively.

2.3.2.Process of numerical simulation

COMSOL Multiphysics is a professional numerical simulator popular in scientific research.Based on the finite element method,COMSOL conducts a numerical simulation that depicts the physical phenomena by solving partial differential equations/equation groups.By setting initial conditions and boundary conditions,graphical results are generated in the simulator,which can help researchers observe the spatial distribution of physical variables.Version 5.3a is used for this numerical simulation.The geometric model of the numerical simulation replicates the physical experiment structure.As shown in Fig.4,two parallel cylinders placed horizontally represent two coal seams with different initial permeability.The vertical cylinder represents the CBM well.In Fig.4,the seepage domain is 50 mm in length and 25 mm in diameter.In this area,the seepage module is loaded.The inlets of the seepage domain are two circular holes where the inlet pressure is applied.Based on physical experimental results,the maximum gas flow rate is 3032 mL/min,and the Reynolds number in the borehole is calculated to be 0.0667.The borehole domain that is 100 mm in length with a diameter of 6 mm is loaded with the laminar flow module.The surface between the seepage domain and the laminar flow domain is the given outlet pressure.The top of the borehole is assigned the casing pressure.

Fig.4.Geometric diagram of the numerical model (unit:mm).

In the numerical model,no flow boundaries are applied to coal surfaces,except for two inlets of the seepage domains and one outlet of the laminar flow domain.During the process of numerical simulation,three parameters vary according to the physical experimental conditions.The permeability,inlet pressure and outlet pressure of the top core are constant at 0.500 mD,7.00 MPa,and 0.50 MPa,respectively.The permeability of the bottom core is set at four levels:0.010,0.050,0.100,and 0.500 mD.Four-level settings are also applied to inlet pressures (8.00,10.00,12.00,and 14.00 MPa) and outlet pressures (0.70,1.00,1.50,and 2.00 MPa)[28].Therefore,64 experimental schemes are projected in the numerical simulation.In the mesh configuration step,the following mesh types are applied in the model:triangular and rectangular mesh.On the circular surface of the seepage domain,a rectangular mesh is used to reduce the amount of calculation,while on the surface of the well and the end face of the seepage domain,a triangular mesh is used to improve the computing accuracy.In addition,the mesh is refined in the inlet,boundary,and corner areas to solve the convergence problem (see Fig.5).The whole geometry is composed of 65,238 tetrahedrons and 1656 pyramids with 6554 triangles and 1656 rectangles covering its surface.

2.3.3.Parameters used during the simulations

Based on the settings of physical experiments and the geometry of the numerical model,the parameters of the numerical simulation are listed in Table 1.

Table 1 Parameters of the numerical simulation.

3.Results

The results of the numerical simulation include the forward gas flow rate and the reversed gas flow rate going through the two simulated coal seams.

3.1.Simulated gas flow rate

To verify the numerical model,a comparison was made between the results of the physical experiments (PE) and the numerical simulation (NS) results under inlet pressures of 8.00 and 14.00 MPa,as shown in Fig.6.In Fig.6,the outlet pressure on thexaxis indicates the outlet pressure of the bottom seam.

When the permeability of the bottom seam is 0.500 mD,the forward gas flow rate in the top seam is approximately 1900 mL/min.When the permeability ranges from 0.010 to 0.100 mD,the forward gas flow rate fluctuates between 1700 and 1750 mL/min(see Fig.6).The outlet pressure does not have an obvious influence on the gas exit rate in the top seam.

The outlet pressure of the bottom seam negatively impacts the gas outflow rate in the bottom seam (see Fig.7).The higher the permeability of the bottom seam,the greater the influence on the bottom seam flow rate.When the permeability of the bottomseams is no greater than 0.100 mD,the gas outflow is less than 800 mL/min.However,when the permeability is 0.500 mD,the gas outflow is more than 1200 mL/min.

The reversed gas flow suggests that the gas backflows towards the coal seam.Compared with the gas outflow,the reversed gas flow rate is two orders smaller,within 20 mL/min (see Fig.8).

The reversed gas flow rate in the bottom seam is smaller than that in the top seam and increases with the outlet pressure of the bottom seam (see Fig.9).From Figs.6–9,it can be found that the gas flow rate data in the top coal seam have a random fluctuation and do not contain the universal trend.When matching the results of the numerical simulation and the physical experiments,it is apparent that the bottom seam has a superior agreement between the PE and NS results to the top seam.One reason can account for this phenomenon.During the PEs and NS,the permeability,inlet pressure and outlet pressure of the bottom coal seam parameters are changed.These changes directly affect the gas flow rate of the bottom coal seam.However,the gas flow rate of the top coal seam is influenced by the interference impact from the gas flow rate of the bottom coal seam through the borehole.This interference causes mechanical energy loss because of the friction between the gas and the rough borehole surface.Thus,the bottom coal seam has a better fit than the top coal seam.

Fig.6.Forward gas flow rate in top seams when the inlet pressure is 8.00 and 14.00 MPa before calibration.

Fig.7.Forward gas flow rate in bottom seams when the inlet pressure is 8.00 and 14.00 MPa before calibration.

Fig.8.Reversed gas flow rate in top seams when the inlet pressure is 8.00 and 14.00 MPa before calibration.

3.2.Calibration of the numerical simulation process

Fig.5.Mesh configuration of the numerical model (unit:mm).

The gas transport in the coal seam and the laminar flow domain is separated by the bottom hole surface.An equation should be applied to couple these two domains to determine the gas flow from the seepage domain to the laminar flow domain,which can be determined by either the pressure continuum or the flow velocity continuum.

Fig.9.Reversed gas flow rate in bottom seams when the inlet pressure is 8.00 and 14.00 MPa before calibration.

Comparison was made between the two methods.In this model,the permeability,inlet pressure and outlet pressure of the bottom part are 0.100 mD,10.00 MPa,and 1.50 MPa,respectively.If the pressure continuum is applied,the gas flow rates in the top coal seam in the seepage domain and the laminar flow domain are 62 and 1749 mL/min,respectively.If the velocity continuum is applied,the gas flow rates are both 1749 mL/min.This is because if the pressure continuum is used,these two domains are not coupled at all.Under this situation,the bottom hole surface is deemed a wall surface with a constant pressure value on both sides in the numerical model.The wall surface is the end of the seepage domain and the beginning of the laminar flow domain,and it will prevent the gas from flowing across.As a result,the gas flow rates on the two sides were different.However,if the gas velocity continuum is applied,these two domains are coupled because the gas velocity is not constant and the gas velocity at the end of the seepage domain determines the gas velocity at the beginning of the laminar flow domain.In summary,the gas velocity continuum should be used for modeling.

The porosity of the porous domain also has an influence on the results of the numerical simulation.During the physical experiments,the porosity of coal samples under a chamber pressure of 0.50 MPa was tested.According to Eqs.(7)–(9),the dynamic permeability is determined by the initial permeability,and the fracture aperture changes with it.In addition,from Eq.(4),the porosity is determined to have a linear relationship with the fracture aperture.Based on Eq.(3),the fracture aperture changes are determined by the confining stress.Thus,under various confining stresses,the permeability and porosity of coal samples are not fixed,as they are influenced by fracture aperture changes.

Fig.10.Forward and reversed gas rate changes based on porosity changes.

Before calibration,the porosity input is tested under a chamber pressure of 0.50 MPa.To analyze the porosity sensitivity,a model is chosen for comparison in which the permeability,inlet pressure and outlet pressure of the bottom parts are 0.100 mD,10.00 MPa,and 1.50 MPa,respectively.When other conditions were constant,the porosity was increased from 4.000% to 13.000%to observe the gas flow rate changes(see Fig.10).Both forward and reversed gas rates increase with porosity.With the porosity increasing from 4.000% to 13.000%,the forward and reversed gas rates improved by 14.96% and 29.11%,respectively.The influence of porosity on the reversed gas rate is higher than that on the forward gas rate.

To improve the accuracy of the numerical simulation,the porosity of the coal sample is adjusted by up to±3%.After calibration,the porosity is as displayed in Table 2.

Table 2 Porosity calibration.

After calibration,new results show a good fit with physical experiments,and the changing rules are more obvious (see Figs.11–14).

3.3.Verification of the calibrated gas flow rate

For the calibrated model,the results of the numerical simulation under inlet pressures of 8.00 and 14.00 MPa are approximately equal to the results of the physical experiments;therefore,the accuracy of the numerical model has been verified.This model is used to predict the gas flow rates under inlet pressures of 10.00 and 12.00 MPa.For these two tested pressures,the modeled results have excellent agreement with the measured experimental results,as illustrated in Figs.15–18.

4.Discussion

4.1.Pressure distribution inside the coal seam

A pressure distribution map was generated along thex-zplane aty=0 in the graphic result of COMSOL(see Fig.19).The pressuredistribution inside the coal seam with variations in permeability ratios,inlet pressure,and outlet pressure ratio were mapped.Two parallel lines are drawn alongy=0,z=0,andx=0–50 mm,andy=0,z=60 mm,andx=0–50 mm.Diagrams are generated to show the pressure increase from left to right.

Fig.11.Forward gas flow rate in top seams when the inlet pressure is 8.00 and 14.00 MPa after calibration.

Fig.12.Forward gas flow rate in bottom seams when the inlet pressure is 8.00 and 14.00 MPa after calibration.

Fig.14.Reversed gas flow rate in bottom seams when the inlet pressure is 8.00 and 14.00 MPa after calibration.

Fig.15.Predicted forward gas flow rate in top seams when the inlet pressure is 10.00 and 12.00 MPa.

Fig.16.Predicted forward gas flow rate in bottom seams when the inlet pressure is 10.00 and 12.00 MPa.

When analyzing the effects of the permeability ratio,the gas pressure at the inlet and outlet of the two seams remained unchanged.The permeability of the top seam is 0.500 mD,while the permeability of the bottom seam increases from 0.010 to 0.500 mD.The gas pressure in the bottom seam is higher than that in the top seam as a whole and then shows a downward trend from the inlet to the outlet (see Fig.19a).In Fig.20a,the permeability ratio does not have obvious effects on the reservoir pressure of the two seams.In CBM engineering,engineers came to a similar conclusion through field work.Li and Wu [58] and Zhang et al.[59]researched the geological features of multiple seams in northern China and determined that the heterogeneity of permeability in multiple seams had limited influence on the reservoir pressure distribution.Shan et al.[60] discovered that the permeability difference only affected the gas production contribution from single seams and did not determine the pressure distribution inside reservoirs based on CBM production data in southwestern China.

Fig.17.Predicted reversed gas flow rate in top seams when the inlet pressure is 10.00 and 12.00 MPa.

Fig.18.Predicted reversed gas flow rate in bottom seams when the inlet pressure is 10.00 and 12.00 MPa.

When analyzing the effects of reservoir pressure changes,the permeability and outlet pressure of the two seams remained unchanged.The inlet pressure of the top seam is constant at 7.00 MPa,while that of the bottom seam increases from 8.00 to 14.00 MPa.The reservoir pressure inside the two seams increases with the inlet pressure of the bottom seam,and the scale is more obvious in the bottom seam(see Fig.19b).When the inlet pressure of the bottom seam increases from 8.00 to 14.00 MPa,the difference in gas pressure between the two seams increases.The average pressure inside the top seam also increases(see Fig.20b).The primary reason is that the high-pressure bottom seam has an inhibitory effect on the top seam,impeding the decrease in pressure.

This phenomenon was also observed in practice at the Fukang coal field,Xinjiang,China.CBM coproduction was not recommended,as the high-pressure gas reservoir inhibited gas production from the low-pressure reservoir [61].In the Qinshui Basin,researchers found that the initial reservoir pressure was essential for the propagation of pressure perturbations through mathematical modeling [62].

When analyzing the effect of distance between seams,the permeability and the inlet pressure of the two seams remained unchanged.The outlet pressure of the top seam is constant at 0.50 MPa while the bottom seam increases from 0.70 to 2.00 MPa(see Fig.19c).In the bottom seams,the pressure gradient decreases with the outlet gas pressure,while in the top seams,the pressure gradient does not have an obvious change (see Fig.20c).The interval distance affects the bottom seam more than the top seam.

In CBM engineering,the distance indeed has a negative influence on the performance of CBM wells.Two CBM wells in Guizhou Province,YMC-1 and GP-1,were compared.YMC-1 coproduced three seams with a distance of 60 m,and gas production stabilized at 4000 m3/d[60,63].GP-1 coproduced eight seams with a distance of 268 m,and the daily gas production was only approximately 400 m3/d.In the Zhijin Basin,Guizhou Province,Qin et al.[64]proposed the concept of unattached multiple superposed CBM systems and suggested that coproduction across several CBM systems should be avoided for long interval distances.Long interval distances inhibit high gas production.

4.2.Sensitivity analysis of production contribution

Production contribution was defined as the ratio of gas production from each seam to the total gas production[27,65].When analyzing the sensitivity of the production contribution,the minimum production contribution conforms to the mathematical equationy=η +τ × lnx(see Fig.21).

Parameter η is the reference value of the production contribution when the top and bottom seams have the same permeability and the same seepage capacity.When they have the same permeability,reservoir pressure,and bottom hole pressure (BHP),based on Darcy’s law,the gas production of each seam is identical,and the reference value of η is 0.5.In CBM engineering,apart from permeability,other reservoir properties,such as production pressure drop[66,67],gas saturation[68,69],and hydrogeology[21,70],also have an effect on gas production.The value of η tends to be less than 0.5 due to the inevitable difference in these reservoir properties.In experiments,the inlet gas pressure and the outlet gas pressure loaded on samples vary in different schemes,so the value of η ranges from 0.3756 to 0.4438 (see Table 3).

Fig.19.Pressure distribution inside coal seams under increasing permeability ratio,increasing inlet pressure difference,and increasing outlet pressure difference.

Parameter τ represents the effectiveness of the permeability ratio on the production contribution and ranges from -0.1211 to-0.0904 (see Table 3),where the minus sign indicates that the change in the permeability ratio has a negative effect on the minimum production contribution.The greater the absolute value of τ,the stronger the effects of the permeability ratio on the production contribution distribution.When the permeability ratio and the difference in outlet gas pressure remain the same,the absolute value of τ decreases with the inlet gas pressure difference,which indicates that the inlet gas pressure difference has the function of balancing the production contribution between coal seams.

Table 3 Ranges of η and τ under different conditions.

The difference in production contribution broadens with the permeability ratio across coal seams.When the ratio is 1,the difference in production contribution in the two seams ranges from 4.81%to 23.35%,while when the ratio is 50,the difference reaches the range of 91.88% to 96.19% (see Fig.21).

Fig.20.Reservoir pressure changes along the x axis under increasing permeability ratio,increasing inlet pressure difference,and increasing outlet pressure difference.

Fig.21.Production contribution changing rules under outlet pressure of bottom seam being 0.70,1.00,1.50,and 2.00 MPa.

The permeability ratio less than 5 has a strong influence on the production contribution.The influence is minor when the ratio exceeds 10.In summary,the permeability ratio is the primary factor influencing the production contribution.Researchers discovered a similar phenomenon when analyzing gas production data[71,72] and conducting physical experiments [73,74].

These observations can be explained by two primary factors.The difference in gas drainage velocity in the two seams widens as the permeability ratio increases.Under coproduction conditions,for the vertically superposed coal seams,their groundwater recharge capacity is almost equal,and the difference in fluid pressure transmission is more obvious as the permeability ratio increases.Fractures and cracks are more developed in highly permeable coal seams,automatically resulting in a higher pressure drawdown funnel.Excessive amounts of gas can be produced from the high permeability seam.In contrast,for low permeability seams,the fracture aperture and length tend to be small,which impedes the drainage of gas and water.During drainage,it is inevitable that pulverized coal moves with the groundwater.When going through the microfractures or the bend in the fractures,the coal may settle due to the low flushing velocity.As a result,congestion occurs in the fractures,and gas and water have difficulty moving from the seams to the borehole along the fractures.Gas production shows a declining trend due to reservoir damage of fine production.

4.3.Sensitivity analysis of the interlayer interference

Reversed gas flow is observed in the initial period of CBM coproduction in both physical experiments and numerical simulations.Reversed gas flow is triggered by interlayer interference.The amount of gas elastic energy stored in the reservoirs varies between seams.Once connected,reversed gas flow inhibits gas production and encourages pulverized coal to settle in fractures.To quantify the magnitude of interlayer interference in single seams,a previous study proposed the concept of a sublayer interlayer interference index (SIII) [28].

where βiis the sublayer interlayer interference index;qirethe reversed gas flow in reservoiri;qiforthe forward gas flow in reservoiri;andithe number of coal seams.

Similar to physical experiments,COMSOL can also quantitatively characterize the SIII caused by gas pressure differences when interlayer interference occurs.Comparing the maximum value of SIII in the top seam,there is an increasing trend with the permeability of the bottom seam,from 0.35% to 0.80% (see Fig.22).

The SIII value of the top seam increases significantly with the inlet pressure of the bottom seam (see Fig.22).COMSOL Multiphysics also has a function for monitoring the reverse gas flow dynamics in the borehole.A slice is generated along thex-zplane,y=0,upon which the gas velocity distribution is mapped.The reverse gas flow velocity(u<0)is extracted through threshold segmentation.In the area of the rainbow bar legend,the area ranging from orange to blue indicates velocities below 0.As shown in the figures,the reverse gas flow is obvious in the area near the borehole,especially near the perforation (see Fig.23).

When the permeability and outlet pressure of the bottom seam remain at 0.100 mD and 0.70 MPa,respectively,the inlet pressure increases from 8.00 to 14.00 MPa(see Fig.23).The reverse gas flow clearly scales with increasing inlet pressure.The red and orange areas spread rapidly in the borehole near the top seam (z=60–1 00 mm),but the red and orange areas only spread slightly into the borehole near the bottom seam (z=0–60 mm).In summary,the reverse gas flow injected into the top seam scales with the reservoir pressure ratio.

In CBM engineering,gas reservoirs are regarded as energy bodies full of elastic energy consisting of the following three parts:the elastic energy of the matrix,water,and gas [75].The gas elastic energy accounts for 96.2% of the total amount.Previous studies discovered that the gas elastic energy released is controlled by gas temperature changes and gas pressure changes.During the numerical simulation,the temperature is constant,ΔT=0°C;thus,the equation can be modified as follows.

whereEEis the gas elastic energy;ω the molar gas constant;T0the initial temperature;P0the initial gas pressure;χ the gas compression coefficient fromP0toP;ΔPthe gas pressure difference ΔP=P-P0;Cpthe heat capacity at constant pressure;andCvthe heat capacity at constant volume.

In the numerical simulation,the inlet and outlet pressures of the bottom seam are higher than those of the top seam,and thus,the top seam is under inhibitory effects from the bottom seam.Based on Eq.(22),the gas elastic energy released under various conditions can be calculated.As mentioned previously,the gas elastic energy has a close relationship with the pressure change.When other conditions remain unchanged,the higher the reservoir pressure of the bottom seam is,the more gas elastic energy it releases.Driven by the gas elastic energy released,gas is injected into the top seam.As shown in Fig.23,the area of reserved gas flow marked in red in the borehole increases with the gas pressure of the bottom seam.So does the SIII of the top seam.

When optimizing coal seams favorable for coproduction,it is suggested that seams in the same fluid pressure system can be coproduced together,as their reservoir pressures are similar [76].The inhibitory effects from the high-pressure coal seam can be eliminated to reduce the magnitude of the interlayer interference on the low-pressure coal seam (see Fig.24).

As shown in Fig.25,the value of SIII in the bottom seam increases significantly with the outlet pressure.Pictures of reserved gas flow under different conditions are selected randomly.When the permeability and inlet pressure of the bottom seam are 0.100 mD and 12.00 MPa,respectively,the outlet pressure of the bottom seam increases from 0.70 to 2.00 MPa.The area of the reversed gas flow marked in red clearly spreads with the magnitude of the outlet pressure.In the borehole,above the top seam (z=60–100 mm),the distribution of red changes slightly,while the distribution of red area increases significantly between the two seams(z=0–60 mm)(see Fig.26).In summary,increasing the interval distance has a strong influence on the interlayer interference occurring in the bottom seam.

Fig.22.Distribution of SIII in the top seam when the permeability of the bottom seam is 0.010,0.050,0.100,and 0.500 mD.

Fig.23.Reversed gas flow distribution for different inlet pressure in bottom seams.

Based on industry experience,CBM engineers generally choose seams with an interval distance of less than 50 m,as these seams are more likely to have better gas production [59].Three reasons may account for this phenomenon.First,in CBM engineering,the BHP of seams is controlled by the liquid column in the well.For the bottom seam,the longer the interval distance,the higher the pressure caused by the liquid column.Given the same critical desorption pressure,the inhibitory effects will be intensified if the interval distance is too large,resulting in insufficient gas desorption and production.In addition,as the bottom seam sees higher pressure,gas more easily flushes from the well into the reservoirs.During coproduction,it is inevitable that there is a fluctuation in the value of BHP,which has a great impact on gas production[62].

where ΔPbhis the bottom hole pressure change;ρmthe liquid density in borehole;h2the liquid column height of bottom coal seam;andh1the liquid column height of top coal seam.

As shown in Eq.(23),the BHP difference of the two seams is proportional to the interval distance (h2-h1).When the distance increases,the increasing static liquid column adds the BHP of the bottom seam,inhibiting gas production from the bottom seam,and thus,the value of SIII in the lower seam increases.

Fig.24.Diagram of the gas elastic energy.

5.Conclusion

Multiple-seam gas coproduction is one potential technology for achieving economic targets.In a previous publication,physical experiments were conducted in the laboratory to replicate the in situ conditions of gas flow dynamics from two coal seams simultaneously.To accelerate research on gas coproduction and reduce the research expenses,the process of physical experiments is digitalized by conducting an associated numerical simulation.Using COMSOL Multiphysics,a conceptualized model is constructed with three perpendicular fractures.The three input parameters,permeability ratio,inlet pressure,and outlet pressure,are identical to those of physical experiments.By calibrating the porosity,the results from the numerical simulation are in good agreement with the physical experiments.After analyzing the verified results,the following conclusions can be drawn.

(1) The distribution of reservoir pressure inside coal seams is visualized on the simulator.By comparing graphic results,it can be concluded that the permeability ratio does not affect the reservoir pressure distribution in the two seams.The reservoir pressure distribution is intrinsically determined by the depressurization effectiveness in each coal seam.Bottom seams have a higher gas elastic energy because of a greater depth and reservoir pressure.The difference in gas elastic energy inhibits the effectiveness of depressurization in top seams.Under the control of inhibition,the reservoir pressure in the top seams shows a slight increment when the reservoir pressure in the bottom seams increases.The reservoir pressure in the bottom seams increases with the interval distance.The bottom seams are under pressure from the liquid column in the borehole.The ever-increasing column length strengthens the inhibition of depressurization in bottom seams.It is more difficult for deeper bottom seams to depressurize;as a result,they have a higher reservoir pressure inside.

Fig.25.Distribution of SIII in the bottom seam when the permeability of the bottom seam is 0.010,0.050,0.100,and 0.500 mD.

Fig.26.Reversed gas flow distribution for different outlet pressure in bottom seams.

(2) It is verified by numerical simulation that the permeability ratio is the controlling factor of the production contribution,and the mathematical equationy=η+τ × lnxcan describe the relationship.Parameter η refers to the production contribution when two coal seams have the same seepage capacity.Parameter τ refers to the effectiveness of the permeability ratio working on the production contribution.When the permeability ratio is 1,the production contribution difference ranges from 11.24%to 24.88%.If the permeability ratio increases to 5,10,and 50,the difference value expands to the range from 48.48% to 58.68%,from 61.65% to 73.23%,and from 91.66%to 99.99%,respectively.Apart from the permeability ratio,the reservoir pressure difference also has an influence on the production contribution.For coal seams with a permeability ratio of 1,when the reservoir pressure of the bottom seam increases from 8.00 to 14.00 MPa,the difference in the production contribution caused by reservoir pressure changes shows an upward trend from 3.10%to 13.64%.For coal seams with permeability ratios of 5,10,and 50,the difference value of the production contribution increases from 4.76% to 8.78%,from 7.81% to 10.31%,and from 6.81% to 8.34%,respectively.Compared with the permeability ratio,the reservoir pressure difference has a limited influence on production contributions.The permeability ratio has the top priority to be selected as a reference for balancing the production contribution,and coal seams with a permeability ratio less than 10 are recommended for coproduction.

(3) SIII defined in physical experiments is used to quantify the magnitude of interlayer interference in numerical simulation.The SIII of the top seam increases with the reservoir pressure difference.For coal seams with a permeability ratio of 1,when the reservoir pressure of the bottom seam increases from 8.00 to 14.00 MPa,the SIII of the top seams increases from 0.37% to 0.76%.For coal seams with permeability ratios of 5,10,and 50,the SIII of the top seams increases with reservoir pressure differences from 0.18% to 0.67%,from 0.13%to 0.38%,and from 0.06%to 0.31%,respectively.The reservoir pressure difference improves the SIII of the top seams by 2.07–4.88 times.The SIII of bottom seams increases with the interval distance.For coal seams with a permeability ratio of 1,when the outlet pressure of the bottom seam increases from 0.70 to 2.00 MPa,the SIII of bottom seams increases from 0.07% to 0.94%.For coal seams with permeability ratios of 5,10,and 50,the SIII of the top seams increases with interval distances from 0.25% to 2.39%,from 0.20% to 2.18%,and from 0.52% to 6.37%,respectively.The interval distance improves the SIII of bottom seams by 9.71–13.18 times.During gas coproduction,bottom seams receive a greater influence from interlayer interference than top seams.As a reference,coal seams that have reservoir pressure differences within 1.50 MPa and interval distance within 50 m can be coproduced together from the perspective of reducing interlayer interference.

Acknowledgements

This research was supported by National Science and Technology Major Project (No.2016ZX05044002-005) and National Natural Science Foundation of China (No.41772155).The first author gratefully acknowledges financial support from China Scholarship Council (No.CSC201906420044) and expresses thanks to Richard Smith and Eric Lysczek for grammar check.