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As an unconventional energy, coalbed methane (CBM) mainly exists in coal bed with adsorption, whose productivity is different from conventional gas reservoir. This paper explains the wellbore pressure drop, surface pipeline network simulation, and reservoir calculation model of CBM. A coupled surface/wellbore/reservoir calculation architecture was presented, to coordinate the gas production in each calculation period until the balance of surface/wellbore/reservoir. This coupled calculation method was applied to a CBM field for predicting production. The daily gas production increased year by year at the first time and then decreased gradually after several years, while the daily water production was reduced all the time with the successive decline of the formation pressure. The production of gas and water in each well is almost the same when the structure is a star. When system structure is a dendritic surface system, the daily gas production ranked highest at the well which is the nearest to the surface system collection point and lowest at the well which is the farthest to the surface system collection point. This coupled calculation method could be used to predict the water production, gas production, and formation pressure of a CBM field during a period of time.

CBM is one of the most important sustainable energy for the strategy of sustainable development in the 21st century. China is abundant with CBM resource. About 36.81 trillion cubic meters is stored in depth of less than 2000 m under the ground in the field [

Coal reservoir and surface pipeline network was connected by CBM wellbore. The wellbore flow parameters directly affect gas production and surface network flow state. In the process of CBM production, the production is directly determined by bottom-hole flow pressure (BHFP). Figure

The annulus fluid distribution in the CBM wellbore.

Cullender and Smith [

Takacs and Guffey [

Steady-state hydraulic calculation for a pipe is used to decide the pipeline pressure drop. Below is the calculation model of gas pipeline pressure drop:

For a pipeline network system with

Usually, the relationship between the pressure loss and the flow rate of each pipe section could be expressed as the form of a vector function:

Pipe section pressure drop could be expressed by the pressure difference between the two endpoints of the section:

Substituting (

Steady-state thermodynamic calculation is based on the analysis of steady-state hydraulic analysis. Gas phase temperature drop of the pipeline could be calculated by the Gertjan Zuilhof temperature drop formula which is frequently used in gas pipeline.

During the solving process, the main aim is to obtain the network node temperature and solve the problem by this parameter. The equation presented by Wei et al. [

Three phases, coal, gas and water, coexist in CBM. The unique characteristics of dual porosity system make the productivity prediction different from the method used in conventional gas reservoir. So far, some people tried to predict the production performance using the CBM reservoir numerical simulation [

CBM is mainly stored as an adsorption state on the coal surface. Langmuir sorption isotherm equation is usually used to describe the relationship between the adsorption gas volume and pressure.

^{3}/ton); ^{3}/ton);

The red curve in Figure ^{3}/t. The adsorption volume increases with pressure, but when the pressure rises to a certain value, the volume does not change, which means that the adsorption of coal surface is under saturation.

Langmuir isothermal adsorption curve.

In addition, the Langmuir pressure coefficient is a parameter which affects the shape of isotherm curve of coal adsorption. The smaller the Langmuir pressure coefficient, the greater the degree of bending of the adsorption curve.

Furthermore, adsorption isotherm curve has obvious effect on coalbed methane production. Coalbed can be divided into 3 states [

The CBM formation reserve equals the sum of the amount of adsorption and free gas.

Material balance method [

Substituting the formation coefficient to (

Original gas in place (OGIP) can be calculated as follows:

Substituting (

At the beginning of undersaturated CBM exploration well, formation water is the main product. Gas production is too small to ignore. Water production in well is constant. The formation pressure difference equation at this time can be written as

Among those,

The declination of formation pressure will result in absolute permeability change in the reservoir. This influence can be described using Palmer-Mansoori model [

With the dehydration of coal, the gas and water in the cracks is in Darcy flow. Coal saturation changes so that the relative gas-water permeability changes as well. So Corey and Rathjens [

Coalbed methane production system simulation and deliverability forecasting can be described below. The following parameters are given:

reservoir parameters: initial reservoir pressure, reservoir temperature, coalbed thickness, and so on,

basic wellbore parameters: tubing diameter, inner diameter, well depth, liquid level depth, drilling fluid density, and so on,

surface pipeline network: network structure, pipe diameter, and so on,

composition of CBM.

reservoir pressure,

bottom hole flowing pressure,

gas rate,

water rate,

node pressure and flow rate of the pipeline network.

The calculation process of BHFP is described as follows:

The pressure of the working fluid level

The gas deviation factor and the friction coefficient at the average pressure and average temperature will be then calculated.

Substitute the results in (

Comparing the calculated result and the assumed value of

The initial value of BHFP

The average deviation coefficient

According to (

After evaluating

Comparing the calculated result and the assumed value of

During the calculation process of gas phase pipeline network, the hydraulic calculation and thermodynamic calculation influence each other; therefore, the entire calculation is a coupling hydraulic/thermodynamic iterative process. The specific calculation steps are described below:

Input basic data of the pipeline network, including pipe length, diameter, absolute roughness, gas composition, ambient temperature, and overall heat transfer coefficient.

The initial value of node pressure vector

The solution (

According to (

The solving sequence of the network node temperature should be established.

Node temperature vector

If

Coal reservoir production can be roughly predicted if the material balance equation and the CBM gas/water production equation are combined with the known BHFP. The specific steps are as follows:

Input basic data of reservoir, including Langmuir volume, Langmuir pressure, bulk density, initial reservoir pressure, and porosity.

OGIP can be obtained by (

If gas reservoir pressure is bigger than desorption pressure, that means the coalbed is undersaturated. Water production rate at this time

If gas reservoir pressure equals the desorption pressure (supersaturated state of the coal is not considered here), that means the coalbed is saturated. Both gas and water will be produced from the coalbed.

The basic assumptions of CBM production system coupling calculation are as follows:

During the gas production process of CBM, although the gas production changes with time, it still can be treated as constant in a small time interval. In this time interval, the flow in the wellbore and the surface pipe network can be regarded as a steady flow.

In the actual production, the working liquid level in the wellbore always changes due to the influence of gas production, water production, and the formation condition. The main factor is the production rate. In this case, the working liquid level is assumed constant.

Figure

CBM reservoir/surface coupling algorithm.

CBM production system coupling calculation model is the unity of CBM well productivity prediction model, wellbore calculation model, and surface pipe network model. The production indexes such as formation pressure, bottom hole pressure, and gas production can be determined by coupling iterations of the three models. This calculation model can be employed to optimizing the production plan. The specific calculation process is described below:

Input the basic data of CBM reservoir, wellbore, and surface network.

Do the surface, wellbore, and reservoir coupling calculation.

Assume the initial iteration value of gas production for each well at this time; then calculate the wellhead pressure for each well according to the surface pipe network model.

According to the calculated initial value of wellhead pressure and gas production, calculate the BHFP for each well using the wellbore model, respectively.

According to the calculated BHFP, calculate the gas production at the end of the production period for each well using the CBM reservoir productivity prediction model.

Compare the calculated value and the assumed value. If the difference satisfies the requirements of the error precision, calculate the cumulative gas production and cumulative water production. If not, replace the calculated value as the initial iteration value and then repeat step (

See whether it reaches the end of the production period or not. If yes, the calculation ends. If not, repeat step (

In the calculation of CBM BHFP, wellhead casing pressure data can be generally read by the wellhead pressure gauge. The pressure difference of pure gas column and the pressure difference of mixed gas liquid column can be calculated from the model introduced above. The sum of these three values is the BHFP. Although many scholars have proposed different methods to calculate BHFP, they did not compare or evaluate the applicable range and calculation accuracy.

In this paper, different calculation models have been studied and effective model with higher calculation accuracy is recommended by comparing different models. Study shows that the results of average temperature, average deviation coefficient method, and the results of Cullender-Smith method are approximately the same [

Comparison of calculated result with measured value.

Relative errors of calculated result.

After comparing these 4 models, the result of Model 1 for dataset 2 is close to the measured value, yet the calculation result error is large, which means the calculation precision of this model changes with the gas well conditions. The same result can be drawn from Model 3 as well. The calculation results of Model 1 for dataset 1 and dataset 3 are both close to the measured result. Using Model 2, we can also obtain the result close to the measured value. The error is within 20% and calculation accuracy is relatively high.

Table

Comparison of the four models.

Calculation method | Application | Calculation accuracy | Advantages/disadvantages |
---|---|---|---|

Model 1 | GCF > 0.3 | Relatively high | High precision, but large amount of calculation, narrow application scope |

Model 2 | All cases | Relatively high | Simple calculation process, high precision, good stability |

Model 3 | All cases | Change with the gas well conditions | Complex calculation process, poor stability |

Model 4 | All cases | Change with the gas well conditions | Large amount of calculation, poor stability |

Coupled calculation method was applied to 2 blocks of a CBM field. System structure is illustrated in Figure

Surface pipeline network system.

Coupling algorithms are used for productivity prediction. The parameters of coal reservoir and gas composition are given in Tables

Parameters of coal reservoir.

Input parameters | Value |
---|---|

Initial reservoir pressure (MPa) | 5.28 |

Reservoir temperature (K) | 304.15 |

Initial porosity (%) | 4.5 |

Formation thickness (m) | 6.2 |

Drainage area ( | 90000 |

Bulk density ( | 1.45 |

Gas content ( | 14.1 |

Langmuir volume ( | 38.16 |

Langmuir pressure (MPa) | 2.38 |

Composition of CBM.

Composition | CH_{4} | C_{2}H_{6} | N_{2} | CO_{2} |
---|---|---|---|---|

Mole present (%) | 96.17 | 0.05 | 3.71 | 0.07 |

Daily well gas productions.

Figure ^{3}/d.

Daily well water productions.

Figure ^{3}/d. Along with the water emergence, the formation pressure decreased gradually to the critical desorption pressure of CBM. Gas begins to desorb. Throughout the whole gas production process, formation water discharged from each gas well reduces gradually. In the 10th year, it reaches 1.97 m^{3}/d. In the later stages of production, water production of each gas well become less and less and almost no water is produced after a period of time.

Reservoir pressures.

Figure

System structure is shown in Figure

Surface pipeline network system.

Daily well gas productions.

Figure

Daily well water productions.

Figure ^{3}/d for each well. Along with the large amount of water abjection, the reservoir pressure reduces gradually to the critical desorption pressure and then gas begins to desorb. During the entire gas production, water production for gas well decreases gradually to 2.02 m^{3}/d in the 10th year. In the late stage of production, water production keeps on decreasing and almost no more water is produced after a period of time.

Reservoir pressures.

Figure

This paper describes a coupling surface/wellbore/reservoir simulation algorithm which can be used to predict gas production and water production for a period of time. Node method is used for the surface system simulation. Thermodynamic and hydraulic calculation are coupled together to calculate. CBM BHFP shows that the combination of Hasan-Kabir analytic method and average temperature average deviation coefficient method can provide a relatively high accuracy. The advantages and disadvantages of different combination models are listed as well. CBM productivity prediction is based on material balance. The method presented in this paper can be used to assist the CBM system analysis for CBM engineers by 2 validation examples.

Coefficient, dimensionless

Element of

Drainage area,

Sectional area of annulus,

Correlating matrix of the node and pipe

Transpose matrix of

Coefficient, dimensionless

Gas formation volume factor,

Water formation factor,

Formation compressibility, MPa^{−1}

Heat capacity of the medium which flows out from node

Heat capacity of the medium in section

Heat capacity of the medium which flows into the network from node

Total compressibility, MPa^{−1}

Water compressibility, MPa^{−1}

Matrix compressibility, MPa^{−1}

Tubing outside diameter, m

Tubing inside diameter, m

Step length of aerated fluid column, m

Internal diameter, m

Absolute roughness, m

Tuning factor, dimensionless

Gas porosity, dimensionless

Gravity acceleration, m/s^{2}

Produced gas,

Formation thickness, m

Aerated fluid column length, m

Gas column length, m

Permeability, md

Initial permeability, md

Final permeability, md

Effective permeability to gas, md

Effective permeability to water, md

Relative permeability to gas, dimensionless

Relative permeability to water, dimensionless

Final relative permeability to gas, dimensionless

Final relative permeability to water, dimensionless

Bulk elastic modulus, MPa

Pipe length, m

Axial constraint modulus, MPa

Gas molar mass, kg/mol

Exponent, dimensionless

Exponential of relative gas permeability curve, dimensionless

Exponential of relative water permeability curve, dimensionless

Original water in place,

Average pressure, MPa

Arbitrary base pressure, MPa

Surface casing pressure, MPa

Pressure at working fluid level, MPa

Initial reservoir pressure, MPa

Langmuir pressure, MPa

Inlet pressure of pipe, MPa

Average reservoir pressure, MPa

Outlet pressure of pipe, MPa

Bottom-hole flowing pressure, MPa

Standard pressure, MPa

Pressure drop of gas column, MPa

Node pressure vector

Pipe pressure drop vector

Mass flow rate, kg/s

Gas rate,

Mass flow of the medium in section

Water rate,

Mass flow of the medium which flows into the network from node

Total mass flow of the medium which flows into node

Gas production rate in standard state,

Node flow vector

Pipe flow vector

External radius of reservoir, m

Liquid gravity, Pa^{−1}

Wellbore radius, m

Apparent wellbore radius, m

Universal gas constant, J/(mol·K)

Definition parameter, dimensionless

Skin factor, dimensionless

Average gas saturation, dimensionless

Water saturation, dimensionless

Irreducible gas saturation, dimensionless

Irreducible water saturation, dimensionless

Initial water saturation, dimensionless

Average water saturation, dimensionless

Temperature,

Ambient temperature,

Temperature of node

Reservoir temperature,

Temperature of the starting point of the pipeline,

Temperature of the medium which flows into the network from node

Standard temperature,

Temperature of the end of section

Apparent velocity, m/s

Gas content,

Langmuir volume,

Reserve volume,

Encroached water,

Produced water,

Gas compressibility factor, dimensionless

Standard gas compressibility factor, dimensionless

Gas factor for unconventional gas reservoir, dimensionless

Poisson ratio, dimensionless

Gas viscosity, Pa·s

Water viscosity, Pa·s

Porosity, dimensionless

Initial porosity, dimensionless

Final porosity, dimensionless

Maximum strain, dimensionless

Matrix shrinkability, MPa^{−1}

Gas relative density, dimensionless

Hydraulic friction coefficient, dimensionless

Bulk density of the coal, t/

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors thank the financial support from the Young Scholars Development Fund of SWPU (201599010096).