Shale gas is a kind of unconventional oil-gas resource with tremendous potential. For thorough understanding of the methane adsorption and micromechanism in organic-matter nanopores of the shale and better acquaintances of the occurrence form, graphite slit-pores were set up as a representation of organic-matter nanopores by using Material Studio, and the grand canonical Monte Carlo method, molecular mechanics and molecular dynamics were used for the simulation of adsorption and diffusion behaviors in organic-matter pores on CH4 and CO2 at the shale gas common burial depth of 2–4 km in the Upper Yangtze Plate.
Tingshan Zhanga,b, Yingjie Hea,b, Yang Yanga,b, Kunyu Wua,c
aState Key Lab of Oil & Gas Reservoir Geology and Exploitation Engineering, Southwest Petroleum University, Chengdu, 610500, China. bSchool of Resources and Environment, Southwest Petroleum University, Chengdu, 610500, China. cInstitute of Exploration and Development, Qinghai Oil Field, CNPC, Dunhuang, 736202, China
Received 15 February 2017; available online 8 February 2018
The results indicated that the adsorptions of CH4 and CO2 were physical and the optimal storage depth was 2 km; The mixed adsorption data showed the rationality of exploit shale gas by injecting CO2 to exchange CH4, and the optimal burial depth was 4 km; The relative density of CH4 and CO2 along the normal direction of the pore inwall showed a trend of symmetric distribution and apparent adsorption stratifications appeared. As a whole, the self-diffusion coefficient of CH4 and CO2 increased with the increase of burial depth, and it’s consistent with the reasons for such changes of adsorption amount and adsorption heat.
American “Shale Gas Revolution” has met with great success in recent years, having set off a wave of global exploration and development of shale gas , , . Shale gas exists in organic rich mudstone in the form of free state and adsorbed state in most cases, with extensive development of organic nanopores in organic rich mudstone, being the important component of reservoir space for clay shale , , , , organic porosity size is immediately associated with content of adsorbed gas . Therefore, it is valuable to research adsorption effect of organic nanopores on shale gas and microcosmic mechanism thereof so as to further evaluate shale gas resource .
Although research of the influence of characteristic factors of shale including mineral composition and pore structure on adsorption and diffusion pattern of shale gas has been conducted for many years , , , , , the relevant researches of adsorption and diffusion mechanism of shale gas done by molecular simulation method under the condition of special hydrocarbon reservoir for shale gas are inadequate, although Liu et al.  adopted molecular dynamic method to simulate similarities and differences in adsorption and desorption of mixture prepared in the different proportions of CH4 to CO2 in carbon nano tube, Cao et al.  made research on separation of CH4/CO2 in CNT different in tube diameter in terms of molecular dynamics, He et al. ,  also verified the feasibility to adopt CNT model to simulate dynamical characteristic of adsorption and diffusion of shale gas in organic nanopores of shale reservoir, but failed to analyze and interpret microscopic distribution as well as adsorption and diffusion mechanism of CH4 and CO2 in organic nanopores based on actual burial depth of shale in terms of geological condition and that the burial depth of organic nanopores is a touchstone to determine whether shale stratum block is available for commercial development , .
Therefore, Grand Canonical Monte Carlo method, molecular mechanic method and molecular dynamic method to simulate adsorption effect of organic pores at the burial depth of shale gas  from 2 km to 4 km on CH4 and CO2 in Sichuan Basin and surrounding in Early Paleozoic Era (Qiongzhusi Formation, Wufeng Formation and Longmaxi Formation) under the condition that 0 km and 6 km are set as burial depth for reference, that surface temperature is 283 K, that pressure is 0.1 MPa, that geothermal gradient is 30 K/km and that pressure gradient is 15 MPa/km so as to calculate quantity and heat of adsorption in organic pore of shale reservoir at various burial depths and make a study of characteristic of microcosmic distribution, relative density, self diffusion coefficient of CH4 and CO2 in organic pore in shale reservoir and determine preferred burial depth of shale gas and optimal range of burial depth for shale gas available for exploitation CO2 replacement technology so as to guide exploration and development of shale gas to a certain extent.
Model building and structural optimization
Adsorption effect of organic pore on shale gas is under the influence of many factors including pore shape, 0diameter, maturity of organic matter, category of organic matter and water saturation , however, the paper, based on basic research, builds CNT model to represent organic pore under the ideal condition for the first time so as to make a further report on relevant research of complex model (irregular shape, increase and decrease in functional group) to be built under multiple conditions mentioned above in future. CNT is an allotrope of carbon made up of hexagonal grid of carbon atom discovered in 1991, having widely been applied to researches on many fields as a result of its advantages including high specific surface area, corrosion resistance and high chemical stability , , .
In recent years, as a type of excellent adsorption material, it has been introduced to hydrocarbon field , . CNT is high in carbon content, having favorable adsorption effect on CH4 as component of shale gas and being able to adjust tube diameter to nanometer scale, which tallies with the performance of organic nano pore in shale reservoir; in addition, the shale sample from shale gas associated with research area shows that organic nano pores are honeycombed in most cases (Fig. 1).
The periodic model of CNT in simulation can be considered as parallel arrangement of the organic pores identical in size, being more consistent with characteristic of organic nanopores compared with graphite slit model; therefore, the paper adopts SWCNT to represent organic nanopore in simulation process. Structure parameter of atom arrangement mode in CNT is indicated as vector (n,m), in case that n = m, it is armchair type; in case that n > m = 0, it is zigzag type; armchair type and zigzag type CNTs are different in conductivity, in case of serving as an external boundary to restrict internal fluid behavior, there is no difference between the two, the paper selects armchair type CNT for simulation. CNT diameter is as shown in formula (1):
where a is lattice constant, a = 2.46 Å in CNT.
Fig. 1. Characteristic of nanopore in Early Silurian shale of Longmaxi Formation in research area.
The paper takes molecular simulation software Material Studio (MS) as operation platform for entire simulation and calculation to build (19,19) armchair type SWCNT to represent organic pore by Single-Wall Nanotube command in Build Nanostructure of Visualizer module, with diameter d = 25.76 Å (the data is based on mean of pore diameters of 56 samples from 5 shale gas wells mentioned in the paper), tube length z = 73.79 Å, and area between SWCNT columnar structures to make up of pore space, and box with lattice parameters a = 29.11 Å, b = 29.11 Å, c = 73.79 Å, α = 90°, β = 90° andγ = 120°used for simulation and directions X, Y and Z set to be periodic boundary condition so as to simulate macroscopic system by infinite repeat in space.
Given support and fixation by other part of rock, accordingly, SWCNT model is considered as rigid structure. In order to obtain stable SWCNT model, first, it is advisable to adopt smart of Forcite model in molecular dynamics to carry out configuration optimization of the initially built SWCNT model, with COMPASS force field ,  applicable to organic matter model, Ewald method for electrostatic interaction, Atom based method of summation for Van Edward force action, truncation radius of 13.5 Å, tooth width of 1 Å, buffer width of 0.5 Å, convergence precision of Ultra-fine. The stable configuration model for CH4 and CO2 are achieved by the same method (Fig. 2a and c).
Fig. 2. Configuration of CH4 and CO2 adsorbed by organic pore (burial depth 4 km). (a) Initial configuration of CH4 adsorbed (b) Initial configuration of CO2 adsorbed; (c) Initial configuration of CH4/CO2 adsorbed; (d) Stable adsorption configuration of CH4 after configuration optimization; (e) Stable adsorption configuration of CO2 after configuration optimization; (f) Stable adsorption configuration of CH4/CO2 after configuration optimization.
Lennard-Jones (LGJ) potential energy model  is adopted to simulate interaction between fluid molecule and carbon atom of SWCNT as well as between fluid molecules mentioned in the paper, it is observed from formula (2) that Van Edward force existing between covalent bond molecules can be accurately described by simulation system by introduction of L-J potential function.
where rij is range between particle i and j; qi and qj are electric quantity of i and j respectively; εij andσij are energy interaction parameter and size interaction parameter respectively; the mixing rule adopted in the paper is Lorentz–Berthelot (L-B), such as (3), (4); the L-J potential energy parameter is as shown in Table 1.
Table 1. L-J potential energy parameter .
“Importance sampling” Metropolis  method of Grand Canonical Monte Carlo is adopted to simulate adsorption of CH4 and CO2 by SWCNT, the adsorption heat and adsorption quantity under the condition of different temperature and pressure are obtained by Fixed Pressure task in Sorption module based on software MS. SWCNT in simulation keeps fixed without initial speed all the while in simulation, with total 6 × 106 steps and 3 × 106 balance steps in simulation and parameter setting for force field identical with that in configuration optimization process mentioned above.
After adsorption configuration is obtained, in order to achieve optimal structure, first, it is advisable to adopt Steepest descent method to carry out optimization of adsorption model and then use Quasi-Newton method to perform secondary optimization of molecule model and then adopt NVT to carry on molecular dynamic operation of optimized model for 1 ns, with Andersen  Nose–Hoover to control temperature, initial speed of every molecule randomly generated by Maxwell–Boltzmann distribution, on the premise that periodic boundary condition and time average are equivalent to average in NVT, Velocity Verlet  algorithm is utilized to solve Newton’s equation of motion to obtain stable absorption configuration of CH4 and CO2, finally, temperature control method is set to be Noes  Nose–Hoover to carry out molecular dynamic operation for 0.5 ns for data collection and analysis; with step length of 1fs in simulation and primary result outputted in every 500 steps.
Results and discussion
Monte Carlo simulation
Monte Carlo is a method to repeatedly generate time series and calculate parameter estimate and statistic so as to analyze their distribution characteristic on the premise of random process . Adsorption and diffusion of shale gas in organic rich mudstone is random event, application of the method to research on adsorption and diffusion mechanism of shale gas is able to better simulate adsorption system of shale gas in complex geological condition , .
Adsorption of CH4 and CO2 by organic pore
Influence of organic pore on adsorption heat and adsorption energy of CH4 under the condition of different pressure (P) and temperature (T) is as shown in Table 2. It is observed from single adsorption of CH4 in Table 2 that with the increase of temperature and pressure, the average adsorption quantity of CH4 shows sharp increase and then slow decrease, the reason for which is that at the beginning of simulation, the increase in temperature is to increase kinetic energy of CH4 in organic pore to intensify movement, more molecules in collision with internal wall of pore are to increase adsorption sites occupied by CH4 molecules on surface of internal wall of pore, resulting in denser arrangement and greater adsorption quantity.
Table 2. Influence of organic pore on adsorption heat and adsorption quantity of CH4 and CO2 at different temperature and pressure.
Burial depth from 0 km to 2 km is larger in temperature and pressure span (2 gradients), therefore, adsorption quantity is on sharp increase, with average adsorption quantity being up to maximum in case of 30 MPa in pressure, 343 K in temperature and 2 km in burial depth; however, with further increase of temperature, CH4 in organic pore is to gain greater kinetic energy to intensify Brownian movement, with kinetic energy of CH4 molecules to break through adsorption energy barrier on surface of internal wall of pore, resulting in decrease of adsorption quantity and approach to stability step by step.
The average adsorption heat for organic pore to adsorb CH4 is also to show relevant change, with adsorption heat from −24.602 to 37.321 kJ/mol, however, present research findings indicate that the adsorption with adsorption heat less than 42 kJ/mol is physical adsorption and the adsorption with adsorption heat more than42 kJ/mol is chemical adsorption, being from 84 to 417 kJ/mol , therefore, adsorption of CH4 by organic pore is physical adsorption.
Since the experimental methods such as isothermal adsorption under present experimental condition are unable to achieve the condition of high temperature and high pressure at the burial depth defined in the paper, in general, the isothermal adsorption experiment pressure is able to reach 40 MPa, in case that the temperature is 30 °C, the obtained adsorption quantity data is not to be compared with simulated adsorption quantity data, therefore, the paper is to bring gas content data and simulated data into comparison. Distribution of wells including Y1, Y2, Y3, Y4 and Y5 in Sichuan Basin and surrounding in Early Paleozoic Era (Qiongzhusi Formation, Wufeng Formation and Longmaxi Formation) is as shown in Fig. 3a, it is observed from natural gas component data from the above mentioned gas wells that primary component is CH4 (more than 54.12%), the maximum percentage of shale gas in adsorption state to total shale gas occurring in nanopore is up to 85% , , therefore, gas containing data is able to reflect primary trend of methane adsorption by shale pore.
Fig. 3. Schematic diagram of wells location & contrast figure of experimental and simulation data.
It is observed from comparison between simulated result (adsorption quantity) and experimental data (gas content) (Fig. 3b) that on the premise of the identical burial depth, simulated data is much higher than experimental data, the reason for which is that SWCNT is an ideal model of shale pore, having better adsorption effect on CH4, on the premise that shale gas is favorable in structure and preservation condition and free of crack, resulting in effusion of shale gas, therefore, simulated value is much higher than experimental value, however, with the increase of burial depth, the two data tend to be identical in distribution to a certain extent, indicating that the built model and set parameter for selected force field are rational, having predictability to a certainty.
In a similar way, the influence of organic pore on adsorption heat and adsorption energy of CO2 under the condition of different pressure (P) and temperature (T) is as shown in Table 2 and Fig. 4. It is observed from single adsorption of CO2 in Table 2 that with the increase of temperature and pressure, the average adsorption quantity of CO2 shows sharp increase and then slow decrease, the reason for which is that at the beginning of simulation, the increase in temperature is to increase kinetic energy of CO2 in organic pore to intensify movement, more molecules in collision with internal wall of pore are to increase adsorption sites occupied by CO2 molecules on surface of internal wall of pore, resulting in denser arrangement and greater adsorption quantity.
Adsorption quantity is on sharp increase at the burial depth from 0 km to 2 km, being up to maximum in case of 30 MPa in pressure, 343 K in temperature and 2 km in burial depth; however, with further increase of temperature, CO2 in organic pore is to gain greater kinetic energy to intensify Brownian movement, with kinetic energy of CO2 molecules to break through adsorption energy barrier on surface of internal wall of pore, resulting in decrease of adsorption quantity, finally, in case that the molecules in adsorption state from free state are equal to molecules in free state from adsorption state, the adsorption achieves dynamic balance. The average adsorption heat for organic pore to adsorb CO2 is also to show relevant change, with adsorption heat from −20.836 to 52.643 kJ/mol, the adsorption is physical adsorption.
Fig. 4. Change in adsorption quantity of CH4 and CO2 by organic pore at different temperature and pressure.
Adsorption of CH4/CO2 by organic pore
Influence of organic pore on adsorption heat and adsorption energy of CH4/CO2 under the condition of different pressure (P) and temperature (T) is as shown in Table 2 It is observed from mixed adsorption of CH4/CO2 in Table 2 that with the increase of temperature and pressure, the average adsorption quantity of CH4/by organic pore still shows the trend of sharp increase and then slow decrease, being up to maximum at the burial depth of 2 km and consistent with the pattern of signal adsorption of CH4, as the result of the same reason, with obvious decrease in adsorption quantity compared with that of single adsorption of CH4 under the influence of competitive adsorption of CO2, the existence of CH4 also decreases adsorption quantity of CO2 by organic pore in evidence, showing the trend different from that of single adsorption of CO2, namely sharp increase and then slow decrease followed by slow increase and then slow decrease, the reason for which is that increase of temperature is to increase kinetic energy of CO2 in the space between slits to intensify movement, more molecules in collision with internal wall of pore are to increase adsorption sites occupied by CO2 molecules on surface of internal wall of pore, resulting in denser arrangement and greater adsorption quantity.
Burial depth from 0 km to 2 km is larger in temperature and pressure span (2 gradients), therefore, adsorption quantity is on sharp increase, with further increase in burial depth, CO2 in pore is to gain greater kinetic energy to intensify Brownian movement, with kinetic energy of CO2 molecules to break through adsorption energy barrier on surface of internal wall of pore, resulting in decrease of adsorption quantity, with further increase in burial depth, the temperature and pressure at which enable CO2 to be under dual control by temperature and pressure, making adsorption quantity fluctuant, with increment of adsorption quantity and increment of diffusion quantity failing to approach to stable equilibrium, namely, at the burial depth from 2 km to 4 km, in case that there is competitive adsorption between CO2 and CH4, they fail to reach the most stable state in adsorption, however, it is observed from maximum adsorption quantity of CO2 that maximum of average adsorption quantity of CO2 is most likely to appear in the vicinity of 4 km in burial depth.
It is also observed from adsorption energy for adsorption of CH4/CO2 by organic pore that the adsorption heat of the two types of gases is less than 42 kJ/mol, being physical adsorption. Under the same condition of temperature and pressure, the adsorption quantity of CO2 is more than that of CH4(Table 2 mixed adsorption of CH4/CO2), there is competitive adsorption between CH4 and CO2 in organic pore, with the most obvious competitive adsorption appearing at the burial depth of 4 km and the slightest competitive adsorption taking place at the burial depth of 3 km Therefore, it is rational and feasible to exploit shale gas by means of CO2 injection to replace CH4, namely, the effect is best at the burial depth of 4 km and the effect is poor at the burial depth of 3 km.