Factorized Smith Method for A Class of High-Ranked Large-Scale T-Stein Equations

We introduce a factorized Smith method(FSM)for solving large-scale highranked T-Stein equations within the banded-plus-low-rank structure framework.To effectively reduce both computational complexity and storage requirements,we develop techniques including deflation and shift,partial truncation and compression,as well as redesign the residual computation and termination condition.Numerical examples demonstrate that the FSM outperforms the Smith method implemented with a hierarchical HODLR structured toolkit in terms of CPU time.

Characteristics of high-rank coal structure parallel and perpendicular to the bedding plane via NMR and X-ray CT

Pores and fractures and their connectivity play a significant role in coalbed methane production.To investigate the growth characteristics and connectivity of pores and fractures in coal parallel and perpendicular to the bedding plane,the pores and fractures of high-rank coal samples collected from the southern Qinshui Basin were measured by low-field nuclear magnetic resonance,X-ray-computed tomography and field emission scanning electron microscopy.Then,the determinants of their connectivity were further discussed.The results show that the high-rank coal samples have similar pore size distributions both parallel and perpendicular to the bedding plane.They primarily contain mesopores(2-50 nm in width),followed by macrospores(> 50 nm in width).The research indicated that the high-rank coal connectivity parallel to the bedding plane is significantly better than that perpendicular to the bedding plane.The connectivity of high-rank coal is mainly determined by throats,and the orientation of the pores and fractures.The two connectivity modes in high-rank coal are "pore connectivity," in which the throats are mainly pores with a low coordination number,and "microfissure connectivity",in which the throats are mainly microfissures with a high coordination number.

Structure and production fluid flow pattern of post-fracturing high-rank coal reservoir in Southern Qinshui Basin

Field geological work, field engineering monitoring, laboratory experiments and numerical simulation were used to study the development characteristics of pore-fracture system and hydraulic fracture of No.3 coal reservoir in Southern Qinshui Basin. Flow patterns of methane and water in pore-fracture system and hydraulic fracture were discussed by using limit method and average method. Based on the structure model and flow pattern of post-fracturing high-rank coal reservoir, flow patterns of methane and water were established. Results show that seepage pattern of methane in pore-fracture system is linked with pore diameter, fracture width, coal bed pressure and flow velocity. While in hydraulic fracture, it is controlled by fracture height, pressure and flow velocity. Seepage pattern of water in pore-fracture system is linked with pore diameter, fracture width and flow velocity. While in hydraulic fracture, it is controlled by fracture height and flow velocity. Pores and fractures in different sizes are linked up by ultramicroscopic fissures, micro-fissures and hydraulic fracture. In post-fracturing high-rank coal reservoir, methane has level-three flow and gets through triple medium to the wellbore; and water passes mainly through double medium to the wellbore which is level-two flow.

Influence of depressurization rate on gas production capacity of high-rank coal in the south of Qinshui Basin, China

A desorption simulation experiment with the condition of simulated strata was designed. The experiment, under different depressurizing rates and the same fluid saturation, was conducted on the sample from 3# coal of Daning coal mine in Jincheng, Shanxi Province. The gas production rate and pressure change at both ends of the sample were studied systematically, and the mechanisms of some phenomena in the experiment were discussed. The experimental results show that, whether at fast or slow depressurizing rate, the methane adsorbed to high-rank coal can effectively desorb and the desorption efficiency can reach above 90%. There is an obvious inflection point on the gas yield curve during the desorption process and it appears after the pressure on the lump of coal reduces below the desorption pressure. The desorption of methane from high-rank coal is mainly driven by differential pressure, and high pressure difference is conducive to fast desorption. In the scenario of fast depressurization, the desorption inflection appears earlier and the gas production rate in the stage of rapid desorption is higher. It is experimentally concluded that the originally recognized strategy of long-term slow CBM production is doubtful and the economic benefit of CBM exploitation from high-rank coal can be effectively improved by rapid drainage and pressure reduction. The field experiment results in pilot blocks of Fanzhuang and Zhengzhuang show that by increasing the drainage depressurization rate, the peak production of gas well would increase greatly, the time of gas well to reach the economic production shortened, the average time for a gas well to reach expected production reduced by half, and the peak gas production is higher.

Structure of different types of coal metamorphism by HTEM

In order to discuss the effect of tectonic stress on the structural evolution of coal, given the importance attached to High-resolution Transmission Electron Microscopy (HTEM), we investigated several aspects of material structures of high-rank Carboniferous period coal, located in the northern foreland basin of the Dabie orogenic belt in eastern China. High powered crystal lattice images of Bright Fields (BF) and Selected Area Diffraction patterns (SAD) of different types of metamorphism in coal were obtained. The results show that the Basic Structural Units (BSU) become increasingly more compact as a function of rising tem-perature and pressure. Under pressure, the local orientation of molecules is strengthened, the arrangement of BSU speeds up and the degree of order is clearly enhanced.

Experimental study on effects of CBM temperature-rising desorption

To study the effects of CBM （coal bed methane） temperature-rising desorption, isothermal adsorption/desorption experiments on three ranks （anthracite, coking coal and lignite） of coal at different temperatures were designed based on the traditional CBM decompression desorption. The experimental results indicate that temperature-rising desorption is more effec- tive in high-rank coal, and ever-increasing temperature of high-rank coal reservoir can reduce the negative effects of coal ma- trix shrinkage in the process of production and improve the permeability of the coal reservoir as well. It is also revealed that the technique of temperature-rising desorption applied in higher-rank coal reservoir can enhance CBM recovery ratio. This study provided theoretical support for the application of temperature-rising desorption technique in practical discharging and mining projects, which can effectively tackle the gas production bottleneck problem.

Experimental study on the coupling effect of pore-fracture system and permeability controlled by stress in high-rank coal

During the coalbed methane(CBM)exploitation,the reservoir permeability can be affected by the effective stress that varies with the reservoir fluid pressure,which is a complex,dynamic and significant engineering problem.To analyze the response characteristics of the pore-fracture system by the changing stress,this work simulated reservoir and fluid pressures during the exploitation by adjusting confining pressure and displacement pressure.Stress sensitivity experiments under different effective stresses were conducted to systematically study the stage variation characteristics of porosity and permeability of coal.The results show that the permeability decreases exponentially with the increase in effective stress,consistent with previous studies.However,the porosity shows a V-shaped trend,which is different from the traditional understanding that it would decrease continuously with rising effective stress.These variation characteristics(of porosity and permeability above)therefore result in a phased porosity sensitivity of coal permeability(PPS).Moreover,the stress sensitivity of the samples was evaluated using the permeability damage rate method(MPDR)and the stress sensitivity coefficient method(MCSS),both of which showed that it ranges from the degree of strong to extremely strong.When the effective stress is lower than 5–6 MPa,the stress sensitivity of the coal reservoir drops rapidly with effective stress rising;when it is higher than 5–6 MPa,the change in stress sensitivity tends to flatten out,and the stress sensitivity coefficient(CSS)goes down slowly with rising effective stress.Finally,suggestions are proposed for the drainage scheme of CBM wells based on the experimental results.

Physical characteristics of high-rank coal reservoirs in different coal-body structures and the mechanism of coalbed methane production

The physical characteristics of coal reservoirs are important for evaluating the potential for gas desorption, diffusion, and seepage during coalbed methane （CBM） production, and influence the performance of CBM wells. Based on data from mercury injection experiments, low-temperature liquid nitrogen adsorption, isothermal adsorption, initial velocity tests of methane diffusion, and gas natural desorption data from a CBM field, herein the physical characteristics of reservoirs of high-rank coals with different coal-body structures are described, including porosity, adsorption/desorption, diffusion, and seepage. Geometric models are constructed for these reservoirs. The modes of diffusion are discussed and a comprehensive diffusion-seepage model is constructed. The following conclusions were obtained. First, the pore distribution of tectonically deformed coal is different from that of normal coal. Compared to normal coal, all types of pore, including micropores （〈10 nm）, transitional pores （10-100 nm）, mesopores （100-1000 nm）, and macropores （〉1000 nm）, are more abundant in tectonically deformed coal, especially mesopores and macropores. The increase in pore abundance is greater with increasing tectonic deformation of coal; in addition, the pore connectivity is altered. These are the key factors causing differences in other reservoir physical characteristics, such as adsorption/desorption and diffusion in coals with different coal-body structures. Second, normal and cataclastic coals mainly contain micropores. The lack of macropores and its bad connectivity limit gas desorption and diffusion during the early stage of CBM production. However, the good connectivity of micropores is favorable for gas desorption and diffusion in later gas production stage. Thus, because of the slow decline in the rate of gas desorption, long-term gas production can easily be obtained from these reservoirs. Third, under natural conditions the adsorption/desorption properties of granulated and mylonitized coal are good, and the diffusion ability is also enhanced. However, for in situ reservoir conditions, the high dependence of reservoir permeability on stress results in a weak seepage of gas; thus, desorption and diffusion is limited. Fourth, during gas production, the pore range in which transitional diffusion takes place always increases, but that for Fick diffusion decreases. This is a reason for the reduction in diffusion capacity, in which micropores and transitional pores are the primary factors limiting gas diffusion. Finally, the proposed comprehensive model of CBM production under in situ reservoir conditions elucidates the key factors limiting gas production, which is helpful for selection of reservoir stimulation methods.

Triple Medium Physical Model of Post Fracturing High-Rank Coal Reservoir in Southern Qinshui Basin

In this paper, influences on the reservoir permeability, the reservoir architecture and the fluid flow pattern caused by hydraulic fracturing are analyzed. Based on the structure and production fluid flow model of post fracturing high-rank coal reservoir, Warren-Root Model is improved. A new physical model that is more suitable for post fracturing high-rank coal reservoir is established. The results show that the width, the flow conductivity and the permeability of hydraulic fractures are much larger than natural fractures in coal bed reservoir. Hydraulic fracture changes the flow pattern of gas and flow channel to wellbore, thus should be treated as an independent medium. Warrant-Root Model has some limitations and can’t give a comprehensive interpretation of seepage mechanism in post fracturing high-rank coal reservoir. Modified Warrant-Root Model simplifies coal bed reservoir to an ideal system with hydraulic fracture, orthogonal macroscopic fracture and cuboid matrix. Hydraulic fracture is double wing, vertical and symmetric to wellbore. Coal bed reservoir is divided into cuboids by hydraulic fracture and further by macroscopic fractures. Flow behaviors in coal bed reservoir are simplified to three step flows of gas and two step flows of water. The swap mode of methane between coal matrix and macroscopic fractures is pseudo steady fluid channeling. The flow behaviors of methane to wellbore no longer follow Darcy’s Law and are mainly affected by inertia force. The flow pattern of water follows Darcy’s Law. The new physical model is more suitable for post fracturing high-rank coal reservoir.

Experimental Simulation on Dynamic Variation of the Permeability of High-Rank Coal Reservoirs

In terms of the coal reservoir permeability of effective stress, coal matrix shrinkage and gas slippage,we conduct the tests of gas permeability under constant confining pressure and effective stress, as well as illustrate the cumulating method of permeability increment caused by the effects of gas slippage and coal matrix shrinkage.The results show that under the constant confining pressure, gas slippage affecting coal permeability changes to effective stress affecting it mainly. The change point increases with the increase of the confining pressure. The gas slippage effect leads to high permeability under low confining pressure, but coal matrix expansion results in the low value as confining and gas pressures increase. Combined with the drainage process of coalbed methane(CBM)well, the permeability is divided into four change stages based on the above analysis about the three effects, which can improve the change regulation understanding. Four stages are the downward phase under effective stress,the conversion phase of effective stress-coal matrix contraction effect(mainly based on effective stress), the rising stage of the effective stress-coal matrix contraction effect(mainly based on coal matrix contraction effect) and the rising phase of coal matrix contraction-slippage effect(mainly based on slippage effect). Permeability of coal reservoir during the process of drainage and production goes through four stages.

Acoustic response characteristics and sensitivity of briquette and raw coal under temperature and pressure control

Acoustic testing is a widely used technique to measure the coal mechanical properties under high temperature and pressure in situ conditions.This study compared the acoustic wave characteristics of briquette and raw coal under various temperature and pressure conditions.The results show that the longitudinal wave velocity(Vp)decreases with an increasing vitrinite content.A large number of the vitrinite content enhances the process in which the temperature and pressure changed the Vp.The Vp of briquette decreases approximately linearly with the temperature compared to raw coal.The Vp of raw coal experiences initially a rapid,then gradual,and finally the moderate increasing trend with the increase in confining pressure.However,in briquette,the Vp increases approximately linearly with the confining pressure.The results indicate that the Vp is more sensitive to temperature under low confining pressure and peaks at 50℃−60℃ than high confining pressure.However,the Vp is less sensitive to temperature under higher confining pressure,and the positive effect of high confining pressure is dominant.Understanding the mechanical properties of coal under high pressure and temperature develops better insight into coalbed methane(CBM)exploration from deep reservoirs.