岩石微孔隙中气体吸附、链状分子运移的计算模拟及其油气地质意义
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摘要
随着常规油气资源勘探难度的增加,煤层气、页岩气等非常规油气资源在能源结构中的地位越来越重要。认识和了解煤层和页岩孔隙中甲烷和二氧化碳的吸附特征及岩石形变规律,对于煤层气、页岩气的资源评价和开发有着十分重要的意义。本文在借鉴前人岩石孔隙表征结果的同时,采用氮气探针气体吸附法分析了4个煤岩样品和11个页岩样品的孔隙结构的特征,发现纳米尺度(<50 nm)孔隙较为丰富。鉴于纳米级孔隙所独有的纳米尺寸效应及其对气体吸附的重要作用,本研究针对这类孔隙-气体的相互作用开展了一系列计算模拟工作,淬火固体密度泛函理论(Quenched solid density functional theory, QSDFT)和DPD方法是本文采用的主要研究方法。
首先,本文采用淬火固体密度泛函理论(Quenched solid density functional theory, QSDFT)研究了地质条件下甲烷和二氧化碳在煤层中的吸附行为。研究的重点是吸附过程中温度,压力以及孔径分布对于煤岩变形的影响。研究结果包括,0.5到50nm的煤层孔在298K和360K下100MPa的压力范围内的吸附量,密度分布曲线以及溶剂化压力曲线。研究发现甲烷吸附导致的溶剂化压力对孔径的变化曲线存在两种主要类型：类型Ⅰ表现为在整个压力范围内的单调膨胀。这种类型在最小的孔中<1.3σff(0.5nm)中最为典型。这类孔的特点是不能容纳超过一层的甲烷分子。类型Ⅱ表现为在低压下的收缩,而后膨胀。类型Ⅱ在能容纳整数倍层数甲烷分子(2-6层)的孔中最为常见。360K下的二氧化碳吸附导致的溶剂化压力与外压的依存关系也存在两种类型的变形行为：第Ⅰ类形变表现为在全压力范围内的单调膨胀,但在极高压下(100MPa)又会表现出收缩或者继续膨胀。该类行为在最小的孔(<0.5nm)中较为典型,该类孔不能容纳超过一层的二氧化碳分子,见0.5nm的密度分布曲线。第Ⅱ类变形行为在低压下表现出收缩,而后膨胀。高压下,该类变形行为也可以出现或膨胀或收缩的现象。第Ⅱa类行为出现在0.6和0.9nm的孔中。所有>0.9nm的孔都表现出第Ⅱb的形变。通过与文献中甲烷和二氧化碳吸附导致形变的实验数据的对比,验证了QSDFT模型的有效性。通过对一个假定模型盆地中甲烷和二氧化碳吸附行为的研究,建立了甲烷和二氧化碳吸附量、溶剂化压力与煤层孔结构以及埋藏深度之间的联系,并对二氧化碳对甲烷的驱替行为进行了初步的探讨。研究发现煤层的变形对于埋藏深度有很强的依赖性,在不同的埋藏深度膨胀或者收缩的发生依赖于煤样品孔径分布的情况。通过对地质条件下煤层中二氧化碳驱替甲烷的模拟,探讨了增强的甲烷开采方案(ECBM)中二氧化碳储量以及二氧化碳注入过程中煤层孔隙结构变化的情况。研究发现,微孔在驱替过程中的应变变化比较大,而介孔的变化较小。不同微孔应变达到极值的深度也不尽相同。对于介孔来说,5nm的孔表现出最小的区别(<0.6%)。而对于微孔来说,体相应变的差异在1nm孔径100m的情况下可以达到1.7%。这么大的应变差异将有可能导致储层渗透率的降低。
其次,本文采用同样的方法研究了甲烷和二氧化碳在页岩中的吸附储量及由吸附研究的变形行为,相应地获得了甲烷和二氧化碳吸附量、溶剂化压力与页岩孔结构以及埋藏深度之间的联系。深度浅的时候,微孔比介孔表现出更大的单位吸附能力。小于1nm的孔的甲烷吸附能力随深度增加而快速增加,到埋藏为1500m时吸附量达到8 mmol/cm3左右的极大值。而2nm和5nm的孔的甲烷吸附量在到达6000m之前一直在持续增加,其对吸附量的贡献在3000m深度之后超过微孔。本文发现甲烷的吸附导致了三种不同的应变-深度关系。第一种,在整个深度范围内都表现为先膨胀后收缩,例如0.5nm和0.7nm的孔。在达到膨胀极值之前(0.5nm的孔1000m下的0.11%,0.7nm的孔为2000m下的0.12%),体相应变随埋藏深度快速增长,之后收缩。第二种,1nm的孔,在极浅部随深度增加表现为收缩,至100m达到一个极小值后缓慢增长,最后在6000m时膨胀至0.11%。第三种,对于≥2 nm的孔,在整个深度范围内其体积应变的变化≤0.04%,与微孔相比其影响可以忽略不计。在将二氧化碳封存到页岩中时,当深度小于1000m的时候,微孔中的所吸附的二氧化碳占主导地位,但当深度大于1000m时,介孔中的存储将变得更加重要。如果页岩层有大量的≤1nm的孔,那么其在6000m的深度之内的形变都有较大变化,有可能对二氧化碳注入过程中页岩孔结构产生影响。
通过对甲烷和二氧化碳在煤层及页岩中的吸附研究,本文发现由流体分子导致的纳米孔隙的吸附变形行为可能存在一定的规律。为了进一步认识形变与流体分子的吸附行为的关系,本文采用QSDFT的方法定量得研究了表面粗糙程度对流体吸附和颗粒之间的相互作用的影响。表面的不均一性对于固体的润湿性和粘着性质有着很重要的影响。然而,大多数计算固体与流体相互作用的理论和模拟方法都假设存在一个标准的平滑的Gibbs流体固体分界面。这个假设导致了靠近固体表面的流体相出现人为的分层现象。具体的表现就是密度分布曲线的明显波动。这种流体密度的成层性导致了溶剂化压力以离孔壁的距离为函数发生波动,但是溶剂化压力的这种明显的波动性却在试验中极少见到。在QSDFT中,表面粗糙成分采用粗糙度参数来定量表示,该粗糙度参数代表了固体表面松散层的厚度。通过对LJ流体在平行板状孔中吸附(模拟了氮气在石墨中的吸附)的例子,本文发现在饱和状态,溶剂化压力随孔径有规律的波动。这种波动随表面粗糙度的增加(从0增加到1/2倍的分子直径)而快速减小。溶剂化压力的波动性与流体密度在匹配孔中流体密度的最大值以及不匹配孔中流体密度的最小值有很好的对应。后者以松散排列和流体的密度减小为特征。该分析表明分子尺度上的表面粗糙度对局限流体的成层排列以及成层性都有很大的抑制作用。另外,本文计算了在吸附过程中溶剂化压力随外压的变化情况,其变化随孔径和粗糙度的不同可以分为几种不同的机制。由于溶剂化压力决定了多孔介质的吸附变形性质,溶剂化压力随外压变化的非单调性很好的对应了石墨等微孔材料的在不同压力下的收缩膨胀性质。
第三,本文采用三维DPD的模拟方法研究了链状大分子在不同外力场的作用下穿越狭窄孔道时链长的行为,以期对链状分子的运移行为进行深入理解。研究发现外力与平均穿越时间存在着反比关系,链长对穿越时间有很大影响,其在良溶剂下的指数关系为1.56,在不良溶剂下的指数关系为1.76。这与τtrans～N1+v的理论计算结果很接近。模拟观测表明穿越过程中的平均回旋半径主要受其初始状态的平衡值的影响。在穿越过程结束的时候,其指数关系为1,这与其受相同外力在无限空间中的运动行为一致。这可能是受到的外力力场强度大以及带电电荷之间相互作用较强造成的(在带电链状大分子穿越静电力场的情况下)
Unconventional energy (e.g. coal bed methane, shale gas) now is playing more important roles in the whole energy system. Understanding the adsorption capacity and deformation change during adsorption of methane and CO2 on coal and shale, may help the exploitation and resoure evaluation. Four coal samples and eleven shale samples were measured by N2 adsorption method. Isotherms as well as pore size distrubtions of these samples were obtained. Base on these exmperimental data, a systematic simulation work were carried out.
Firstly, the quenched solid density functional theory (QSDFT) is employed to study the adsorption of methane and CO2 on coal at geological conditions. The main focus is made on coal deformation in the course of adsorption that may result either in expansion/swelling or contraction, depending on pressure, temperature, and pore size. The results of methane adsorption capacity, density profile and salvation pressure on coal in pores from 0.5nm to 50nm at 298 K and 360 K with pressure up to 100 MPa are given. Two qualitatively different types of deformation behavior are found depending on the pore width:Type I shows a monotonic expansion in the whole pressure range. This behavior is characteristic for the smallest pores<1.3σff (0.5nm) that cannot accommodate more than one layer of methane. Type II displays contraction at low pressures followed by expansion. Type II behavior is found for several groups of pores, which can accommodate dense packing with integer number (from 2 to 6) of adsorbed layers. Two typical deformation behaviors at 360 K could be summarized from the CO2 solvation pressure dependence on the external pressure. Type I behavior shows a monotonic expansion in the whole pressure range, but at high pressures it may either continue to expand or contract. This behavior is typical for the smallest pores<1.3σff (0.5 nm) that cannot accommodate more than one layer of CO2, as shown by the density profile in 0.5 nm pore. Type II behavior displays contraction at low pressures followed by expansion. At high pressure, it also may expand or contract again. Type Ha is found for 0.6 nm and 0.9 nm pores. All other pores>0.9 nm present the typeⅡb behavior.Then, the results of QSDFT model arecompared with literature experimental data, and the model is then employed to study the adsorption behavior of model coals at elevated pressures and temperatures. An instructive example of CO2 sequestration into coal bed is given. We established the relationships between the methane and CO2 capacity and the solvation pressure it exerts on the coal matrix and the depth of coal bed for pores of different sizes. The replacement process of methane by CO2 is discussed. We found that the coal deformation depends on the bed depth, and at different depths it either swell or contract depending on the pore size distribution. Through calcualtion on the replacement of methane by CO2 under geological condition, CO2 capcity and the structure change in the ECBM scenario were discussed. The difference in the volumetric strain induced by adsorption of CO2 and methane is the smallest in the case of 5nm pore (0.6%). For micropores (≤2nm), the volumetric strain difference can be as large as 1.7% in the case of 0.7 nm pore at 100 m depth, which may cause significant reduction in permeability of the reservoir through deformation.
Secondly, similiar model is employed to study the adsorption capacity of methane and CO2 in shale and the adsorption induced deformation behavior. Correspondingly, the relationships between the methane and CO2 capacity and the solvation pressure it exerts on the shale matrix and the depth of shale for pores of different sizes is discussed. When the depth is small, the adsorption capacity (per unit volume) of micropore is bigger than that of mesopore. Methane adsorptin capacity in pores From the study on adsorption behavior of methane and CO2 in coal bed and shale, I found that the adsorption induced deformation behavior may have some internal relatinship with pore width. In order to better understanding this relationship, I present a quantitative description of the effects of surface roughness on fluid adsorption and inter-particle interactions based on the quenched solid density functional theory (QSDFT). Surface heterogeneity affects significantly wetting and adhesion properties. However, most of the theories and simulation methods of calculating solid-fluid interactions assume a standard thermodynamic model of the Gibbs'dividing solid-fluid interface, which is molecularly smooth. This assumption gives rise to an artificial layering of the fluid phase near the surface that is displayed in oscillating density profiles. This layering brings about oscillations of the solvation (or disjoining) pressure as a function of the gap distance, which are rarely observed in experiments. In QSDFT, the surface roughness is quantified by the roughness parameter, which represents the thickness of the surface "corona" -the region of varying solid density. Drawing on the example of a LJ fluid confined to slit pores with the parameters mimicking nitrogen at its boiling temperature on carbon, it shows that while the solvation pressure at saturation conditions oscillates with the pore width in the case of smooth surfaces, these oscillations rapidly diminish with the increase of the roughness parameter from 0 to just 1/2 of the molecular diameter. The solvation pressure oscillations are correlated with the respective oscillations of the fluid density with maxima corresponding to the pore widths commensurate to the ordered layering in confined fluid and minima corresponding to the incommensurate pore widths. The latter are characterized by a loose packing and reduced density. This analysis demonstrates that the molecular scale roughness on the level of one molecular diameter frustrates the order and hinders the layering in confined fluid. Further, I calculate the variation of solvation pressure in the course of adsorption in pores and show qualitatively different regimes depending of the pore width and degree of roughness. Since the solvation pressure determines the adsorption-induced deformation of compliant porous bodies, the non-monotonic dependence of the solvation pressure corresponds to alternating stages of contraction and expansion that is typical for carbons and other microporous materials.
Finally, this study used 3D DPD approach to study the behavior of a polymer chain translocating through a nanopore under different external fields in order to better understanding the expellling process of hydrocarbon from source rock. An inversed linear scaling relationship was found between the external force and average translocation time. For the chain length effect, the scaling exponent under good solvent condition is 1.56, under bad solvent is 1.76, close toτtrans～N1+v. The observation reveals that the average radius of gyration is still dominated by its equilibrium value at the beginning of the translocation process. At end of the translocation process, the scaling is close to 1, which indicates a pure pulling condition by the external force. This might be due to the large magnitude of the external force and strong electrostatic interaction between charged bead (in the case of charge polymer chain and electrostatic force).
首先,本文采用淬火固体密度泛函理论(Quenched solid density functional theory, QSDFT)研究了地质条件下甲烷和二氧化碳在煤层中的吸附行为。研究的重点是吸附过程中温度,压力以及孔径分布对于煤岩变形的影响。研究结果包括,0.5到50nm的煤层孔在298K和360K下100MPa的压力范围内的吸附量,密度分布曲线以及溶剂化压力曲线。研究发现甲烷吸附导致的溶剂化压力对孔径的变化曲线存在两种主要类型：类型Ⅰ表现为在整个压力范围内的单调膨胀。这种类型在最小的孔中<1.3σff(0.5nm)中最为典型。这类孔的特点是不能容纳超过一层的甲烷分子。类型Ⅱ表现为在低压下的收缩,而后膨胀。类型Ⅱ在能容纳整数倍层数甲烷分子(2-6层)的孔中最为常见。360K下的二氧化碳吸附导致的溶剂化压力与外压的依存关系也存在两种类型的变形行为：第Ⅰ类形变表现为在全压力范围内的单调膨胀,但在极高压下(100MPa)又会表现出收缩或者继续膨胀。该类行为在最小的孔(<0.5nm)中较为典型,该类孔不能容纳超过一层的二氧化碳分子,见0.5nm的密度分布曲线。第Ⅱ类变形行为在低压下表现出收缩,而后膨胀。高压下,该类变形行为也可以出现或膨胀或收缩的现象。第Ⅱa类行为出现在0.6和0.9nm的孔中。所有>0.9nm的孔都表现出第Ⅱb的形变。通过与文献中甲烷和二氧化碳吸附导致形变的实验数据的对比,验证了QSDFT模型的有效性。通过对一个假定模型盆地中甲烷和二氧化碳吸附行为的研究,建立了甲烷和二氧化碳吸附量、溶剂化压力与煤层孔结构以及埋藏深度之间的联系,并对二氧化碳对甲烷的驱替行为进行了初步的探讨。研究发现煤层的变形对于埋藏深度有很强的依赖性,在不同的埋藏深度膨胀或者收缩的发生依赖于煤样品孔径分布的情况。通过对地质条件下煤层中二氧化碳驱替甲烷的模拟,探讨了增强的甲烷开采方案(ECBM)中二氧化碳储量以及二氧化碳注入过程中煤层孔隙结构变化的情况。研究发现,微孔在驱替过程中的应变变化比较大,而介孔的变化较小。不同微孔应变达到极值的深度也不尽相同。对于介孔来说,5nm的孔表现出最小的区别(<0.6%)。而对于微孔来说,体相应变的差异在1nm孔径100m的情况下可以达到1.7%。这么大的应变差异将有可能导致储层渗透率的降低。
其次,本文采用同样的方法研究了甲烷和二氧化碳在页岩中的吸附储量及由吸附研究的变形行为,相应地获得了甲烷和二氧化碳吸附量、溶剂化压力与页岩孔结构以及埋藏深度之间的联系。深度浅的时候,微孔比介孔表现出更大的单位吸附能力。小于1nm的孔的甲烷吸附能力随深度增加而快速增加,到埋藏为1500m时吸附量达到8 mmol/cm3左右的极大值。而2nm和5nm的孔的甲烷吸附量在到达6000m之前一直在持续增加,其对吸附量的贡献在3000m深度之后超过微孔。本文发现甲烷的吸附导致了三种不同的应变-深度关系。第一种,在整个深度范围内都表现为先膨胀后收缩,例如0.5nm和0.7nm的孔。在达到膨胀极值之前(0.5nm的孔1000m下的0.11%,0.7nm的孔为2000m下的0.12%),体相应变随埋藏深度快速增长,之后收缩。第二种,1nm的孔,在极浅部随深度增加表现为收缩,至100m达到一个极小值后缓慢增长,最后在6000m时膨胀至0.11%。第三种,对于≥2 nm的孔,在整个深度范围内其体积应变的变化≤0.04%,与微孔相比其影响可以忽略不计。在将二氧化碳封存到页岩中时,当深度小于1000m的时候,微孔中的所吸附的二氧化碳占主导地位,但当深度大于1000m时,介孔中的存储将变得更加重要。如果页岩层有大量的≤1nm的孔,那么其在6000m的深度之内的形变都有较大变化,有可能对二氧化碳注入过程中页岩孔结构产生影响。
通过对甲烷和二氧化碳在煤层及页岩中的吸附研究,本文发现由流体分子导致的纳米孔隙的吸附变形行为可能存在一定的规律。为了进一步认识形变与流体分子的吸附行为的关系,本文采用QSDFT的方法定量得研究了表面粗糙程度对流体吸附和颗粒之间的相互作用的影响。表面的不均一性对于固体的润湿性和粘着性质有着很重要的影响。然而,大多数计算固体与流体相互作用的理论和模拟方法都假设存在一个标准的平滑的Gibbs流体固体分界面。这个假设导致了靠近固体表面的流体相出现人为的分层现象。具体的表现就是密度分布曲线的明显波动。这种流体密度的成层性导致了溶剂化压力以离孔壁的距离为函数发生波动,但是溶剂化压力的这种明显的波动性却在试验中极少见到。在QSDFT中,表面粗糙成分采用粗糙度参数来定量表示,该粗糙度参数代表了固体表面松散层的厚度。通过对LJ流体在平行板状孔中吸附(模拟了氮气在石墨中的吸附)的例子,本文发现在饱和状态,溶剂化压力随孔径有规律的波动。这种波动随表面粗糙度的增加(从0增加到1/2倍的分子直径)而快速减小。溶剂化压力的波动性与流体密度在匹配孔中流体密度的最大值以及不匹配孔中流体密度的最小值有很好的对应。后者以松散排列和流体的密度减小为特征。该分析表明分子尺度上的表面粗糙度对局限流体的成层排列以及成层性都有很大的抑制作用。另外,本文计算了在吸附过程中溶剂化压力随外压的变化情况,其变化随孔径和粗糙度的不同可以分为几种不同的机制。由于溶剂化压力决定了多孔介质的吸附变形性质,溶剂化压力随外压变化的非单调性很好的对应了石墨等微孔材料的在不同压力下的收缩膨胀性质。
第三,本文采用三维DPD的模拟方法研究了链状大分子在不同外力场的作用下穿越狭窄孔道时链长的行为,以期对链状分子的运移行为进行深入理解。研究发现外力与平均穿越时间存在着反比关系,链长对穿越时间有很大影响,其在良溶剂下的指数关系为1.56,在不良溶剂下的指数关系为1.76。这与τtrans～N1+v的理论计算结果很接近。模拟观测表明穿越过程中的平均回旋半径主要受其初始状态的平衡值的影响。在穿越过程结束的时候,其指数关系为1,这与其受相同外力在无限空间中的运动行为一致。这可能是受到的外力力场强度大以及带电电荷之间相互作用较强造成的(在带电链状大分子穿越静电力场的情况下)
Unconventional energy (e.g. coal bed methane, shale gas) now is playing more important roles in the whole energy system. Understanding the adsorption capacity and deformation change during adsorption of methane and CO2 on coal and shale, may help the exploitation and resoure evaluation. Four coal samples and eleven shale samples were measured by N2 adsorption method. Isotherms as well as pore size distrubtions of these samples were obtained. Base on these exmperimental data, a systematic simulation work were carried out.
Firstly, the quenched solid density functional theory (QSDFT) is employed to study the adsorption of methane and CO2 on coal at geological conditions. The main focus is made on coal deformation in the course of adsorption that may result either in expansion/swelling or contraction, depending on pressure, temperature, and pore size. The results of methane adsorption capacity, density profile and salvation pressure on coal in pores from 0.5nm to 50nm at 298 K and 360 K with pressure up to 100 MPa are given. Two qualitatively different types of deformation behavior are found depending on the pore width:Type I shows a monotonic expansion in the whole pressure range. This behavior is characteristic for the smallest pores<1.3σff (0.5nm) that cannot accommodate more than one layer of methane. Type II displays contraction at low pressures followed by expansion. Type II behavior is found for several groups of pores, which can accommodate dense packing with integer number (from 2 to 6) of adsorbed layers. Two typical deformation behaviors at 360 K could be summarized from the CO2 solvation pressure dependence on the external pressure. Type I behavior shows a monotonic expansion in the whole pressure range, but at high pressures it may either continue to expand or contract. This behavior is typical for the smallest pores<1.3σff (0.5 nm) that cannot accommodate more than one layer of CO2, as shown by the density profile in 0.5 nm pore. Type II behavior displays contraction at low pressures followed by expansion. At high pressure, it also may expand or contract again. Type Ha is found for 0.6 nm and 0.9 nm pores. All other pores>0.9 nm present the typeⅡb behavior.Then, the results of QSDFT model arecompared with literature experimental data, and the model is then employed to study the adsorption behavior of model coals at elevated pressures and temperatures. An instructive example of CO2 sequestration into coal bed is given. We established the relationships between the methane and CO2 capacity and the solvation pressure it exerts on the coal matrix and the depth of coal bed for pores of different sizes. The replacement process of methane by CO2 is discussed. We found that the coal deformation depends on the bed depth, and at different depths it either swell or contract depending on the pore size distribution. Through calcualtion on the replacement of methane by CO2 under geological condition, CO2 capcity and the structure change in the ECBM scenario were discussed. The difference in the volumetric strain induced by adsorption of CO2 and methane is the smallest in the case of 5nm pore (0.6%). For micropores (≤2nm), the volumetric strain difference can be as large as 1.7% in the case of 0.7 nm pore at 100 m depth, which may cause significant reduction in permeability of the reservoir through deformation.
Secondly, similiar model is employed to study the adsorption capacity of methane and CO2 in shale and the adsorption induced deformation behavior. Correspondingly, the relationships between the methane and CO2 capacity and the solvation pressure it exerts on the shale matrix and the depth of shale for pores of different sizes is discussed. When the depth is small, the adsorption capacity (per unit volume) of micropore is bigger than that of mesopore. Methane adsorptin capacity in pores
Finally, this study used 3D DPD approach to study the behavior of a polymer chain translocating through a nanopore under different external fields in order to better understanding the expellling process of hydrocarbon from source rock. An inversed linear scaling relationship was found between the external force and average translocation time. For the chain length effect, the scaling exponent under good solvent condition is 1.56, under bad solvent is 1.76, close toτtrans～N1+v. The observation reveals that the average radius of gyration is still dominated by its equilibrium value at the beginning of the translocation process. At end of the translocation process, the scaling is close to 1, which indicates a pure pulling condition by the external force. This might be due to the large magnitude of the external force and strong electrostatic interaction between charged bead (in the case of charge polymer chain and electrostatic force).
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