Determination of Diffusion Coefficients of Ethane in Water at High Pressure and Temperature with In-Situ Raman Spectroscopy
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摘要: 乙烷和甲烷是深部天然气藏中的重要组成部分, 精确测量其扩散系数对于正确理解深部页岩储层中的烃类气体的分布运移及其分异具有重要意义.目前乙烷在水中的扩散系数数据局限在低压和283~333K温度范围内, 缺少天然气储层高温高压条件下的数据.本研究利用显微激光拉曼光谱, 在高压透明毛细管中原位观测了20MPa下273~393K温度范围内乙烷在纯水中的扩散, 测定了各温度下的扩散系数, 并用Speedy-Angell指数方程拟合出乙烷扩散系数D(乙烷)(m2/s)与温度T(K)之间的关系式: D(C2H6)=D0[(T/Ts)-1]γ, 式中: D0=13.8055×10-9m2/s, Ts=237.4K, γ=1.7397.相同温度压力条件下, 测得的乙烷的扩散系数小于甲烷的扩散系数.据此计算了2种气体通过低渗透盖层的扩散量的差异, 发现甲烷和乙烷溶解扩散的分异程度随盖层厚度、扩散时间而显著变化.Abstract: Ethane and methane are two main components of natural gas. Accurate diffusion coefficients at high temperature for ethane and methane are the key to calculate the diffusion and fractionation of gases in deep natural gas reservoirs, especially in unfractured shale and other geological materials with low permeability. However, the diffusion coefficients for ethane at pressures and temperatures near the reservoir conditions are scarce in the literature. In this study, diffusive transfer of ethane in water at 20MPa and from 273 to 393K was observed in a high-pressure optical capillary cell via Raman spectroscopy. Diffusion coefficients were then determined by the least-square method. The relationship between diffusion coefficients [D(C2H6) in m2/s] and temperature (T in K) was derived with Speedy-Angell power-law equation as: D(C2H6)=D0[(T/Ts)-1]γ, where D0=13.8055×10-9m2/s, Ts=237.4K, γ=1.7397. The diffusion coefficients of ethane are much smaller than those of methane at the same condition. The amount of methane and ethane diffused through some thick low permeability layers are calculated and the results show that such diffusivity difference can cause a significant fractionation of methane and ethane in thick shale layer.
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Key words:
- ethane /
- methane /
- pure water /
- diffusion coefficient /
- Raman spectroscopy /
- diffusion amount
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图 1 高压广阔温度下乙烷在纯水溶液中的扩散观测实验装置
实验中所需阀门(阴影部分)均为HIP耐高压三通阀门，右上图为采集到的纯水和乙烷的拉曼光谱
Fig. 1. A schematic diagram of system for study of diffusion of ethane in pure water at wide temperature and high-pressure
图 2 高压毛细管中乙烷由气液界面向水柱末端扩散示意
I.气液界面；F.水柱末端；A~E.拉曼光谱采集位置；L.扩散路径总长
Fig. 2. A schematic diagram of diffusion of ethane from the interface to the end of water in the high-pressure optical cell
图 3 20MPa，25℃时B点处乙烷浓度随时间变化光谱
3400-1cm附近为水的拉曼峰；2900-1cm附近为乙烷的拉曼峰
Fig. 3. Time-dependent Raman spectra of ethane collected at the spot of B, at different time after the water was pressurized by ethane to 20MPa at 298K
图 4 20MPa不同温度下各测点上峰强度比实测值与计算值随时间的变化
圆圈代表A点(距离气液界面20μm)，乘号代表管尾附近的E点，菱形、四边形、三角形分别代表B、C、D三点.虚线代表A点处峰强度比的平均值，点线代表通过最小二乘法拟合得到的B点处的峰强度比，实线代表C、D、E三点处通过扩散系数计算结果得到的拟合曲线
Fig. 4. Measured values and calculated values of Raman peak intensity ratio HR(C2H6/H2O), as a function of time after water was pressurized by ethane at different temperatures at specific pressure of 20MPa
图 5 本文实验所得扩散系数与前人实验或计算所得扩散系数随温度变化的对比
a.温度范围270~400K；b.温度范围270~335K；乘号、四边形、菱形、三角形为实验数据；点线、虚线为模型计算数据
Fig. 5. Comparison of our results with previously measured or calculated data on the diffusion coefficients of ethane in water
图 6 乙烷在纯水中扩散系数的对数与温度倒数的函数关系
圆圈代表的数据为本研究测定的扩散系数；虚线是根据实验数据利用VTF方程进行拟合得到；实线是由Power-Law方程拟合实验数据得到
Fig. 6. Logarithms of ethane diffusion coefficients in water as a function of reciprocal absolute temperature
图 7 甲烷、乙烷通过盖层扩散示意
Fig. 7. A schematic diagram for study of diffusion of methane and ethane through the cap rocks
图 8 甲烷、乙烷通过不同厚度盖层岩石的扩散量
Fig. 8. Diffusion amount of methane and ethane through cap rocks of different thickness
图 9 不同厚度盖层岩石中乙烷、甲烷气体扩散量的比值
Fig. 9. Ratio of diffusion amount of methane and ethane through cap rocks of different thickness
表 1 压力20MPa，各温度下甲烷、乙烷在纯水中的扩散系数及置信度95%时的误差
Table 1. Diffusion coefficients (D) of ethane and methane in pure water measured at different temperatures (T) at specific pressure (P) of 20MPa and the deviation of diffusion coefficients
P (MPa) T (K) D(C2H6) (10-9m2·s-1) 误差(%) D(CH4) (10-9m2·s-1) 误差(%) 20 273 0.517 14.89 0.702 9.97 20 283 0.793 8.20 20 298 1.230 5.69 1.640 6.10 20 353 4.150 10.84 4.980 6.83 20 393 6.350 8.50 8.680 7.60 注：表中甲烷的扩散系数及其误差值引自 Guo et al.(2013) .
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