A mathematical diffusion model of carbon isotopic reversals inside ultra-tight Longmaxi shale matrixes

Developing mathematical models for high Knudsen number(Kn)flow for isotopic gas fractionation in tight sedimentary rocks is still challenging.In this study,carbon isotopic reversals(δ^(13)C_(1)>δ^(13)C_(2))were found for four Longmaxi shale samples based on gas degassing experiments.Gas in shale with higher gas content exhibits larger reversal.Then,a mathematical model was developed to simulate the carbon isotopic reversals of methane and ethane.This model is based on these hypotheses:(i)diffusion flow is dominating during gas transport process;(ii)diffusion coefficients are nonlinear depending on concentration gradient.Our model not only shows a good agreement with isotopic reversals,but also well predicts gas production rates by selecting appropriate exponents m and m^(*) of gas pressure gradient,where m is for ^(12)C and m^(*)is for ^(13)C.Moreover,the(m−m^(*))value has a positive correlation with fractionation level.(m1−m1^(*))of methane are much higher than that of ethane.Finally,the predicted carbon isotopic reversal magnitude(δ^(13)C_(1)−δ^(13)C_(2))exhibits a positive relationship with total gas content since gas in shale with higher gas content experiences a more extensive high Kn number diffusion flow.As a result,our model demonstrates an impressive agreement with the experimental carbon isotopic reversal data.

Geochemical characteristics of abiogenic alkane gases

Recently abiogenic alkanes have been found in various locations in the world and other celestial bodies. The chemical composition of abiogenic alkane gases varies widely. The content of methane is low and nearly no C2+ is found in the abiogenic alkane gases from fluid inclusions in volcanic rocks or hot springs in China. In the unsedimented submarine hydrothermal vent system C1/C2+ ratios are much greater than those for the thermogenic gases, mostly >800 and in some cases up to 8,000. In the Songliao Basin, China, C1/C2+ of some abiogenic gases are often less than 150. Abiogenic alkane gases which have been found in nature often have carbon isotopic reversal among C1–C4 alkanes (δ13C1>δ13C2>δ13C3>δ13C4), whereas both regular and reversed hydrogen isotope distribution pattern among C1–C4 alkanes have been reported. The δ13C of abiogenic methane is mainly greater than ?30‰ though laboratory synthesized methane can have δ13C as low as ?57‰, and its δD1 values vary widely and overlap with biogenic gases. High 3He/4He ratios often indicate the addition of mantle-derived helium and are related to abiogenic gases. However, some biogenic gases can also have high 3He/4He ratios up to 8. The CH4/3He end-member is often lower than 106 for abiogenic alkane gases while greater than 1013 for biogenic gases, and the values between these two end-members often reflect the mixing of biogenic and abiogenic gases.

Carbon isotope reversal of desorbed gas in Longmaxi shale of Jiaoshiba area,Sicuhan Basin

Through analysis of components and carbon isotope compositions of gas desorbed from shale cores,the carbon isotope reversal phenomenon in the shale gas from the Silurian Longmaxi Formation of Jiaoshiba area in Sichuan Basin were well studied.Results showed that compared with the wellhead gas,the desorbed gas from Longmaxi shale had significantly more wet components and more heavy carbon isotope values;carbon isotope values of each component became heavier with the desorption time,δ^(13)C_(1)values of different samples had maximum positive variations of 12.3-23.9‰,butδ^(13)C_(2)values only had maximum positive variations of 0.8e2.3‰,indicating carbon isotope values of methane changed more obviously than that of heavy hydrocarbon.The above results were consistent with previous results of shale core desorption experiments carried out by other researchers.Shale gas in strata might have no carbon isotope reversal,and the phenomenon thatδ^(13)C_(1)values changed more significantly thanδ^(13)C_(2)values during the core desorption was not caused by diffusion rate differences among different components,but mainly due to different desorption stages of methane and ethane,i.e.,the ethane was in its early desorption stage while the methane was in its later desorption stage;during the production process,phase differences among different components of alkane gas and differences in the desorption stages induced by adsorption,could be the major cause for total reversal of carbon isotopes of shale gas in Longmaxi Formation,but it also could not excluded that mixture of kerogen cracking gas and crude oil cracking gas probably had a partial or more major contribution to the carbon isotope reversal.

Carbon isotope evidence for shale gas preservation conditions and large methane release over million years:A case study of shale gas reservoirs of Wufeng and Longmaxi Formations in the Sichuan Basin

Although carbon isotope reversal and its reasons in shale gas reservoirs have been widely recognized,the application of the reversal is yet to be investigated.A study on high-maturity shale from Wufeng and Longmaxi Formations in the Sichuan Basin not only reveals the relationship between the degree of isotopes inversion and the production capacity(e.g.,estimated ultimate recovery(EUR))of the gas well but also indicates the preservation conditions of shale gas reservoirs.(1)Although there are differences in gas isotopes in different shale gas reservoirs,the isotope fractionation of shale gas is small during the production stage of gas wells,even when the wellbore pressure drops to zero.The main cause of the difference in carbon isotopes and their inversion degree can be the uplift time during the Yanshan period and the formation pressure relief degree of shale gas reservoirs in distinct structural positions.Thus,carbon isotope inversion is a good indicator of shale gas preservation condition and EUR of shale gas wells.(2)The degree of carbon isotope inversion correlates strongly with shale gas content and EUR.The calculation formula of shale-gas recoverable reserves was established using△δ^(13)C(δC_(1)-δC_(2))and EUR.(3)The gas loss rate and total loss amount can be estimated using the dynamic reserves and isotopic difference values of gas wells in various shale gas fields,which also reflects the current methane loss,thereby demonstrating great potential for evaluating global methane loss in shales.