Numerical simulation of non-Archie electrophysical property of saturated rock with lattice Boltzmann method

Petroleum Science, Feb 2009

The electrophysical property of saturated rocks is very important for reservoir identification and evaluation. In this paper, the lattice Boltzmann method (LBM) was used to study the electrophysical property of rock saturated with fluid because of its advantages over conventional numerical approaches in handling complex pore geometry and boundary conditions. The digital core model was constructed through the accumulation of matrix grains based on their radius distribution obtained by the measurements of core samples. The flow of electrical current through the core model saturated with oil and water was simulated on the mesoscopic scale to reveal the non-Archie relationship between resistivity index and water saturation (I-Sw). The results from LBM simulation and laboratory measurements demonstrated that the I-Sw relation in the range of low water saturation was generally not a straight line in the log-log coordinates as described by the Archie equation. We thus developed a new equation based on numerical simulation and physical experiments. This new equation was used to fit the data from laboratory core measurements and previously published data. Determination of fluid saturation and reservoir evaluation could be significantly improved by using the new equation.

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Numerical simulation of non-Archie electrophysical property of saturated rock with lattice Boltzmann method

Pet.Sci. Numerical simulation of non-Archie electrophysi- cal property of saturated rock with lattice Boltzmann method Yue Wenzheng 0 1 2 Tao Guo 0 1 2 Liu Dongming 4 Yang Wendu 3 0 Research Centre of Well Logging, CNPC Key Laboratory of Well Logging, China University of Petroleum , Beijing 102249 , China 1 Key Laboratory of Earth Prospecting and Information Technology, China University of Petroleum , Beijing 102249 , China 2 State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum , Beijing 102249 , China 3 Sichuan Petroleum Administration Logging Company Ltd., CNPC , Chongqing 401147 , China 4 CNPC Logging Changqing Business Division , Xi'an, Shaanxi 710201 , China The electrophysical property of saturated rocks is very important for reservoir identification and evaluation. In this paper, the lattice Boltzmann method (LBM) was used to study the electrophysical property of rock saturated with fluid because of its advantages over conventional numerical approaches in handling complex pore geometry and boundary conditions. The digital core model was constructed through the accumulation of matrix grains based on their radius distribution obtained by the measurements of core samples. The flow of electrical current through the core model saturated with oil and water was simulated on the mesoscopic scale to reveal the non-Archie relationship between resistivity index and water saturation (I-Sw). The results from LBM simulation and laboratory measurements demonstrated that the I-Sw relation in the range of low water saturation was generally not a straight line in the log-log coordinates as described by the Archie equation. We thus developed a new equation based on numerical simulation and physical experiments. This new equation was used to fit the data from laboratory core measurements and previously published data. Determination of fluid saturation and reservoir evaluation could be significantly improved by using the new equation. Non-Archie relation; digital core model; lattice Boltzmann method; numerical simulation; rock physical experiment 1 Introduction The I-Sw relation of a formation is important for reservoir evaluation with well logging data. Archie (1942) first formulated the I-Sw relation based on a large number of core experiments on the sandstones of the Gulf of Mexico. where I is the resistivity index, Sw is the water saturation of rock, n is the saturation exponent and b is the Archie parameter. In the Archie equation, the I-Sw relation is linear in the log-log coordinates. In the past decades, the non-Archie phenomenon of reservoir rocks, i.e., the I-Sw relation is not linear in the log-log coordinates as shown in Fig. 1, has been increasingly observed and reported by log analysts and petroleum engineers (Diederix, 1982; Li, 1989; Worthington, 2000; 2006; Man and Jing, 2001; 2002; Li et al, 2008) . (1) 100 log I 10 Archie These researchers have studied this so-called ‘non-Archie phenomenon’ of porous rocks extensively and have found that the non-Archie phenomenon generally becomes more evident an inverse power function of water saturation as described by the Archie equation. However, the change rate of tortuosity of the current path started to decrease gradually when the clusters of oil expanded to connect each other to form the continuous phase in the pore space after the water saturation was lower than 0.15. Therefore, the nonlinear phenomenon of the I-Sw relation in the log-log coordinates might be caused by the non-constant change rate of the current path tortuosity due to the fluid distribution. It is clear that the fluid distribution is an important factor leading to the non-Archie phenomenon. Actually, all the eight data groups are similar. In this figure, the solid line is the result calculated by our new equation while the dashed line is the result of Archie equation. The diamonds are the data from laboratory measurements. It is clear that this new equation fits the measured data better than the Archie equation and therefore represents a more precise conductivity model and a more actual mechanism of current flow in fluid saturated porous medium. It can lead to a more precise evaluation of oil-bearing reservoirs with a high resistivity index. By comparing the simulated results above with the physical experiments on core samples we did before, we can see that the I-Sw relation in the log-log coordinates is a curve, i.e., with a non-constant exponent n changing with water saturation, instead of a straight line as described by the Archie equation. The Archie equation actually gives an approximate I-Sw relation in the range of high water saturation. Having realized the fact that exponent n was a function of water saturation, we thus developed a new equation of the non-Archie I-Sw relation for calculating fluid saturation and reservoir evaluation. This more general equation, based on the results of LBM simulation of the electrical property of a porous medium saturated with fluid, can be applied to calculating formation fluid saturation for the reservoir rocks of both Archie and non-Archie types. This new equation is essentially different from the Archie equation in that the saturation exponent n is no longer a constant but a function of water saturation as below: where Y and U are two constants related to pore structure and porosity. To demonstrate the applicability of this new equation, especially for the non-Archie rocks, we used both equations to fit the data obtained by laboratory measurements to observe the differences between them. To show the data more clearly without losing generality, we plotted here only one of the eight data groups in Fig. 7. (5) log 100 I 10 1 0.1 Sw 1 log 5 Conclusions 1) An algorithm was proposed to construct the digital core models with the sizes of matrix grains controlled by the porosity and the grain size distribution of core samples from laboratory measurements. The advantages of our method lie in that the distribution of grain sizes of digital core models can be identical to that of the real core samples. 2) The lattice Boltzmann method was used to study the electrophysical property of rock model saturated with fluid. The simulated results clearly demonstrated that the relation of I-Sw was affected by the distribution of fluid filling in pore space. The non-Archie phenomenon would appear if water saturation was lower than 0.15, and the I-Sw relation deviated gradually to the water saturation axis non-linearly with decreasing water saturation. 3) Based on the results, we developed a new equation for the non-Archie I-Sw relation for calculating fluid saturation and reservoir evaluation. This new equation was used to fit the data from laboratory core measurements and previously published data. Determination of fluid saturation and reservoir evaluation could be significantly improved by using the new equation. Acknowledgements This research was sponsored by the project No. 50404001 from the National Natural Science Foundation of China, the National Key Fundamental Research & Development Project Archie G E. The electrical resistivity log as an aid in determining some reservoir characteristics . Trans. AIME . 1942 . 146 : 54 - 61 Boyd J , Buick J and Green S. A second-order accurate lattice Boltzmann non-Newtonian flow model . Journal of Physics A: Mathematical and General . 2006 . 39 : 14241 - 14247 Cheng Y and Suo L S. Lattice Boltzmann scheme to simulate twodimensional fluid transient . Journal of Hydrodynamics B . 2003 . 2 : 19 - 23 Chen S Y and Doolen G D. Lattice Boltzmann method for fluid flow . Annual Review of Fluid Mechanics . 1998 . 30 : 329 - 364 Diederix K M. Anomalous relationships between resistivity index and water saturations in the rotliegend sandstone . Transaction of SPWLA 23rd Annual Logging Symposium . 1982 . Paper X Ding H , Shu C , Yeo K S, et al. Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method . Computer Methods in Applied Mechanics and Engineering . 2004 . 193 ( 9 -11): 727 - 744 Haydock D. Lattice Boltzmann simulations of the time-averaged forces on a cylinder in a sound field . Journal of Physics A: Mathematical and General . 2005 . 38 : 3265 - 3277 Hazi G. Accuracy of the lattice Boltzmann method based on analytical solutions . Physical Review E . 2003 . 67 ( 5 ): 056705 . 1 - 056705 . 5 Jing X D , Gillespie A and Trewin B M. Resistivity index from nonequilibrium measurements using detailed in-situ saturation monitoring . Society of Petroleum Engineers Paper. Offshore European Conference , Aberdeen. 1993 . 456 - 464 Kutay M E , Aydilek A H and Masad E. Laboratory validation of lattice Boltzmann method for modeling pore-scale flow in granular materials . Computers and Geotechnics . 2006 . 33 ( 8 ): 381 - 395 Kutay M E , Aydilek A H , Masad E , et al. Computational and experimental evaluation of hydraulic conductivity anisotropy in hotmix asphalt . International Journal of Pavement Engineering . 2007 . 8 ( 1 ): 29 - 43 Li N . General forms of the resistivity-porosity and resistivity-oil/gas saturation relations, as well as the determination of their optimum approximation function types . Chinese Journal of Geophysics . 1989 . 32 ( 5 ): 580 - 591 (in Chinese) Li X D , Yu J and Li M. Theoretic research of reservoir rock with nonArchie characteristics . Oil-Gasfield Surface Engineering . 2008 . 27 ( 1 ): 32 - 33 (in Chinese) Ma B , Lei S Y , Hao J Z , et al. Simulation of fluid flow in micro-channel by lattice Boltzmann method . Journal of Guangxi Normal University (Natural Science Edition) . 2003 . 21 ( 2 ): 20 - 24 (in Chinese) Man H N and Jing X D. Network modelling of strong and intermediate wettability on electrical resistivity and capillary pressure . Advances in Water Resources . 2001 . 24 ( 3-4 ): 345 - 363 Man H N and Jing X D. Network modelling of mixed-wettability on electrical resistivity, capillary pressure and wettability indices . Journal of Petroleum Science and Engineering . 2002 . 33 ( 1-3 ): 101 - 122 Tao G. Elastic and transport properties of some sandstones ( PhD thesis) . London: Imperial College of Science, Technology & Medicine, University of London. 1992 Worthington P F. Recognition and evaluation of low-resistivity pay . Petroleum Geoscience . 2000 . 6 ( 1 ): 77 - 92 Worthington P F. Quality assurance of the evaluation of hydrocarbon saturation from resistivity data . SPE Annual Technical Conference and Exhibition, Texas . 2006 . Paper 103075 Yan G W , Dong Y F and Liu Y H. An implicit Lagrangian lattice Boltzmann method for the compressible flows . International Journal for Numerical Methods in Fluids . 2006 . 51 ( 12 ): 1407 - 1418 Yue W Z , Tao G and Zhu K Q. Simulation of electrical transport properties in oil-water saturated porous media with 2-D lattice gas automata . Chinese Journal of Geophysics . 2005 . 48 ( 1 ): 189 - 195 (in Chinese)


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Wenzheng Yue, Guo Tao, Dongming Liu, Wendu Yang. Numerical simulation of non-Archie electrophysical property of saturated rock with lattice Boltzmann method, Petroleum Science, 2009, 24-28, DOI: 10.1007/s12182-009-0005-0