利用核函数法中的自适应带宽同时对一维空间两个储集层属性参数进行粗化
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摘要
在多孔介质流体流动模拟中,应用网格粗化方法必须在保留重要储集层参数的空间分布的前提下,首先利用大网格粗化原始地质模型(尤其是孔隙型介质),并用数值方法求解。提出了根据属性参数的空间分布、以核函数的自适应带宽为基础的网格粗化新方法,该方法既减少了网格数量,同时也保留原始精细模型的主要非均质性特征。该方法的关键点在于可以同时对两种储集层属性参数进行网格粗化。首先计算每个储集层属性参数的带宽量或最优门槛值并得到粗化结果,然后根据最大带宽和最小带宽采用两种不同的方法对两个属性参数同时粗化。现在已经能够实现利用不同方法建立储集层两个属性参数的最终粗化模型,不同方法的网格单元数和网格位置都相同。最小带宽法的粗化误差小于最大带宽法。图6表1参29
Upscaling of primary geological models with huge cells, especially in porous media, is the first step in fluid flow simulation.Numerical methods are often used to solve the models. The upscaling method must preserve the important properties of the spatial distribution of the reservoir properties. An grid upscaling method based on adaptive bandwidth in kernel function is proposed according to the spatial distribution of property. This type of upscaling reduces the number of cells, while preserves the main heterogeneity features of the original fine model. The key point of the paper is upscaling two reservoir properties simultaneously. For each reservoir feature, the amount of bandwidth or optimal threshold is calculated and the results of the upscaling are obtained. Then two approaches are used to upscaling two properties simultaneously based on maximum bandwidth and minimum bandwidth. In fact, we now have a finalized upscaled model for both reservoir properties for each approach in which not only the number of their cells, but also the locations of the cells are equal. The upscaling error of the minimum bandwidth approach is less than that of the maximum bandwidth approach.
Upscaling of primary geological models with huge cells, especially in porous media, is the first step in fluid flow simulation.Numerical methods are often used to solve the models. The upscaling method must preserve the important properties of the spatial distribution of the reservoir properties. An grid upscaling method based on adaptive bandwidth in kernel function is proposed according to the spatial distribution of property. This type of upscaling reduces the number of cells, while preserves the main heterogeneity features of the original fine model. The key point of the paper is upscaling two reservoir properties simultaneously. For each reservoir feature, the amount of bandwidth or optimal threshold is calculated and the results of the upscaling are obtained. Then two approaches are used to upscaling two properties simultaneously based on maximum bandwidth and minimum bandwidth. In fact, we now have a finalized upscaled model for both reservoir properties for each approach in which not only the number of their cells, but also the locations of the cells are equal. The upscaling error of the minimum bandwidth approach is less than that of the maximum bandwidth approach.
引文
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[29]HARDLE W K,WERWATZ A,MULLER M,et al.Nonparametric and semiparametric models:An introduction[J].Springer Series in Statistics,2004,8(6):167-188.
[2]KOLDITZ O,CLAUSER C.Numerical simulation of flow and heat transfer in fractured crystalline rocks:Application to the hot dry rock site in Rosemanowes(U.K.)[J].Geothermics,1998,27(1):1-23.
[3]DURLOFSKY L J.Use of higher moment for the description of upscaled,prosess independent relative permeabilities[J].SPE Journal,1997,36(2):1-11.
[4]MILES D,BARZANDJI O H,BRUINING J,et al.Upscaling of small-scale heterogeneities to flow units for reservoir modeling[J].Marine and Petroleum Geology,2006,23(9):931-942.
[5]CHEN T,CLAUSER C,MARQUART G,et al.A new upscaling method for fractured porous media[J].Advances in Water Resources,2015,80:60-68.
[6]FARMER C L.Upscaling:A review[J].International Journal for Numerical Methods in Fluids,2002,40(1):63-78.
[7]DADVAR M,SAHIMI M.The effective diffusivities in porous media with and without nonlinear reactions[J].Chemical Engineering Science,2007,62(5):1466-1476.
[8]HOCHSTETLER D L,KITANIDIS P K.The behavior of effective rate constants for bimolecular reactions in an asymptotic transport regime[J].Journal of Contaminant Hydrology,2013,144(1):88-98.
[9]PEREIRA J M,NAVALHO J E,AMADOR A C,et al.Multi-scale modeling of diffusion and reaction-diffusion phenomena in catalytic porous layers:Comparison with the 1D approach[J].Chemical Engineering Science,2014,117:364-375.
[10]RATNAKAR R R,BHATTACHARYA M,BALAKOTAIAH V.Reduced order models for describing dispersion and reaction in monoliths[J].Chemical Engineering Science,2012,83:77-92.
[11]ZHOU H Y,LI L P,GóM-HERNáNDEZ J J.Three-dimensional hydraulic conductivity upscaling in groundwater modeling[J].Computers&Geosciences,2010,36(10):1224-1235.
[12]HUANG J,GRIFFITHS D V.Determining an appropriate finite element size for modelling the strength of undrained random soils[J].Computers and Geotechnics,2015,69:506-513.
[13]DEWANDEL B,MARéCHAL J C,BOUR O,et al.Upscaling and regionalizing hydraulic conductivity and effective porosity at watershed scale in deeply weathered crystalline aquifers[J].Journal of Hydrology,2012,416(10):83-97.
[14]FLECKENSTEIN J H,FOGG G E.Efficient upscaling of hydraulic conductivity in heterogeneous alluvial aquifers[J].Hydrogeology Journal,2008,16(7):1239-1250.
[15]DESBARATS A J.Spatial averaging of hydraulic conductivity in three-dimensional heterogeneous porous media[J].Mathematical Geology,1992,24(3):249-267.
[16]RASAEI M R,SAHIMI M R.Upscaling of the permeability by multiscale wavelet transformations and simulation of multiphase flows in heterogeneous porous media[J].Computational Geoscience,2009,13(2):187-214.
[17]GODOY V A,ZUQUETTE L V,GOMEZ-HERNANDEZ J.Stochastic analysis of three dimensional hydraulic conductivity upscaling in a heterogeneous tropical soil[J].Computers and Geotechnics,2018,100(2):174-187.
[18]CHEN T,CLAUSER C,MARQUART G,et al.Upscaling permeability for three-dimensional fractured porous rocks with the multiple boundary method[J].Hydrogeology Journal,2018,26(1):1-14.
[19]JOURNEL A G,DEUTSCH C,DESBARATS A J.Power averaging for block effective permeability[R].California:SPE California Regional Meeting,1986.
[20]WARREN J E,PRICE H S.Flow in heterogeneous porous media[J].SPE Journal,1961,1(3):153-169.
[21]RENARD P H,MARSILY G.Calculating equivalent permeability:Areview[J].Advances in Water Resources,1997,20(5):253-278.
[22]PANDA M N,MOSHER C C,CHOPRA A.Application of wavelet transforms to reservoir-data analysis and scaling[J].SPE Journal,2000,39(1):92-101.
[23]SAHIMI M.Fractal-wavelet neural-network approach to characterization and upscaling of fractured reservoirs[J].Computers&Geosciences,2000,26(8):877-905.
[24]RASAEI M R,SAHIMI M R.Upscaling and simulation of waterflooding in heterogeneous reservoirs using wavelet transformations:Application to the SPE-10 model[J].Transport in Porous Media,2008,72(3):311-338.
[25]DONOHO D L.De-noising by soft-thresholding[J].IEEE Transactions on Information Theory,1995,41(3):613-627.
[26]GE X M,FAN Y R,LI J T,et al.Pore structure characterization and classification using multifractal theory:An application in Santanghu Basin of western China[J].Journal of Petroleum Science and Engineering,2015,127:297-304.
[27]GE X M,FAN Y R,LI J T,et al.Noise reduction of nuclear magnetic resonance(NMR)transversal data using improved wavelet transform and exponentially weighted moving average(EWMA)[J].Journal of Magnetic Resource,2015,251:71-83.
[28]ROSENBLATT M.Remarks on some nonparametrice stimates of a density function[J].Annals of Mathematical Statistics,1956,27(7):832-837.
[29]HARDLE W K,WERWATZ A,MULLER M,et al.Nonparametric and semiparametric models:An introduction[J].Springer Series in Statistics,2004,8(6):167-188.