Upscaling Uncertain Permeability Using Small Cell Renormalization

Sedimentary rocks have structures on all length scales from the millimeter to the kilometer. These structures are generally associated with variations in rock permeability. These need to be modeled if we are to make predictions about fluid flow through the rock. However, existing computers are not powerful enough for us to be able to represent all scales of heterogeneity explicitly in our fluid flow models—hence, we need to upscale. Small cell renormalization is a fast method for upscaling permeability, derived from an analogue circuit of resistors. However, it assumes that the small scale permeability distribution is known. In practice, this is unlikely. The only information available about small scale properties is either qualitative, derived from the depositional setting of the reservoir, or local to the wells as a result of coring or logging. The influence of small scale uncertainty on large scale properties is usually modelled by the Monte Carlo method. This is time-consuming and inaccurate if not enough realisations are used. This paper describes a new implementation of renormalization, which enables the direct upscaling of uncertain small-scale permeabilities to produce the statistical properties of the equivalent coarse grid. This is achieved by using a perturbation expansion of the resistor-derived equation. The method is verified by comparison with numerical simulations using the Monte Carlo method. The prediction of expected large-scale permeability and its standard deviation are shown to be accurate for small cell standard deviations of up to 40% of the mean cell value, using just the first nonzero term of the perturbation expansion. Inclusion of higher order terms allows larger standard deviations to be modeled accurately. Evaluation of cross-terms allows correlations of actual cell values, over and above the background structure of mean cell values. The perturbation method is significantly faster than conventional Monte Carlo simulation. It needs just two calculations whereas the Monte Carlo method needs many thousands of realisations to be generated and renormalized to converge. This results in significant savings in computer time.     

四川龙门山地区阳新组灰岩地质特征及用途

二叠系阳新组灰岩厚度240~350 m，走向延伸大于50 km，出露面积15 km²以上，资源储量极为丰富.研究区0.6 km²范围内资源量为5193×10⁴ t.阳新组灰岩CaO含量49.87%~55.74%，MgO含量0.24%~2.80%，SiO₂含量0.38%~5.80%之间，SO₃含量0.01%~0.40%，K₂O+Na₂O含量0.02%~0.12%，均达到Ⅰ级水泥用料要求.饱和抗压强度41.6~82.4 MPa，坚固性1%~3%，压碎指标8.2%~9.6%；所有指标均符合建筑石料用要求.对阳新组灰岩地质特征、物理化学指标的分析评价显示，其可广泛运用于水泥、建筑石料等领域，具有重要的经济价值和意义.     

含水层中海水入侵的数学模型

提出了考虑过渡带的适合潜水含水层和承压含水层的海水入侵数学模型,导出了相应的方程和定解条件.经实例验证,模型是合理和可靠的.     

2D Coupled 3D:A New Numerical Model for Dual - Structured - Aquifer System

２Ｄ　Ｃｏｕｐｌｅｄ　３Ｄ：Ａ　Ｎｅｗ　Ｎｕｍｅｒｉｃａｌ　Ｍｏｄｅｌ　ｆｏｒＤｕａｌ－Ｓｔｒｕｃｔｕｒｅｄ－Ａｑｕｉｆｅｒ　Ｓｙｓｔｅｍ￥ＣｈｅｎＣｈｏｎｇｘｉ；ＦａｎｇＳｈｕｚｈｅｎ；ＬｉｎＭｉｎ（ＦａｃｕｌｔｙｏｆＥｎｖｉｒｏｎｍｅｎｔａｌＳｃ...     

彭县塘坝子—葛仙山景点石灰岩溶洞景观及旅游资源开发前景

塘坝子-葛仙山景点,地处举世瞩目的龙门山推覆-滑覆构造带上,已成为拟建中的“龙门山地质公园”的重要组成部分。其独特的石灰岩岩溶地貌和溶洞景观,是成都旅游区和彭县景区内宝贵的旅游景观配套资源,除旅游开发价值较高外,亦是离成都市区较近较理想的人防各战疏散基地,因而具有一定的资源综合开发潜力。对该景点的尽早开发,还可缓解邻区旅游热点的人满之患。     

一降水工程的施工和从中引出的思考

基坑降水是岩土工程中经常遇到的施工问题。本文展示了一个降水工程实例，从中引伸出本工程尚未遇到而在其他项目中可能会出现并应及时解决的一些技术问题，引起同行的关注与重视。     

Predicting DNAPL entrapment and recovery: the influence of hydraulic property correlation

The influence of aquifer property correlation on multiphase fluid migration, entrapment and recovery was explored by incorporating correlated and uncorrelated porosity, permeability, and capillary pressure-saturation (P_c-Sat) parameter fields in a cross-sectional numerical multiphase flow model. Comparison of two-dimensional entrapped organic saturation distributions for a simulated tetrachloroethylene (PCE) spill in ensembles of aquifer realizations suggests that the degree of spatial correlation in P_c-Sat parameters exerts a controlling influence on dense nonaqueous phase liquid (DNAPL) spreading and redistribution in saturated aquifers. The predicted evolution of DNAPL source zones and resultant remediation efficiency under surfactant enhanced aquifer remediation (SEAR) also appear to be strongly influenced by the spatial correlation of aquifer parameters and multiphase flow constitutive relationships. Results for a limited number of realizations selected from each ensemble showed that removal of 60% to 99% of entrapped PCE could reduce dissolved contaminant concentration and mass flux by approximately two orders of magnitude under natural gradient conditions. Aqueous phase contaminant mass flux did not vary uniformly as a function of % DNAPL removed, however, and notable differences in behavior were observed for models incorporating correlated versus uncorrelated P_c-Sat and permeability fields. Although these results must be confirmed through analysis of additional realizations, it is likely that similar or larger differences between correlated and uncorrelated system behavior will be observed in aquifers with greater spatially variability than that of the nonuniform, homogeneous sand aquifer studied here. Funding for this research was provided by the United States Environmental Protection Agency, Great Lakes and Mid-Atlantic Center for Hazardous Substance Research under Grant No. R-825540, the Michigan Department of Environmental Quality under Contract No. Y80011, and the Strategic Environmental Research and Development Program under Project No. CU-1293. The content of this publication does not necessarily represent the views of these agencies and has not been subject to agency review.     

Dissolved oxygen and nitrate of groundwater in Choshui Fan-Delta,western Taiwan

Dissolved oxygen (DO) and nitrate concentrations of groundwater from a total of 191 new monitoring wells, with a maximum depth up to 300 m, in the Choshui fan delta of Taiwan were measured to delineate the regional patterns of the two components. Unconfined aquifers of the proximal part of the fan delta contain 1~7 mg/l of DO, and a 250-m deep well still has an unusual value of 1.83 mg/l. DO concentrations decrease downgradient along flow paths to below detection limit (0.01 mg/l) in shallow confined aquifers during the last 40 years, possibly due to oxidation of organic matters in sediments. A plume of high nitrate-N concentrations (0.5–17 mg/l) originating from the proximal part of the fan delta has been developing, possibly since 1956, due to agricultural fertilizers. From 1997 to 2001, the concentration has increased at a rate of ca. 0.28 mg/l per year.     

塔里木与扬子新元古代热-构造事件特征、序列和时代——扬子与塔里木连接(YZ-TAR)假设

淄博市大武水源地是中国北方罕见的特大型岩溶-裂隙地下水水源地,地下水开采量为52×10~4m~3/d。为了对岩溶地下水进行有效监测,需要建立最优的地下水监测网。文中在对岩溶地下水流系统分析的基础上,建立了地下水流系统确定性-随机性数学模型,运用有限元与卡尔曼滤波耦合的模拟递推算法,对大武水源地地下水监测网进行了优化设计,结果显示:现有地下水位动态监测网难以达到监测目标,最优地下水位监测网由14个监测井,每月监测一次的监测频率组成,比现有地下水位监测网减少了2个监测井。     

Une dépression piézométrique naturelle en hausse au Sahel (Sud-Ouest du Niger)A rising piezometric depression in the Sahel (southwestern Niger)

In southwest Niger, the Continental Terminal water table displays a natural hollow shape about 10 m in depth over an area of 4000 km². A 10-year survey of this hollow aquifer has shown that current recharge is above $\text{20 }\text{mm}\text{yr}{}^{\mathrm{?1}}$. The water table has risen continuously since the 1950–1960s as a result of land clearance. This shows a disequilibrium in the aquifer balance. The long-term recharge rate is estimated by radioisotopes to be around $\text{1 }\text{mm}\text{yr}{}^{\mathrm{?1}}$. This figure fits with the only possible origin of the piezometric depression, i.e. evapotranspiration losses in its centre. To cite this article: G. Favreau et al., C. R. Geoscience 334 (2002) 395–401.