Fluid flow properties for different classes of intermediate wettability as studied by network modelling

Most clastic reservoirs display an intermediate type of wettability. Intermediate wettability covers several local wetting configurations like fractional wet and mixed-wet where the oil-wet sites could either be in the large or smaller pores. Clastic reservoirs show a large variation in fluid flow properties. A classical invasion–percolation network simulator is used to investigate properties of different intermediate wet situations. Variation in wetting properties like contact angles, process dependent contact angles, contact angle distribution, and fraction of oil wet sites are investigated. The fluid flow properties analysed in particular are residual oil saturation and normalized endpoint relative permeability. Results from network modelling have been compared to reservoir core analysis data. The network models applied are at the capillary limit, while the core flood results are clearly viscous influenced. Even though network modelling does not cover all the physics involved in fluid displacement processes, results show that data from simulations are sufficient to present trends in fluid flow properties which are comparable to experimental data.     

Flow behaviour in the presence of wettability heterogeneities

The physical processes occurring during fluid flow and displacement within porous media having wettability heterogeneities have been investigated in specially designed heterogeneous visual models. The models were packed with glass beads, areas of which were treated with a water repellent to create wettability variations. Immiscible displacement experiments show visually the effect of wettability heterogeneities on the formation of residual oil and recovery due to capillary trapping. This work demonstrates by experiment the importance of incorporating reservoir heterogeneity into pore displacement analysis, essential for the correct interpretation of core data and for directing the route for scale-up of the processes to reservoir scale.     

Simulation of capillary pressure curves using bond correlated site percolation on a simple cubic network

A stochastic approach to network modelling has been used to simulate quasi-static immiscible displacement in porous media. Both number-based and volume-based network saturation results were obtained. Number-based results include: number-based saturation curves for primary drainage, secondary imbibition and secondary drainage, fluid distribution data, and cluster trapping history. Using pore structure data of porous media, it is possible to convert the number-based curves to capillary pressure — saturation relationships. Pore size distribution functions and pore shapes which are thought to closely represent Berea sandstone samples were used to predict the capillary curves. The physical basis of these calculations is a one-to-one correspondence between the cumulative node and bond index fractions in the network analysis, and the cumulative number-based distributions of pore body and pore throat diameters, respectively. The oil-water capillary pressure curve simulated for primary drainage closely resembles those measured experimentally. The agreement between the simulated and the measured secondary imbition and secondary drainage curves is less satisfactory.     

Experimental study of two-phase flow in three sandstones. II. Capillary pressure curve measurement and relative permeability pore space capillary models

By means of the porous plate method and mercury porosimetry intrusion tests, capillary pressure curves of three different sandstones were measured. The testing results have been exploited jointly with three relative permeability models of the pore space capillary type (Burdine’s model type), these models are widely used and in rather distinct fields. To do so, capillary pressure has been correlated to saturation degree using six of the most popular relations encountered in the literature. Model predictions were systematically compared to the experimentally measured relative permeabilities presented in the first part of this work. Comparison indicated that the studied models underestimate the water relative permeability and over-estimate that of the non-wetting phase. Moreover, this modeling proves to be unable to locate the significant points that are the limits of fields of saturation where the variation of the relative permeabilities becomes consequent. We also showed that, if pore structure is modeled as a “bundle of capillary tubes”, model predications are independent of the capillary pressure curve measuring method.     

An Integral Method to Calculate Water Saturation in a Centrifuge Experiment to Determine Capillary Pressure

The centrifuge method is commonly used to determine the capillary pressure of a porous medium, and the original approximating method for data analysis developed by Hassler and Brunner is still being used. Its limitations are, however, not well understood. Application to analyze experiments where one of the assumptions was obviously violated had been given in the literature. While the result appeared to be quite reasonable, it was not clear how close was it to reality. One of the objectives of this paper is to review the assumptions that is required to develop this method, so that the experimental condition in which it is applicable can be established. The other objective is to derive a completely different solution technique to this problem. There is no need to assume that the ratio of the inlet radius to the exit radius of the core to the center of the centrifuge be close to 1. With the freedom from this limitation it is, therefore, possible to construct machines at lower cost and to improve on the data quality by allowing longer cores.     

Discussion of Techien Chen, 1997, ‘An Integral Method to Calculate Water Saturation in a Centrifuge Experiment to Determine Capillary Pressure’

That discussion recognizes that the above paper deals with one of the main problems for reserves and reservoir evaluation, i.e. the determination of capillary pressure curves using the centrifuge technique. However, it is explained that the subject was not properly addressed and that sections of the paper are out of date, confusing or eventually wrong. For a more relevant overview on the subject, it is recommended to refer to the corresponding survey by the Society of Core Analysts.     

Effect of capillary pressure on the approach to residual saturation

The approach to residual oil saturation during the immiscible displacement of oil as predicted by the multiphase Darcy equations is studied. It is well known that when the capillary pressure term is neglected, one arrives at the Buckley-Leverett formulation according to which the inlet face attains residual oil saturation instantaneously. This result may, however, be strongly influenced by the inclusion of the capillary pressure term. In this paper it is shown that when the relative permeability and capillary pressure functions have power law dependencies on the saturation deviation from residual oil condition, the long time solution exhibits a power law decay toward residual saturation. Moreover, the power law decay solution is found to be unique and independent of the initial condition. The relationship of this solution to the classical Buckley-Leverett result is shown. Finally, generalization to the time varying flow rate case is addressed. As a verification of the theoretical conjectures, the power law solution is compared with direct numerical simulation of the two phase flow equations.     

天然气水合物分解对地层稳定性影响的离心机实验模拟

水合物分解后将引起地层强度的降低,可能造成海床沉陷、滑塌以及海洋结构物基础的破坏。针对该问题,首先以南海浅层粉砂为沉积物骨架,采用生物厌氧发酵技术合成水合物沉积物,然后进行水合物热分解引起地层响应的离心机实验模拟,获得了水合物分解引起地层变形与滑塌的特征以及孔隙压力发展的物理过程,为研究水合物分解引起海床失稳的条件进行了新的尝试。     

Identification of the four orthotropic plate stiffnesses using a single open-hole tensile test

The identification of mechanical parameters for real structures is still a challenge. With the improvement of optical full-field measurement techniques, it has become easier, but in spite of many publications showing the feasibility of such methods, experimental results are still scarce. In this paper we present a first step towards a global approach of mechanical identification for composite materials. The chosen mechanical test is an open-hole tensile test according to standard recommendations. For the moment, experimental data are provided by a moiré interferometry setup. The global principle of the identification developed in this paper is to minimize a discrepancy between experimental and theoretical results, expressed as a cost function, using a Levenberg-Marquardt algorithm. This approach has the advantage of having high adaptability, largely because the optical system, the signal processing as well as the mechanical aspects, can be taken into consideration by the model. In this paper we consider different types of cost functions, which are tested using an identifiability criterion. Although mechanically based cost functions have been studied, a simpler mathematical form is finally more efficient. Two different models were tested. The first is an analytical model based on the Lekhnitskii approach. This approach has the advantage of being a meshless solution; however, the results appeared to be partially false due to boundary effects, leading to a second approach, a classical finite element analysis. The resulting identified values are similar to values from classical mechanical tests (within 6%). which, in practice, validates our approach.     

离心机上辨识陀螺加速度计二次项系数的优化试验设计

提出了一种在带有反转平台的精密离心机上标定陀螺加速度计误差模型二次项系数K 2的D-最优试验方案。应用该D-最优试验方案,通过重复试验,能够在测试点最少的情况下获得高测试精度,实现陀螺加速度计误差模型系数的最优(D-最优的)辨识。推导了测量随机误差、试验方案的测试点、测试点的重复测试次数以及误差模型系数方差之间的关系式。精度分析的结果表明,应用D-最优试验方案,采取重复试验的方法,能够有效地减小二次项系数K的估计量的方差,从而提高K的辨识精度。     

Experimental Study and Fractal Analysis of Heterogeneity in Naturally Fractured Rocks

Capillary pressure curves of six low porosity and low permeability core samples from The Geysers geothermal field were measured using the mercury-intrusion approach to characterize the heterogeneity of rock. One high permeability Berea sandstone core sample was analyzed similarly, for comparison. The maximum pressure of mercury intruded into the rock was about 200 MPa to reach the extremely small pores. Experimental data showed that the capillary pressure curves of The Geysers rock are very different from that of the Berea sandstone. It was found that the frequently used capillary pressure models could not be used to represent the data from The Geysers rock samples. This might be because of the fractures in the rock. To this end, a fractal technique was proposed to model the features of the capillary pressure curves and to characterize the difference in heterogeneity between The Geysers rock and Berea sandstone. The results demonstrated that the rock from The Geysers geothermal field was fractal over a scaling range of about five orders of magnitude. The values of the fractal dimension of all the core samples (six from The Geysers and one Berea sandstone) calculated using the proposed approach were in the range from 2 to 3. The results showed that The Geysers rock with a high density of fractures had a greater fractal dimension than Berea sandstone which is almost without fractures. This shows that The Geysers rock has greater heterogeneity, as expected.     

陀螺仪漂移测试小角度伺服法实验方案的改进

为了提高陀螺仪的使用精度,研究了陀螺仪漂移测试的伺服法实验技术.依托973项目,在国内首次完成了高精度单自由度静压液浮陀螺仪的伺服法实验.找到了影响小角度伺服法实验测试精度的主要误差源,即小角度伺服法实验的方法误差,通过对该误差的分析,提出了改进的小角度伺服实验方案.建立了小角度伺服法实验方法误差的仿真模型,用改进方案和原始方案分别进行了仿真和实验,结果表明改进方案同原始方案相比,陀螺仪漂移误差模型中的三项系数辨识精度均有提高.     

离心机上辨识加速度计模型参数的优化试验设计

本文针对离心机上测试加速度计时可以在多个球面上布测试点的特点,研究了双球面组合试验计划的优化设计问题,得出了Ｄ 最优准则下一个优化的组合试验计划测度比,并进行了工程简化,得到了一个实用的准Ｄ 最优组合试验计划。     

土石混合体直剪离散元数值试验研究

工程中普遍存在的土石混合体以其复杂的工程地质力学性质越来越受研究者的关注。由于"块石"的存在使得土石混合体在细观层次上呈现明显的结构性特征,这种结构性将影响甚至控制着其变形破坏机制及宏观力学特征。本文借助三维颗粒离散元分析软件YADE分别从含石量、试样尺寸、强度特性等角度对土石混合体的力学性质开展了一系列的数值直剪试验研究工作,并取得了一些有意义的研究成果:在含石量及粒度组成相同的情况下土石混合体的宏观抗剪强度及剪胀性随着试样尺寸的增加而呈现降低趋势,而在相同试样尺寸下将随着含石量的增加而增加;内部块石的存在影响着其细观应力状态,从而影响其宏观力学特性。     

Simulation of Gas Dipole Tests in Fractures at the Intermediate Scale Using a New Upscaling Method

A high-level radioactive waste disposal site may lead to gas generation by different physical mechanisms. As these sites are to be located in areas with low water flow, any small amount of gas can lead to relative high gas pressures, so that multiphase flow analysis becomes relevant. The movement of gas and water through the system has two important implications. Firstly, water flow takes place in unsaturated conditions, and thus travel times of the radioactive particles transported are affected; and secondly, gas can also carry radioactive particles. Therefore, one of the key points in such studies is the time when gas would break through the biosphere under a number of different flow conditions. In fractured zones, gas would flow preferentially through the most conductive features. We consider a two-dimensional system representing an isolated fracture. In each point we assign a local porosity and permeability and a local pressure-saturation relationship. A dipole (injector-producer) gas flow system is generated and the variation in water saturation is studied. A simple method is proposed for obtaining upscaled values for several parameters involved in two-phase flow. It is based on numerical simulation on a block scale assuming steady-state conditions and absence of capillary pressure gradients. The proposed method of upscaling is applied to simulate a dipole test using a coarser grid than that of the reference field. The comparison between the results in both scales shows an encouraging agreement.     

混合χ~2检测法在组合导航系统故障检测中的应用

为提高SINS/GPS组合导航系统的可靠性,在分析了残差χ~2检测法和双状态χ~2检测法的基础上,提出一种混合χ~2检测法。该方法中残差χ~2检验法和双状态χ~2检验法并行工作且共用同一个卡尔曼滤波器,同时残差χ~2检验法的检测结果决定了对双状态χ~2检验法的两个状态递推器的操作:当残差χ~2检验法检测到组合导航系统故障时,则通过控制开关使卡尔曼滤波结果不对两个状态递推器进行状态重置,反之,如果残差χ~2检验法检测系统正常,则允许卡尔曼滤波结果对状态递推器进行状态重置,从而有效地解决了残差χ~2检验法对软故障不敏感的问题和双状态χ~2检验法的两个状态递推器易受污染的问题,组合导航系统故障诊断结果由残差χ~2检测法和双状态χ~2检测法共同决定。仿真实验分析表明,该方法能够降低虚警率,有效地提高组合导航系统故障诊断的准确性和可靠性。     

Pore Network Modelling of Electrical Resistivity and Capillary Pressure Characteristics

In order to model petrophysical properties of hydrocarbon reservoir rocks, the underlying physics occurring in realistic rock pore structures must be captured. Experimental evidence showing variations of wetting occurring within a pore, and existence of the so-called 'non-Archie' behaviour, has led to numerical models using pore shapes with crevices (for example, square, elliptic, star-like shapes, etc.). This paper presents theoretical derivations and simulation results of a new pore space network model for the prediction of petrophysical properties of reservoir rocks. The effects of key pore geometrical factors such as pore shape, pore size distribution and pore co-ordination number (pore connectivity) have been incorporated into the theoretical model. In particular, the model is used to investigate the effects of wettability and saturation history on electrical resistivity and capillary pressure characteristics. The petrophysical characteristics were simulated for reservoir rock samples. The use of the more realistic grain boundary pore (GBP) shape allows simulation of the generic behaviour of sandstone rocks, with various wetting scenarios. The predictions are in close agreement with electrical resistivity and capillary pressure characteristics observed in experiments.     

Empirical Measures of Wettability in Porous Media and the Relationship between Them Derived From Pore-Scale Modelling

The wettability of a crude oil/brine/rock system is of central importance in determining the oil recovery efficiency of water displacement processes in oil reservoirs. Wettability of a rock sample has traditionally been measured using one of two experimental techniques, viz. the United States Bureau of Mines and Amott tests. The former gives the USBM index, I _USBM, and the latter yields the Amott–Harvey index, I _AH. As there is no well-established theoretical basis for either test, any relationship between the two indices remains unclear.Analytical relationships between I _AH and I _USBM for mixed-wet and fractionally-wet media have been based on a number of simplifying assumptions relating to the underlying pore-scale displacement mechanisms. This simple approach provides some guidelines regarding the influence of the distribution of oil-wet surfaces within the porous medium on I _AH and I _USBM. More detailed insight into the relationship between I _AH and I _USBM is provided by modelling the pore-scale displacement processes in a network of interconnected pores. The effects of pore size distribution, interconnectivity, displacement mechanisms, distribution of volume and of oil-wet pores within the pore space have all been investigated by means of the network model.The results of these analytical calculations and network simulations show that I _AH and I _USBM need not be identical. Moreover, the calculated indices and the relationship between them suggest explanations for some of the trends that appear in experimental data when both I _USBM and I _AH have been reported in the literature for tests with comparable fluids and solids. Such calculations should help with the design of more informative wettability tests in the future.     

Influence of polymer conformation on the entrance length in capillary flow

An analysis of the flow of polymer solutions through capillaries by means of pressure profiles was performed in this work. The experiments were carried out with aqueous solutions of flexible and semirigid macromolecules, Polyox and Xanthan respectively. The influence of the macromolecules' conformation on the flow field development is reflected on the different magnitudes of the entry length, being of the order of 60 diameters for the solutions of rigid macromolecules, and of the order of 10 diameters for flexible ones. In addition, the calculated end effects were larger for the rigid macromolecules than for the flexible ones. From these results, it is found that an increase in the entrance length is observed when the pseudoplastic behavior of the polymer solutions is increased.Dedicated to Prof. Dr. J. Meissner on the occasion of his retirement from the chair of Polymer Physics at the Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland