Modeling of Rock Permeability Damage and Repairing Dynamics Due to Invasion and Removal of Particulate from Drilling Fluids

The investigation discussed in this paper was motivated by the need for model which is able to simulate both permeability reduction of hydrocarbon formations due to the mud-component invasion during over-balance drilling, casing/cementing, workover operations, and dynamics of permeability repairing during well cleanup. The paper focuses on development and validation of model to describe internal mud cake (IMC) dynamics, placing special emphasis on dynamics of the IMC removing during well cleanup procedure. Set of laboratory experiments with clay slurry injection and subsequent brine water backflow in samples of Bentheimer sandstone is discussed. The specific of these experiments is that backflow was carried out with alternating rates (“multirate” backflow). It is shown that the conventional deep-bed filtration model is not able to reproduce the dynamics of multirate backflow. The stochastic model we suggest takes into account pore size distribution and describes the mobilization of trapped particles within individual groups of pores within a “pore ensemble.” We provide simulation results to show that the suggested model reasonably reproduces permeability dynamics during both clay slurry injection and brine water backflow stages.     

基于粗粒化分子动力学的自由水与水化硅酸钙孔隙水冻结模拟

水化硅酸钙是水泥基材料的主要水化产物,其孔隙内的水分是影响水泥基材料抗冻性的主要因素。本文基于粗粒化分子动力学方法研究水化硅酸钙孔隙水的冻结机制,针对水的粗粒化P₄粒子和水化硅酸钙胶体颗粒,建立了水化硅酸钙孔隙水的冻结模型。根据此模型计算了不同孔径孔隙水冰点,分析了水泥基材料孔径孔隙在冻融破坏中的危害程度;模拟得到了水化硅酸钙孔隙内水的冻结分布特征和密度分布特征。研究工作表明,本文建立的模型有效提高了分子动力学模拟水化硅酸钙孔隙水冻结问题的规模,为后续进行水泥基材料的冻融破坏分析提供了研究基础。     

Evolution of properties in hydration of cements—A numerical study

The present work develops a numerical method for analysis of the microstructure and property evolution in the hydration of the cement. A time-dependent micro-mechanical model is established to investigate the microstructure development and the effective property evolution of the cement paste, while the input parameters of the model are based on experimental data. It is assumed that the cement paste composite consists of the anhydrous cement particles, cement gel and pores. The cement particles have a periodically spatial array and are wrapped by the cement gel. The Young’s modulus and Poisson’s ratio of the cement paste are calculated by direct average method and two-scale expansion method. The comparisons between the numerical results and experimental data show that this model can simulate the evolution of the microstructure and properties during the hydration of the cements quite satisfactorily.     

Study on the rheological properties of Portland cement pastes with polycarboxylate superplasticizers

The coupling effects of temperature and time on the fluidity of fresh cement mixtures were investigated. Mini-cone tests on cement mortars and rheological tests on cement pastes under different temperatures (0 to 60 °C) were conducted to characterize the development of the fluidity of fresh cement mixtures over time. In addition, total organic carbon tests were performed to quantify the adsorption amount of superplasticizers on the cement surface. The amount of free water in cement pastes was determined via centrifugation. Isothermal calorimetry was employed to characterize the hydration kinetics of cement under different temperatures. Results show that the spread diameter of mortars decreases in a roughly linear fashion over elapsed time. Higher temperature facilitates a sharper decrease in fluidity with time, although the initial fluidity of fresh mortars is not significantly affected by temperature. Higher temperature results in a greater amount of adsorbed polycarboxylate ester/ether on the cement surface and a lower amount of free water in fresh cement pastes, which is believed to result from the higher hydration rate of cement. The evolution of rheological properties over time can be attributed to the development of hydration degree. Relative hydration degree is introduced to indicate the development of rheological properties with time. Two models to describe the evolution of yield stress and plastic viscosity for fresh cement pastes were developed.     

适宜海水钻井液体系新前置液实验和现场试验

前置液是影响固井质量的重要因素之一，对于海水钻井液体系，如何选用前置液是一个新的 课题. 提出了一种适宜于海水钻井液体系的新型前置液，对其在固井过程中的各种性能 进行了室内实验研究，结果表明：新型前置液与海水钻井液、固井水泥浆及盐水等环境流体 有良好的相容性，对井壁具有稳定作用，其中的固体颗粒及表面活性剂有利于冲刷海水钻井 液形成的泥饼. 在此基础上，将新型前置液应用于胜利油田的固井作业，进行现场试验，发 现：应用新型前置液后，环空水泥浆界面清晰，混浆段长度缩短，第2界面的胶结质量有明 显提高.     

浆体管道输送水击压力波波速的探讨

 在考虑自由气体存在的影响下，推导出浆体水击压力波波速的 计算公式.分析表明很少量的气体存在会使波速明显降低. 气体体积 浓度较大时波速随浆体浓度的增大而减小，重质物料的减小趋势较 为明显；气体体积浓度较小时轻质物料波速随浓度的增加而增加. 相同条件下非均质流波速比伪均质流波速大，两者差异主要受浆体 中固体物料的密度和浆体体积浓度影响. 考虑气体影响作用的浆击 波速计算值与实测结果更吻合.     

A Parametric Model for Predicting Relative Permeability-Saturation-Capillary Pressure Relationships of Oil–Water Systems in Porous Media with Mixed Wettability

A parametric two-phase, oil–water relative permeability/capillary pressure model for petroleum engineering and environmental applications is developed for porous media in which the smaller pores are strongly water-wet and the larger pores tend to be intermediate- or oil-wet. A saturation index, which can vary from 0 to 1, is used to distinguish those pores that are strongly water-wet from those that have intermediate- or oil-wet characteristics. The capillary pressure submodel is capable of describing main-drainage and hysteretic saturation-path saturations for positive and negative oil–water capillary pressures. At high oil–water capillary pressures, an asymptote is approached as the water saturation approaches the residual water saturation. At low oil–water capillary pressures (i.e. negative), another asymptote is approached as the oil saturation approaches the residual oil saturation. Hysteresis in capillary pressure relations, including water entrapment, is modeled. Relative permeabilities are predicted using parameters that describe main-drainage capillary pressure relations and accounting for how water and oil are distributed throughout the pore spaces of a porous medium with mixed wettability. The capillary pressure submodel is tested against published experimental data, and an example of how to use the relative permeability/capillary pressure model for a hypothetical saturation-path scenario involving several imbibition and drainage paths is given. Features of the model are also explained. Results suggest that the proposed model is capable of predicting relative permeability/capillary pressure characteristics of porous media mixed wettability.     

固井工程中的流动问题

固井是油气井在建过程中的重要工程,一般分下套管和注水泥两个过程．本文结合作者近年来的研究,着重阐述了钻井液、前置液、水泥浆在环形空间中流动的流体力学问题,包括：高温高压下的水泥浆流变性、偏心环形空间中浆液的流动特性、钻井液-前置液和前置液-水泥浆界面的稳定性等,介绍了国内外学者对这些问题的研究进展,提出了今后应深入研究的问题．     

Slurry flow metering by pressure differential devices

A simple system for measuring slurry concentrations and flow rates by pressure difference devices has been studied. Solids concentrations have been determined by pressure measurements in vertically upwards and downwards sections of the flow, and flow rates measured by a venturi meter located alternately in horizontal, vertically upwards and vertically downwards flows. The venturi performance has been described in terms of a discharge coefficient based on mixture density, and the concentration measurements have been compared to values determined by weigh tank samples. A range of sand slurries with median particle size from 150 to 740μm and an ilmenite slurry with a median particle size of 170μm have been tested. A limited number of tests on a 17μm sand slurry have also been recorded.For fine sand slurries (150μm or below) it was found that the water value of venturi-discharge coefficient applied, so that the accuracy of flow measurements will be limited only by the accuracy of the pressure and specific weight measurements. Experimental values of specific weight from the vertical loop section were on average within 1% of the values from the weigh tank, where the majority of this scatter was caused by the limitations of the weigh tank method.For coarser slurries, the venturi-discharge coefficients depended primarily on solids concentration, with a secondary dependence on Reynolds number, and values were below the water value. An analysis of the flow based on a one-dimensional momentum balance indicated that relative velocity between the phases could account for these low values of discharge coefficient. This was verified by high-speed photography of the flow which suggested a movement of particles towards the centre of the flow at the throat.The overall indications are that the combination of a vertical loop section of flow (for concentration or specific weight measurements) and a venturi meter (for flow rates) provides a simple and accurate means of metering slurry flows. For fine slurries only water calibrations or calibrations from Standards are required.     

Elastic behavior of saturated porous materials under undrained freezing

The elastic behavior of saturated porous materi- als under undrained freezing is investigated by using a poro- mechanical approach. Thermodynamic equilibria are used to describe the crystallization process of the partially frozen solution in bulk state and confined state in pores. By phase transition at freezing, fusion energy, thermal contraction of solid, solution and ice crystals, volume changes of crystallization build up remarkable pore pressure that induces expansion or shrinkage of solid matrix. Owing to the lower chemical potential when pore water mixes with salts, fewer ice forms in pores. Penetration of ice into the porous materials increases the capillary pressure, but limits effect on the pore liquid pressure and the strain of solid matrix. On the contrary, the pore pressure induced by solution density rises as salt concentration increases and causes significant shrinkage of solid matrix.     

Analytical Determination of Flow Patterns in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-Voids

This article presents the analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, occluded macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for the pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its size is characterized by the macro-porosity. Confrontations are made with numerical solutions in order to investigate the applicability of the analytical pressure and velocity solutions to microstructures of finite size.     

Shear thickening and shear-induced agglomeration of chemical mechanical polishing slurries using electrolytes

Chemical mechanical polishing is a fundamental technology used in the semiconductor manufacturing industry to polish and planarize a wide range of materials for the fabrication of microelectronic devices. During the high-shear (～1,000,000 s^?1) polishing process, it is hypothesized that individual slurry particles are driven together to form large agglomerates (≥0.5 µm). These agglomerates are believed to trigger a shear-induced thickening effect and cause defects during polishing. We examined how the addition of various monovalent salts (CsCl, KCl, LiCl, and NaCl) and electrostatic stabilizing bases (KOH, NaOH, or CsOH) influenced the slurry’s thickening behavior. Overall, as the added salt concentration was increased from 0.02 to 0.15 M, the shear rate at which the slurry thickened (i.e., the critical shear rate) decreased. Slurries with added CsCl, NaCl, and LiCl thickened at comparable shear rates (～20,000–70,000 s^?1) and, in general, followed ion hydration theory (poorly hydrated ions caused the slurry to thicken at lower shear rates). However, slurries with added KCl portrayed thickening behavior at higher critical shear rates (～35,000–100,000 s^?1) than other chloride salts. Also, slurries stabilized with CsOH thickened at higher shear rates (～90,000–140,000 s^?1), regardless of the added salt cation or concentration, than the slurries with KOH or NaOH. The NaOH-stabilized slurries displayed thickening at the lowest shear rates (～20,000 s^?1). The thickening dependence on slurry base cation indicates the existence of additional close-range structure forces that are not predicted by the Derjaguin–Landau–Verwey–Overbeek colloidal stability theory.     

Pore-Scale Network Modeling of Three-Phase Flow Based on Thermodynamically Consistent Threshold Capillary Pressures. I. Cusp Formation and Collapse

We present a pore-scale network model of two- and three-phase flow in disordered porous media. The model reads three-dimensional pore networks representing the pore space in different porous materials. It simulates wide range of two- and three-phase pore-scale displacements in porous media with mixed-wet wettability. The networks are composed of pores and throats with circular and angular cross sections. The model allows the presence of multiple phases in each angular pore. It uses Helmholtz free energy balance and Mayer–Stowe–Princen (MSP) method to compute threshold capillary pressures for two- and three-phase displacements (fluid configuration changes) based on pore wettability, pore geometry, interfacial tension, and initial pore fluid occupancy. In particular, it generates thermodynamically consistent threshold capillary pressures for wetting and spreading fluid layers resulting from different displacement events. Threshold capillary pressure equations are presented for various possible fluid configuration changes. By solving the equations for the most favorable displacements, we show how threshold capillary pressures and final fluid configurations may vary with wettability, shape factor, and the maximum capillary pressure reached during preceding displacement processes. A new cusp pore fluid configuration is introduced to handle the connectivity of the intermediate wetting phase at low saturations and to improve model’s predictive capabilities. Based on energy balance and geometric equations, we show that, for instance, a gas-to-oil piston-like displacement in an angular pore can result in a pore fluid configuration with no oil, with oil layers, or with oil cusps. Oil layers can then collapse to form cusps. Cusps can shrink and disappear leaving no oil behind. Different displacement mechanisms for layer and cusp formation and collapse based on the MSP analysis are implemented in the model. We introduce four different layer collapse rules. A selected collapse rule may generate different corner configuration depending on fluid occupancies of the neighboring elements and capillary pressures. A new methodology based on the MSP method is introduced to handle newly created gas/water interfaces that eliminates inconsistencies in relation between capillary pressures and pore fluid occupancies. Minimization of Helmholtz free energy for each relevant displacement enables the model to accurately determine the most favorable displacement, and hence, improve its predictive capabilities for relative permeabilities, capillary pressures, and residual saturations. The results indicate that absence of oil cusps and the previously used geometric criterion for the collapse of oil layers could yield lower residual oil saturations than the experimentally measured values in two- and three-phase systems.     

A stochastic model for filtration of particulate suspensions with incomplete pore plugging

A population balance model for particulate suspension transport with capture of particles by porous medium accounting for complete and incomplete plugging of pores by retained particles is derived. The model accounts for pore space accessibility, due to restriction on finite size particle movement through the overall pore space, and for particle flux reduction, due to transport of particles by the fraction of the overall flux. The novel feature of the model is the residual pore conductivity after the particle retention in the pore and the possibility of one pore to capture several particles. A closed system of governing stochastic equations determines the evolution of size distributions for suspended particles and pores. Its averaging results in the closed system of hydrodynamic equations accounting for permeability and porosity reduction due to plugging. The problem of deep bed filtration of a single particle size suspension through a single pore size medium where a pore can be completely plugged by two particles allows for an exact analytical solution. The phenomenological deep bed filtration model follows from the analytical solution.     

Constitutive unsaturated hydro-mechanical model based on modified mixture theory with consideration of hydration swelling

This paper has extended modified mixture theory with consideration of hydration swelling in unsaturated rock. By using non-equilibrium thermodynamics and Biot elasticity, a fully coupled formulation including hydration swelling term is derived. Standard arguments of non-equilibrium thermodynamics are used to derive the Darcy’s law for unsaturated flow. Helmholtz free energy has been used to give the relationship between the stress and pore pressure. The chemical potential of water in pore space and clay platelets has been included in the analysis of water sensitive materials such as shale. Finally, a simple numerical example has been presented for illustrative purpose, the results show that the swelling parameter has a strong influence on stress and strain.     

Microscale Visual Study of End Effects at Permeability Discontinuities

The physical effect of multiphase fluid distribution and flow at permeability boundaries has not been fully investigated, particularly at the pore scale (1–100 μm), although such behaviour can significantly affect the overall scaled-up reservoir trapping capacity and production performance. In this article, microscale physical models have been used to qualitatively study the pore scale flow events at permeability boundaries, both high to low and vice versa, to gain a better understanding of the role of these boundaries and water saturation on multiphase displacement behaviour at the pore scale. We have used etched glass models of stripes of large and small (a factor of two) pores with circular matrix. Capillary pressure, which is the controlling parameter is itself dependant on pore size and its spatial distribution, the magnitude of the interfacial tensions and the wettability between the fluids and the solid surface of the models. Sometimes, the only way the non-wetting fluid can penetrate the boundary is through a fortuitous leakage, whereby the presence of an initial saturation reduces the controlling capillary pressure. Examples are demonstrated including mechanisms of end-effects and how capillary boundary resistance (due to capillary forces) can be broken down and fluid movement across the boundary can develop. These micromodel experiments show vividly that connate water can assist in these processes, particularly oil trapping and leakage of water across a permeability boundary.     

Evaporation heat transfer in thin biporous media

 This paper deals with the evaporation heat transfer mechanism in thin biporous media that have two characteristic capillary pore radii. The character of the two levels of pore sizes allows the liquid phase to easily occupy the void space of the small pores and vapor phase to occupy the void space of the big pores. Compared with mono-porous media, biporous media increase the number of small evaporating menisci with high heat transfer performance. Evaporation heat transfer in pores of porous media is analyzed in detail. The results indicate that the average heat transfer coefficient increases with the capillary pore size reduction. Under the assumption of the uniform structure of biporous media, a calculation method to predict heat transfer performance for the evaporation in thin biporous media is given. The preliminary results reflect the behavior of observed vaporization heat transfer in thin biporous media well. Received on 22 February 2000     

Towards a theory of nonequilibrium multiphase filtration flow

A new theoretical model of joint filtration flow of immiscible incompressible fluids is presented. This model takes into account relaxation processes due to the exchange of the fluids between pores of different sizes, and these relaxation processes are driven by capillary forces. The fluids occupy connected regions in the four-dimensional space formed by three coordinates and the pore length scale. When fluid exchange between pores of given sizes is effected by way of successive flow through pores of all intermediate sizes, the fluid pressure within each region is governed by a hyperbolic equation, the role of time being played by the pore linear scale. Pressure jumps across hypersurfaces separating these regions are equal to corresponding values of capillary pressure. A supplementary condition at any such hypersurface requires the speed of its displacement in the four-dimensional space to coincide with the normal velocity components of both the adjoining fluids. As a result, a new formulation of multiphase filtration flow problems is gained with allowance made for capillary relaxation in the porous space.     

Investigation of Various Pressure Transient Techniques on Permeability Measurement of Unconventional Gas Reservoirs

Chloride ingress into concrete is a major cause for material degradation, such as cracking due to corrosion-induced steel reinforcement expansion. Corresponding transport processes encompass diffusion, convection, and migration, and their mathematical quantification as a function of the concrete composition remains an unrevealed enigma. Approaching the problem step by step, we here concentrate on the diffusivity of cement paste, and how it follows from the microstructural features of the material and from the chloride diffusivity in the capillary pore spaces. For this purpose, we employ advanced self-consistent homogenization theory as recently used for permeability upscaling, based on the resolution of the pore space as pore channels being oriented in all space directions, resulting in a quite compact analytical relation between porosity, pore diffusivity, and the overall diffusivity of the cement paste. This relation is supported by experiments and reconfirms the pivotal role that layered water most probably plays for the reduction of the pore diffusivity, with respect to the diffusivity found under the chemical condition of a bulk solution.     

Prediction of elastic modulus and Poisson’s ratio for unsaturated concrete

Many concrete structures are located in water environment, but the underwater concrete is usually unsaturated even though it has been soaked in the water for a very long time. Some experiments have proven that the mechanical properties of concrete are affected by the saturation degree of fluid and aspect ratio of pores. Several publications discussed the saturated concrete qualitatively, but few gave quantitative analysis especially for the unsaturated concrete. In terms of the microstructure of unsaturated concrete, equivalent medium and inclusion-based theory of composite materials, a model is proposed to explain the changes happened in the wet concrete and to predict the elastic parameters (including elastic modulus and Poisson’s ratio) of unsaturated concrete. The viscosity of water in pores, micro-cracks and the further hydration of cement are taken into account in this paper by means of the definition of saturation concept according to the effect of pore water on the modulus of concrete. In this model, both stiff effect of water and soft effect of cracks on the concrete are introduced to describe the bulk modulus, at the same time the effect of shear rate on the shear modulus is considered. The comparison between the theoretical models and experimental results in the extreme state indicates that the model proposed in this paper is valid to predict the elastic properties of unsaturated concrete.