Upscaling relative permeabilities in a structured porous medium

Upscaling of multi-phase flow problems for a heterogeneous porous medium requires modification of constitutive functions at the grid-block scale. A particular type of heterogeneity that has important environmental consequences involves thin, continuous streaks of high permeability through lower-permeability background rocks. These streaks, which may correspond to features like abandoned wells in mature sedimentary basins, can become preferential flow paths for an invading fluid. Quantification of flow through these types of heterogeneities in deep, geological formations is necessary for estimates of migration and possible leakage of injected fluids such as hazardous liquid wastes, municipal liquid wastes, and, possibly, carbon dioxide. One of the important constitutive functions for proper estimation of flow through these flow paths is the relative permeability function. In the simple case of a single high-permeability streak in a uniform rock matrix, with both materials having identical (local) relative permeability functions, the upscaled relative permeability must be changed significantly to capture the proper leakage. Standard petroleum reservoir pseudo-functions for relative permeability capture the general features of the upscaled function, but they still produce errors of several hundred percent in the leakage estimation. Detailed three-dimensional numerical simulations and associated upscaled calculations demonstrate the proper form for the upscaled relative permeability, and provide a modified derivation of pseudo-functions to capture the leakage behavior in upscaled models.     

Estimation of heat discharge rates using infrared measurements by a helicopter-borne thermocamera over the geothermal areas of Unzen volcano, Japan

Unzen volcano is situated on Shimabara Peninsula, western Kyushu, Japan. On the flank of the volcano, the Obama, Unzen and Shimabara hot springs are aligned in a direction from the southwest to the northeast across the peak. At Obama and Shimabara, heat is transferred mainly by water flow. But at Unzen heat is transferred by the discharge of natural steam and by conduction as well as water flow. In order to estimate the heat discharge by mechanisms other than water flow, infrared measurements by a helicopter-borne thermocamera were conducted over the Unzen hot spring area. The heat discharge was calculated from the thermal image by a method based on heat balance of the ground surface resulting in a value of 1.9 × 10⁶ cal/s (7.9 MW). The heat discharged by all mechanisms including that by water flow is estimated to be 5.0 × 10⁶ cal/s (21 MW). Similar preliminary estimates have been made for heat discharge at the Obama and Shimabara hot springs giving values of about 1.2 × 10⁷ cal/s (50 MW) and 1.0 × 10⁵ cal/s (0.4 MW), respectively. These values indicate that the heat discharge decreases with distance from the southwest to the northeast direction across the volcano. The total heat discharge from three hot spring areas on Unzen volcano is about 1.7 × 10⁷ cal/s (71 MW).The heat balance method appears useful for quantitative analysis of regional trends but its accuracy may not be always sufficient for detailed surveys. Several methods of determining heat flow, including the heat balance method, were compared at a test field in the Unzen hot spring area. The values obtained by the heat balance method coincide roughly with the other results but more detailed analysis is necessary to improve the accuracy of current methods of geothermal measurements.     

Fluid flow from pore pressure measurements off La Palma, Canary Islands

In situ subseafloor pore pressure results from the western flank of the island of La Palma, Canary Islands, are presented. The data obtained with a Pop Up Pore Pressure Instrument (PUPPI) provide constraints on the fluid circulation and its causes in a very special context: The sediment piles near an intraplate oceanic island built on the continental rise of the Northwest African Margin. The ambient pore pressures estimated from 2 to 4 days long record are negative in almost all cases with values, at depths of a few meters below sea floor, usually on the order of −10 to −70 Pa. Excess pore pressures develop only in the distal most areas. The permeabilities and compressibilities obtained respectively from the decay of the insertion pressures and the amplitude of the tidally induced pore pressure variations range between 2.5×10⁻¹⁸ and 6.6×10⁻¹⁶ m² and, 6.2×10⁻⁹ and 1.5×10⁻⁷ Pa⁻¹. According to these permeabilities fluid flow is estimated to be mostly downward and usually on the range between 0 and −0.3 mm y⁻¹. However, from the excess pore pressure profile a complex pattern of fluid circulation is inferred where horizontal fluid motion cannot be neglected. Horizontal flow is probably controlled by significant contrasts in the permeability of the different layers. The prevailing downward fluid flow is abnormal for a classical passive margin. We thus interpret these results as the superposition to the loss of fluids by sediment compaction (on the continental rise), of a large-scale flow system stimulated by thermal buoyancy (100 km wide) related to the volcanic activity on the island of La Palma.     

Modelling Feedback of Chemical Reactions on Flow Fields in Hydrothermal Systems

Coupled reactive transport models of hydrothermal systems provide new insights and deeper understanding of the processes occurring due to fluid flow, heat transfer, solute transport, and chemical reactions. Basic concepts of species transport (diffusion, dispersion, and advection) and chemical precipitation and dissolution reactions are discussed, and five end-member types of reactive transport environments are introduced. One of these reactive transport environments, named ‘reactions within thermal gradients’, is used to demonstrate how free thermal convection can lead to redeposition of minerals and, due to the feedback of reaction on the flow field, a change of the convection pattern. The direct consequence of changing the flow field is a significant variation of the temperature distribution within the modelled area. With the example it is shown how reactive transport simulation can be applied for the detailed study of fossil and recent hydrothermal systems.     

A unified approach to a class of slow dynamos

Abstract

Dynamo action in a highly conducting fluid with small magnetic diffusivity η is particularly sensitive to the topology of the flow. The sites of rapid magnetic field regeneration, when they occur, appear to be located at the stagnation points or in regions where the particle paths are chaotic. Elsewhere only slow dynamo action is to be expected. Two such examples are the nearly axially symmetric dynamo of Braginsky and the generalisation to smooth velocity fields of the Ponomarenko dynamo. Here a method of solution is developed, which applies to both these examples and is applicable to other situations, where magnetic field lines are close to either closed or spatially periodic contours. Particular attention is given to field generation in the neighbourhood of resonant surfaces where growth rates may be intermediate between the slow diffusive and fast convective time scales. The method is applied to the case of the two-dimensional ABC-flows, where it is shown that such intermediate dynamo action can occur on resonant surfaces.     

裂缝-孔隙介质储层渗透率表征及其影响因素分析

含裂缝多孔介质渗透率预测是非常规油气资源勘探开发的一个紧迫问题.现有多孔介质岩石物理模型通常利用圆形孔管模拟宏观岩石孔隙空间,难以定量描述软孔隙/裂缝在压力作用下的闭合情况,缺乏裂缝/孔隙间流量交换的连通机制.本文提出含三维裂缝/软孔隙网络多孔介质模型,将储层岩石裂缝/软孔隙表示为椭圆截面微管,建立了周期性压力作用下微...     

Estimation of groundwater velocity in localized fracture zones from well temperature profiles

In fractured rocks, well temperature logs often exhibit abrupt temperature changes over a small distance, typically surging or dropping several degrees over several tens of meters. The abrupt temperature changes usually occur in localized fracture zones or small faults. Away from these zones, temperature quickly restores itself to the background linear conductive profile. A theoretical model is presented herein to interpret the pattern of such abrupt temperature changes. I illustrate that this type of temperature profile originates from a different physical process than the physical processes found in some other typical temperature patterns in large scales. I also demonstrate that, using the field data, the theoretical model can be effectively used to estimate fluid flow velocity in fracture zones or local faults. Using the temperature profiles from two boreholes, fluid flow velocity in fracture zones is estimated to be as high as 1.1×10⁻⁶ m/s. Although fracture flow is a highly localized feature, it can reach three orders of magnitude higher than fluid flow in the hosting rock matrices.     

Estimates of effective permeability for non-Newtonian fluid flow in randomly heterogeneous porous media

An understanding of the interplay between non-Newtonian effects in porous media flow and field-scale domain heterogeneity is of great importance in several engineering and geological applications. Here we present a simplified approach to the derivation of an effective permeability for flow of a purely viscous power–law fluid with flow behavior index n in a randomly heterogeneous porous domain subject to a uniform pressure gradient. A standard form of the flow law generalizing the Darcy’s law to non-Newtonian fluids is adopted, with the permeability coefficient being the only source of randomness. The natural logarithm of the permeability is considered a spatially homogeneous and correlated Gaussian random field. Under the ergodic hypothesis, an effective permeability is first derived for two limit 1-D flow geometries: flow parallel to permeability variation (serial-type layers), and flow transverse to permeability variation (parallel-type layers). The effective permeability of a 2-D or 3-D isotropic domain is conjectured to be a power average of 1-D results, generalizing results valid for Newtonian fluids under the validity of Darcy’s law; the conjecture is validated comparing our results with previous literature findings. The conjecture is then extended, allowing the exponents of the power averaging to be functions of the flow behavior index. For Newtonian flow, novel expressions for the effective permeability reduce to those derived in the past. The effective permeability is shown to be a function of flow dimensionality, domain heterogeneity, and flow behavior index. The impact of heterogeneity is significant, especially for shear-thinning fluids with a low flow behavior index, which tend to exhibit channeling behavior.     

Persistency of flow patterns in a water repellent sandy soil – Conclusions of TDR readings and a time-delayed double tracer experiment

On a former waste water disposal field with water repellent sandy soil under grass vegetation we analyzed the persistency of flow patterns on a 150 m × 25 m plot by (i) continuous TDR-measurements on a 2 m × 1 m transect combined with seasonal soil moisture sampling campaigns, and (ii) a time-delayed double tracer experiment on a second 3 m × 1 m transect. Here, we applied bromide under wettable soil conditions in spring and chloride under water repellent soil conditions in autumn. At the end of the tracer experiment, after a travel time of 328 days for Br and 87 days for Cl, respectively, the transect was excavated and sampled in high spatial resolution. Tracer concentration, water content, water drop penetration times (WDPT), and soil organic matter content (SOM) of each sample were analyzed in order to characterize flow patterns. The TDR readings were used to predict the effective cross section (ECS) of subsurface flow and flow shifts over the season.During summer, when ECS is low and consecutive precipitation events occur, flow paths – once created – persist over time. However, over longer times (from autumn to autumn), the spatial arrangements of the flow paths can change completely. The Cl distribution showed typical fingering structures with high concentrations in the less water repellent flow paths. In contrast, Br was found mostly in the dry, hydrophobic areas indicating that it was transported before the soil became water repellent. Consequently, the flow patterns generated in spring and early summer differ completely from those in autumn and winter because of water repellent structures established during the vegetative period. These structures could be identified using a critical water content (θ_crit) concept, considering both soil water content and SOM.As not all soil parts being active during to season, four flow categories could be identified: about 10% permanent (=stable flow paths), 45% periodic (i.e. water repellent in summer), 40% occasional (water repellent in summer and autumn), and 5% permanent water repellent.     

Micro-computed tomography pore-scale study of flow in porous media: Effect of voxel resolution

A fundamental understanding of flow in porous media at the pore-scale is necessary to be able to upscale average displacement processes from core to reservoir scale. The study of fluid flow in porous media at the pore-scale consists of two key procedures: Imaging - reconstruction of three-dimensional (3D) pore space images; and modelling such as with single and two-phase flow simulations with Lattice-Boltzmann (LB) or Pore-Network (PN) Modelling. Here we analyse pore-scale results to predict petrophysical properties such as porosity, single-phase permeability and multi-phase properties at different length scales. The fundamental issue is to understand the image resolution dependency of transport properties, in order to up-scale the flow physics from pore to core scale. In this work, we use a high resolution micro-computed tomography (micro-CT) scanner to image and reconstruct three dimensional pore-scale images of five sandstones (Bentheimer, Berea, Clashach, Doddington and Stainton) and five complex carbonates (Ketton, Estaillades, Middle Eastern sample 3, Middle Eastern sample 5 and Indiana Limestone 1) at four different voxel resolutions (4.4 µm, 6.2 µm, 8.3 µm and 10.2 µm), scanning the same physical field of view. Implementing three phase segmentation (macro-pore phase, intermediate phase and grain phase) on pore-scale images helps to understand the importance of connected macro-porosity in the fluid flow for the samples studied. We then compute the petrophysical properties for all the samples using PN and LB simulations in order to study the influence of voxel resolution on petrophysical properties. We then introduce a numerical coarsening scheme which is used to coarsen a high voxel resolution image (4.4 µm) to lower resolutions (6.2 µm, 8.3 µm and 10.2 µm) and study the impact of coarsening data on macroscopic and multi-phase properties. Numerical coarsening of high resolution data is found to be superior to using a lower resolution scan because it avoids the problem of partial volume effects and reduces the scaling effect by preserving the pore-space properties influencing the transport properties. This is evidently compared in this study by predicting several pore network properties such as number of pores and throats, average pore and throat radius and coordination number for both scan based analysis and numerical coarsened data.     

Influence of permeability on hydrothermal circulation in the sediment-buried oceanic crust

1 Introduction Hydrothermal circulation is the key process of hydrothermal activity. Modern seafloor hydrothermal circulation can be divided into three parts: convective cells in the oceanic curst, interface between seafloor and ocean and hydrothermal plume. Hydrothermal convection in the crust is the dominant part of the whole seafloor hydrothermal circulation. The distribu-tion and nature of hydrothermal system in the oceanic crust are controlled by crust thermal structures and permeability …     

Image-based relative permeability upscaling from the pore scale

High resolution images acquired from X-ray μ-CT are able to map the internal structure of porous media on which multiphase flow properties can be computed. While the resolution of a few micrometers may be sufficient for capturing the pore space of many sandstones, most carbonates exhibit a large amount of microporosity; pores which are below the image resolution and are not resolved at specific resolution. Neglecting the effect of micropores on fluid flow and transport properties of these rocks can cause erroneous results in particular at partial saturations. Current image-based pore scale models typically only consider macropores for simulating fluid flow. In this paper, we quantify the effect of microporosity on the effective permeability of the wetting phase for heterogeneous model structures with varying amount of micro-to-macro porosity. A multi-scale numerical approach is proposed to couple an average effect of micropores with an explicit representation of macropores. The Brinkman equation is solved using a lattice Boltzmann formulation to facilitate the coupling of Darcy and Stokes equations in micropores and macropores, respectively. The results show good agreement between the fine scale solution and the results of the upscaled models in which microporous regions are homogenised. The paper analyses in particular the choice of the momentum sink parameter at low wetting phase saturations. It is shown that this parameter can be found using either a flux-based calculation of permeability of microporous regions or chosen purely on the basis of the effective permeability of these regions.     

Higher-order compositional modeling with Fickian diffusion in unstructured and anisotropic media

We present advances in compositional modeling of two-phase multi-component flow through highly complex porous media. Higher-order methods are used to approximate both mass transport and the velocity and pressure fields. We employ the Mixed Hybrid Finite Element (MHFE) method to simultaneously solve, to the same order, the pressure equation and Darcy's law for the velocity. The species balance equation is approximated by the discontinuous Galerkin (DG) approach, combined with a slope limiter. In this work we present an improved DG scheme where phase splitting is analyzed at all element vertices in the two-phase regions, rather than only as element averages. This approximation is higher-order than the commonly employed finite volume method and earlier DG approximations. The method reduces numerical dispersion, allowing for an accurate capture of shock fronts and lower dependence on mesh quality and orientation. Further new features are the extension to unstructured grids and support for arbitrary permeability tensors (allowing for both scalar heterogeneity, and shear anisotropy). The most important advancement in this work is the self-consistent modeling of two-phase multi-component Fickian diffusion. We present several numerical examples to illustrate the powerful features of our combined MHFE–dg method with respect to lower-order calculations, ranging from simple two component fluids to more challenging real problems regarding CO₂ injection into a vertical domain saturated with a multi-component petroleum fluid.     

泥质砂岩液相渗透率计算新方法

液相渗透率描述了岩石的渗流特性,是评价储层与预测油气产能的重要参数.液相渗透率是指盐水溶液在岩石孔隙中流动且与岩石孔隙表面黏土矿物发生物理化学作用时所测得的渗透率;液相渗透率的实验测量条件更加接近实际地层泥质砂岩的条件,使得液相渗透率更能反映地层条件下泥质砂岩的渗流特性;然而,现有的液相渗透率评价模型较少,且模型未能揭示液相渗透率与溶液矿化度之间的关系.基于此,开展了液相渗透模型推导与计算方法研究;文中首先将岩石等效为毛管束模型,推导建立了液相渗透率与比表面、喉道曲折度、总孔隙度、黏土束缚水孔隙度等参数之间的关系;其次,根据岩石物理体积模型,推导建立了黏土束缚水孔隙度与阳离子交换容量、溶液矿化度等参数的关系;最终,将黏土束缚水孔隙度引入液相渗透率计算公式,建立了基于总孔隙度、阳离子交换容量、溶液矿化度、比表面、喉道曲折度等参数的液相渗透率理论计算模型.液相渗透率计算模型与两组实验数据均表明,液相渗透率随阳离子交换容量的增大而降低,随溶液矿化度的增大而增大.然而,液相渗透率理论计算模型的实际应用中喉道曲折度、比表面等参数求取困难,直接利用理论模型计算液相渗透率受到限制.在分析液相渗透率与孔隙渗透率模型的基础上,建立了液相渗透率与空气渗透率之间的转换模型,形成了利用转化模型计算液相渗透率的新方法.为进一步验证液相渗透率与空气渗透率转化模型的准确性,基于两组实验数据,利用转换模型计算了液相渗透率;液相渗透率计算结果与岩心测量液相渗透率实验结果对比显示,液相渗透率计算结果与实际岩心测量结果吻合较好,文中建立的液相渗透率与空气渗透率转化模型合理可靠.     

A Study of Permeability Changes Due to Cold Fluid Circulation in Fractured Geothermal Reservoirs

Reservoir behavior due to injection and circulation of cold fluid is studied with a shear displacement model based on the distributed dislocation technique, in a poro‐thermoelastic environment. The approach is applied to a selected volume of Soultz geothermal reservoir at a depth range of 3600 to 3700 m. Permeability enhancement and geothermal potential of Soultz geothermal reservoir are assessed over a stimulation period of 3 months and a fluid circulation period of 14 years. This study—by shedding light onto another source of uncertainty—points toward a special role for the fracture surface asperities in predicting the shear dilation of fractures. It was also observed that thermal stress has a significant impact on changing the reservoir stress field. The effect of thermal stresses on reservoir behavior is more evident over longer circulation term as the rock matrix temperature is significantly lowered. Change in the fracture permeability due to the thermal stresses can also lead to the short circuiting between the injection and production wells which in turn decreases the produced fluid temperature significantly. The effect of thermal stress persists during the whole circulation period as it has significant impact on the continuous increase in the flow rate due to improved permeability over the circulation period. In the current study, taking into account the thermal stress resulted in a decrease of about 7 °C in predicted produced fluid temperature after 14 years of cold fluid circulation; a difference which notably influences the potential prediction of an enhanced geothermal system.