A Direct Inverse Model to Determine Permeability Fields from Pressure and Flow Rate Measurements

The determination of the permeability field from pressure and flow rate measurements in wells is a key problem in reservoir engineering. This paper presents a Double Constraint method for inverse modeling that is an example of direct inverse modeling. The method is used with a standard block-centered finite difference method. With an a priori grid block permeability field as input, two forward runs are made: the first is constrained with the measured pressures; the second is constrained with the measured flow rates. We calculate the pressures in the grid block centers from the first run, while from the second run we calculate the fluxes through the faces between the grid blocks. Substitution of these pressures and fluxes into Darcy’s law then yields the transmissibilities at the faces and hence the permeabilities in the grid blocks. In this way the “hard” data (measured pressures and flow rates) are always honored while the “soft”, geological data can be incorporated at the discretion of the geologist. Using a synthetic example, we demonstrate the method and compare the results with another method: Ensemble Kalman Filtering. The two methods agree within the scope of their applicability. The Double Constraint method focuses initially on determining spatial distributions of the permeability field for single-phase, steady state flow. For history matching an extension is required to non-steady state, two-phase flow conditions, which is already possible with EnKF. We are currently investigating the possibility of combining the two methods, whereby the strengths of the two methods could be fully exploited.     

Simulated annealing technique in discrete fracture network inversion: optimizing the optimization

Simulated annealing (SA) has the capacity to handle complex problem of fracture heterogeneity. However, its applications to characterization and modeling of an actual discrete fracture network are limited. Borrowing the context of geothermal reservoirs (where extensive discrete fractures exist), this paper attempts to solve several key practical issues that persist in current models: objective function’s (OF’s) formulation, modification scheme, and stop criteria. The improvements are examined in a case study on an actual fracture outcrop, where results are compared with a current and advanced SA work.     

An Elastic Stress–Strain Relationship for Porous Rock Under Anisotropic Stress Conditions

A stress–strain relationship within porous rock under anisotropic stress conditions is required for modeling coupled hydromechanical processes associated with a number of practical applications. In this study, a three-dimensional stress–strain relationship is proposed for porous rock under elastic and anisotropic stress conditions. This relationship is a macroscopic-scale approximation that uses a natural-strain-based Hooke’s law to describe deformation within a fraction of pores and an engineering-strain-based Hooke’s law to describe deformation within the other part. This new relationship is evaluated using data from a number of uniaxial and triaxial tests published in the literature. Based on this new stress–strain relationship, we also develop constitutive relationships among stress, strain, and related stress-dependent hydraulic/mechanical properties (such as compressibility, shear modulus, and porosity). These relationships are demonstrated to be consistent with experimental observations.     

初始裂隙对岩溶水紊流形成的影响

岩溶地区地下发育着大量的溶洞和地下河管道,地下水流状态既有层流也有紊流,而紊流是溶洞管道形成的重要条件。紊流的形成受到岩石初始裂隙的影响,初始裂隙的张开度、分布、走向、迹长、密度等因素都影响着裂隙发育过程中水流状态的变化。通过对不同统计特征的初始裂隙网络进行水流和溶蚀的数值模拟发现,以张开度标准差反映的裂隙网络非均匀性越强,模拟紊流出现的时间就越早;主要裂隙的存在使裂隙网络的非均性增强,主要裂隙与水力梯度总方向的角度越小,紊流出现的时间就越早;当裂隙平均迹长过小时会导致裂隙连通性较差,影响裂隙水流和溶蚀作用;裂隙密度,尤其是主要裂隙密度,对岩溶发育的影响较大。相对于次要裂隙,如果主要裂隙密度偏小,紊流形成时间会大大增加,甚至很难形成紊流。当初始裂隙张开度小于0.001 cm,增大水力梯度仍没有紊流发生,岩溶几乎不发育。      

Embedded discontinuity finite element modeling of fluid flow in fractured porous media

In many geomaterials, particularly rocks and clays, permeability is greatly enhanced by the presence of fractures. Fracture sets create an overall permeability that is anisotropic, enhanced in the directions of the fractures. In modeling the fractures via a finite element method, for example, meshing around these fractures can become quite difficult and result in computationally intensive systems. In this article, we develop a relatively simple method for including the fractures within the elements. Flow through the bulk medium is assumed to be governed by Darcy’s law, and the flow on the fracture by a generalization of the law. This model is embedded in a finite element framework, with the fractures passing through the elements. In this formulation, elements with fractures are given an enhanced permeability in the direction of the fractures. With these enhancements, the material essentially becomes anisotropically more permeable in the direction of fracture sets.     

A new model for flow in shale-gas reservoirs including natural and hydraulic fractures

In this work, we construct a new coupled Multiscale/Discrete Fracture Model for compressible flow in a multiporosity shale gas reservoir containing networks of natural and hydraulic fractures. The geological formation is characterized by four distinct length scales and levels of porosity. The window of observation of the finest (nanoscale) portraits the nanopores within organic matter containing adsorbed gas. At the microscale, the medium is formed by two solid phases: organic, composed by kerogen aggregates, and inorganic (clay, quartz, calcite). Such phases are separated by the network of partially-saturated interparticle pores where microscopic free gas flow influenced by Knudsen effects along with gas diffusion in the immobile water phase occur simultaneously. The upscaling of the local flow to the mesoscale gives rise to a nonlinear homogenized pressure equation in the shale matrix which lies adjacent to the system of natural fractures. Homogenization of the coupled matrix/preexisting fractures to the macroscale leads to a microstructural model of dual porosity type. Such homogenized model is subsequently coupled with the hydrodynamics in the network of induced fractures which, in the context of the discrete fracture modeling, are treated as (n ? 1), (n = 2, 3) lower dimensional objects. In order to handle numerically the nonlinear interaction between the different flow equations, we adopt a superposition argument, firstly proposed by Arbogast (1996), in each iteration of a fixed-point algorithm. The resultant governing equations are discretized by the finite element method and numerical simulations of gas production in stratified arrangements of the fracture networks are presented to illustrate the potential of the multiscale approach.     

Experimental modeling of structure-forming deformations in rift zones of mid-ocean ridges

The modern methods of physical modeling of structure-forming deformations in extension zones of oceanic lithosphere are discussed; the methods differ in their experimental equipment, model material, and experimental techniques. The simulation performed with an elastic-ductile model has demonstrated that extension of a brittle lithospheric layer results in disruption of its continuity and in formation of a rift valley according to the mechanism of running fracture propagation. The modeling results provide insights into qualitative pattern of faulting and fracturing within a rift zone, specific features of rift segmentation, and development of various structural elements (axis bends, echelons of fractures, nontransform offsets, small and large overlaps, etc.) under various geodynamic conditions of spreading. The modeling has shown that origination and evolution of structures of various types depend on the lithosphere’s thickness beneath the rift axis; the width of the lithosphere’s heating zone; the spreading orientation; and, to a lesser degree, on the spreading rate. A relatively rectilinear rift broken into particular segments bounded by small-amplitude offsets with or without minor overlaps arises in the case of both a small width of the heating zone, closely related to the axial magma chamber, and a small thickness of the lithosphere (fast-spreading conditions). In the case of a wide heating zone caused by ascent of an asthenospheric wedge or a mantle plume, offsets of rift are more pronounced and deformations embrace a wider region. If, as a result, the thickness of the lithosphere increases, the rift will be less linear and the structural heterogeneity will become more contrasting. In addition to the thickness of the lithosphere, the angle between the rift zone and the extension axis also controls the rift configuration: the greater the angle, the more conspicuous the en echelon arrangement of fractures. For any spreading type, the propagating front of linear microfractures that disrupt the upper brittle layer of the lithosphere predates the origin of mesoscopic fractures and predetermines a general trend of the rift zone. This indicates that the fractures of various sizes propagate simultaneously.     

Scale dependence of mineral dissolution rates within single pores and fractures

The possibility that gradients in concentration may develop within single pores and fractures, potentially giving rise to scale-dependent mineral dissolution rates, was investigated with experimentally validated reactive transport modeling. Three important subsurface mineral phases that dissolve at widely different rates, calcite, plagioclase, and iron hydroxide, were considered. Two models for analyzing mineral dissolution kinetics within a single pore were developed: (1) a Poiseuille Flow model that applies laboratory-measured dissolution kinetics at the pore or fracture wall and couples this to a rigorous treatment of both advective and diffusive transport within the pore, and (2) a Well-Mixed Reactor model that assumes complete mixing within the pore, while maintaining the same reactive surface area, average flow rate, geometry, and multicomponent chemistry as the Poiseuille Flow model. For the case of a single fracture, a 1D Plug Flow Reactor model was also considered to quantify the effects of longitudinal versus transverse mixing. Excellent agreement was obtained between results from the Poiseuille Flow model and microfluidic laboratory experiments in which pH 4 and 5 solutions were flowed through a single 500 μm diameter by 4000 μm long cylindrical pore in calcite. The numerical modeling and time scale analysis indicated that rate discrepancies arise primarily where concentration gradients develop under two necessary conditions: (1) comparable rates of reaction and advective transport, and (2) incomplete mixing via molecular diffusion. For plagioclase and iron hydroxide, the scaling effects are negligible at the single pore and fracture scale because of their slow rates. In the case of calcite, where dissolution rates are rapid, scaling effects can develop at high flow rates from 0.1 to 1000 cm/s and for fracture lengths less than 1 cm. Under more normal flow conditions where flow is usually slower than 0.001 cm/s, however, mixing via molecular diffusion is effective in homogenizing the concentration field, thus eliminating any discrepancies between the Poiseuille Flow and the Well-Mixed Reactor model. The analysis suggests that concentration gradients are unlikely to develop within single pores and fractures under typical geological/hydrologic conditions, implying that the discrepancy between laboratory and field rates must be attributed to other factors.     

Interpreting amenities,envisioning the future: common ground and conflict in North Carolina’s rural coastal communities

This paper contributes to ongoing discussions about the implications of rural change and amenity migration for members of diverse rural communities. We engage with recent amenity migration and political ecology literature that focuses on social constructions of nature and landscapes, and how these constructions affect the attitudes and opinions of community members. We use our case study of a mail-based survey in Down East, North Carolina to suggest that the ways in which people conceptualize the particular ‘natures’ and landscapes of a place matters in terms of shaping people’s attitudes with respect to ongoing processes of change. We find that people’s opinions about environment, culture, and land use are often superficially similar but that when conflicts arise or particular actions are considered, substantial differences in people’s underlying conceptual frameworks are revealed. In particular we find that despite widespread shared appreciation of the environment and culture Down East, differing interpretations of these key terms lead to potential misunderstandings and land use planning challenges.     

Benford’s Law in Time Series Analysis of Seismic Clusters

Benford’s analysis is applied to the recurrence times of approximately 17,000 seismic events in different geological contexts of Italy over the last 6 years, including the Mt. Etna volcanic area and the seismic series associated with the destructive M _w 6.3, 2009 L’Aquila earthquake. A close conformity to Benford’s law and a power-law probability distribution for the recurrence times of consecutive events is found, as typical of random multiplicative processes. The application of Benford’s law to the recurrence event times in seismic series of specific seismogenic regions represents a novel approach, which enlarges the occurrence and relevance of Benford-like asymmetries, with implications on the physics of natural systems approaching a power law behaviour. Moreover, we propose that the shift from a close conformity of Benford’s law to Brownian dynamics, observed for time separations among non-consecutive events in the study seismic series, may be ruled by a periodical noise factor, such as the effects of Earth tides on seismicity tuning.     

Rank statistical analysis of nickel sulphide resources of the Norseman-Wiluna Greenstone Belt,Western Australia

Estimating the undiscovered mineral resources of a terrane is a challenging, yet essential, task in mineral exploration. We apply Zipf’s law rank statistical analysis to estimate the undiscovered nickel sulphide resources in the Norseman-Wiluna Greenstone Belt, Western Australia. The analysis suggests that about 3.0 to 10.0 Mt of nickel sulphide resources are yet to be discovered in this belt, compared to the currently known total nickel sulphide endowment of 10.8 Mt. This undiscovered nickel sulphide endowment is likely to be hosted by incompletely delineated deposits and undiscovered deposits in less explored komatiites in the belt. Using the more detailed data subset of the Kambalda domain, this study manipulates Zipf’s law to estimate the sizes of undiscovered deposits, in addition to the domain’s total nickel sulphide endowment estimate. Importantly, regression analysis shows that the gradient of the line of best fit through the logarithmic rank-size plot for the detailed Kambalda data subset is −1. This gradient, which is the key Zipf’s law constant k, has the value of −0.92 for the Norseman-Wiluna Greenstone Belt which is collectively less mature than the Kambalda domain. This result corroborates the use of k = −1 in Zipf’s law predictive analyses of mineral resources for deposit populations for which the value of k = −1 has not yet been attained due to exploration immaturity.     

Experimental Validation of Modified Barton’s Model for Rock Fractures

Among the constitutive models for rock fractures developed over the years, Barton’s empirical model has been widely used. Although Barton’s failure criterion predicts peak shear strength of rock fractures with acceptable precision, it has some limitations in estimating the peak shear displacement, post-peak shear strength, dilation, and surface degradation. The first author modified Barton’s original model in order to address these limitations. In this study, the modified Barton’s model (the peak shear displacement, the shear stress–displacement curve, and the dilation displacement) is validated by conducting a series of direct shear tests.     

Development of methods for constructing models for intra-year irregularity in the Earth’s rotation

The development of methods for the construction of stochastic, dynamical models for intra-year irregularity of the Earth’s rotation is considered. A correlational model based on harmonically additive and parametrically random, colored and broadband, gravitational-tidal perturbations from the Sun and Moon is developed. One-dimensional and multi-dimensional characteristic functions are found for the case of Gaussian and non-Gaussian colored and broadband fluctuations in the irregularity of the Earth’s rotation. Examples of computer modeling of the irregularity in the Earth’s rotation based on a priori and a posteriori IERS data are presented.     

Benford’s Law Applied to Hydrology Data—Results and Relevance to Other Geophysical Data

Benford’s Law gives the expected frequencies of the digits in tabulated data and asserts that the lower digits (1, 2, and 3) are expected to occur more frequently than the higher digits. This study tested whether the law applied to two large earth science data sets. The first test analyzed streamflow statistics and the finding was a close conformity to Benford’s Law. The second test analyzed the sizes of lakes and wetlands, and the finding was that the data did not conform to Benford’s Law. Further analysis showed that the lake and wetland data followed a power law. The expected digit frequencies for data following a power law were derived, and the lake data had a close fit to these expected digit frequencies. The use of Benford’s Law could serve as a quality check for streamflow data subsets, perhaps related to time or geographical area. Also, with the importance of lakes as essential components of the water cycle, either Benford’s Law or the expected digit frequencies of data following a power law could be used as an authenticity and validity check on future databases dealing with water bodies. We give several applications and avenues for future research, including an assessment of whether the digit frequencies of data could be used to derive the power law exponent, and whether the digit frequencies could be used to verify the range over which a power law applies. Our results indicate that data related to water bodies should conform to Benford’s Law and that nonconformity could be indicators of (a) an incomplete data set, (b) the sample not being representative of the population, (c) excessive rounding of the data, (d) data errors, inconsistencies, or anomalies, and/or (e) conformity to a power law with a large exponent.     

Investigation on the Characteristics of Pore Water Flow During CRS Consolidation Test

Several experimental methods have been proposed for consolidation test such as: constant loading rate, constant gradient and constant rate of strain (CRS). Unfortunately, there are no unique criteria for performing the CRS consolidation test. Also, there are considerable differences among the standards proposed for the test. In the present paper, authors have tried to find the reasons for differences among standards, by studying the basic assumptions made on the characteristics of the pore water flow during consolidation process. In the course of study, CRS consolidation tests were carried out under different strain rates on remolded samples. The results of the tests have indicated that the Darcy’s law is not valid throughout the CRS test and therefore, any consolidation equation based on Darcy’s law would not provide accurate results. The results of the current experiments also showed that with regard to the applied strain rates, there are three different flow regimes governing the process named as: pre-linear (non-Darcy flow), linear (Darcy flow) and post-linear (non-Darcy flow). Experimental results also showed that distinction between boundaries of linear and nonlinear flow is possible from the excess pore pressure developed during the tests.     

Kinematics of throughgoing fractures in jointed rocks

Throughgoing fractures play a major role in subsurface fluid flow yet the kinematics of their formation, which directly impact rock flow properties, are often difficult to establish. We investigate throughgoing fractures in the Monterey Formation of California that developed by the coalescence of pre-existing joints. At Lompoc Landing, throughgoing fractures fall into three main groups: linked, linked with aperture, and breccia zones. The segmented nature of their walls provides numerous piercing points to firmly establish the sense of displacement. Analysis of displacement vectors derived from piercing points demonstrates that the NW–SE trending throughgoing fractures, often interpreted as strike–slip faults, are in fact extensional structures in origin. We suggest that this method may be applied to throughgoing fractures that form by the same mechanism in other geologic settings. Establishing kinematics of throughgoing fractures will lead to a better understanding of their contribution to subsurface fluid flow.     

Constitutive Relationships for Elastic Deformation of Clay Rock: Data Analysis

Geological repositories have been considered a feasible option worldwide for storing high-level nuclear waste. Clay rock is one of the rock types under consideration for such purposes, because of its favorable features to prevent radionuclide transport from the repository. Coupled hydromechanical processes have an important impact on the performance of a clay repository, and establishing constitutive relationships for modeling such processes are essential. In this study, we propose several constitutive relationships for elastic deformation in indurated clay rocks based on three recently developed concepts. First, when applying Hooke’s law in clay rocks, true strain (rock volume change divided by the current rock volume), rather than engineering strain (rock volume change divided by unstressed rock volume), should be used, except when the degree of deformation is very small. In the latter case, the two strains will be practically identical. Second, because of its inherent heterogeneity, clay rock can be divided into two parts, a hard part and a soft part, with the hard part subject to a relatively small degree of deformation compared with the soft part. Third, for swelling rock like clay, effective stress needs to be generalized to include an additional term resulting from the swelling process. To evaluate our theoretical development, we analyze uniaxial test data for core samples of Opalinus clay and laboratory measurements of single fractures within macro-cracked Callovo-Oxfordian argillite samples subject to both confinement and water reduced swelling. The results from this evaluation indicate that our constitutive relationships can adequately represent the data and explain the related observations.     

Partially to fully saturated flow through smooth,clean, open fractures: qualitative experimental studies

Fractures are both rough and irregular but can be expressed by a simple model concept of two smooth parallel plates and the associated cubic law governing discharge through saturated fractures. However, in natural conditions and in the intermediate vadose zone, these assumptions are likely violated. This paper presents a qualitative experimental study investigating the cubic law under variable saturation in initially dry free-draining discrete fractures. The study comprised flow visualisation experiments conducted on transparent replicas of smooth parallel plates with inlet conditions of constant pressure and differing flow rates over both vertical and horizontal inclination. Flow conditions were altered to investigate the influence of intermittent and continuous influx scenarios. Findings from this research proved, for instance, that saturated laminar flow is not likely achieved, especially in nonhorizontal fractures. In vertical fractures, preferential flow occupies the minority of cross-sectional area despite the water supply. Movement of water through the fractured vadose zone therefore becomes a matter of the continuity principle, whereby water should theoretically be transported downward at significantly higher flow rates given the very low degree of water saturation. Current techniques that aim to quantify discrete fracture flow, notably at partial saturation, are questionable. Inspired by the results of this study, it is therefore hypothetically improbable to achieve saturation in vertical fractures under free-draining wetting conditions. It does become possible under extremely excessive water inflows or when not free-draining; however, the converse is not true, as a wet vertical fracture can be drained.     

Hydrogen penetration in water through porous medium: application to a radioactive waste storage site

Hydrogen penetration in water through porous medium was analyzed in the paper. A two-phase compositional model approach was considered. The first part of the work deals with the thermodynamic analysis of the hydrogen–water system. The thermodynamic model was calibrated using the experimental data of hydrogen solubility in water. The phase densities, viscosities and phase concentrations were presented in an analytical form. Moreover, the domain of validity of analytical laws—such as Henry’s, Raoult’s and Kelvin’s laws—for the estimation of phase properties was presented for the analyzed system. The second part deals with two-phase hydrodynamic behaviors. An analytical solution for the non-compressible flow was constructed. In general case, the influence of relative permeabilities on the flow regimes was analyzed numerically. The notion pseudo-saturation was introduced to define phase appearance. Actually, mobile gas created a time displaced front relatively slower than mobile gas flow. Diffusion becomes really important for low mobile gas case as the penetration accelerates for the large range of saturation. In contrast, the mass exchange phenomena have a small influence on the flow type. Thus, the regimes of hydrogen penetration in liquid were shown really sensitive to the relative permeability form.     

Modeling of rainfall-triggered shallow landslide

By integrating hydrological modeling with the infinite slope stability analysis, a rainfall-triggered shallow landslide model was developed by Iverson (Water Resour Res 36:1897-1910, 2000). In Iverson’s model, the infiltration capacity is assumed to be equivalent to the saturated hydraulic conductivity for finding pressure heads analytically. However, for general infiltration process, the infiltration capacity should vary with time during the period of rain, and the infiltration rate is significantly related to the variable infiltration capacity. To avoid the unrealistically high pressure heads, Iverson employed the beta-line correction by specifying that the simulated pressure heads cannot exceed those given by the beta line. In this study, the suitability of constant infiltration capacity together with the beta-line correction for hydrological modeling and landslide modeling of hillslope subjected to a rainfall is examined. By amending the boundary condition at ground surface of hillslope in Iverson’s model, the modified Iverson’s model with considering general infiltration process is developed to conduct this examination. The results show that the unrealistically high pressure heads from Iverson’s model occur due to the overestimation of infiltration rate induced from the assumption that the infiltration capacity is identical to the saturated hydraulic conductivity. Considering with the general infiltration process, the modified Iverson’s model gives acceptable results. In addition, even though the beta-line correction is applied, the Iverson’s model still produces greater simulated pressure heads and overestimates soil failure potential as compared with the modified Iverson’s model. Therefore, for assessing rainfall-triggered shallow landslide, the use of constant infiltration capacity together with the beta-line correction needs to be replaced by the consideration of general infiltration process.