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Water‐rock interaction cannot be ignored for shale reservoirs with high‐salinity formation brine and complex rock composition, and stimulated by massive slick‐water fracturing treatment. However, there have been few studies on the flowback model fully coupled with different effects of water‐rock interaction. This paper presents the development of a coupled hydro‐chemical‐mechanical model for modeling water‐rock interaction in fractured shale during the post‐fracturing flowback period. The model considers distinguishing water‐rock interaction phenomena, that is, mineral dissolution, clay swelling and chemical osmosis, and accounts for multi‐phase flow in a fractured shale reservoir. The coupling and solution method and a numerical simulator were developed. Numerical simulation indicates that the swelling volume of clay minerals occupies the pores and leads to a decline in matrix porosity, while mineral dissolution increases both the matrix porosity and the solute concentration in the aqueous phase in matrix pores. Clay swelling mainly affects the shape of the porosity ratio profiles. The effect of mineral dissolution becomes increasingly stronger as flowback progresses. Mineral dissolution mainly affects the relative positions of the porosity ratio curves with the progress of flowback. The water‐rock interaction coupled flowback modeling and the numerical simulation results in this study quantify the effects of chemical osmosis, clay swelling and mineral dissolution. Results from this study provide new insights into the mechanisms of fracturing‐fluid flowback and value to flowback transient analysis. Key Points: A hydro‐chemical‐mechanical model involving mineral dissolution, clay swelling and osmosis to model water‐rock interaction is proposedMineral dissolution rates, clay swelling volumes, and the matrix porosity influenced by water‐rock interaction are studiedClay swelling and mineral dissolution mainly affect the shapes and relative positions of matrix porosity ratio curves, respectively [ABSTRACT FROM AUTHOR]

In recent years, higher-order geostatistical methods have been used for modeling of a wide variety of large-scale porous media, such as groundwater aquifers and oil reservoirs. Their popularity stems from their ability to account for qualitative data and the great flexibility that they offer for conditioning the models to hard (quantitative) data, which endow them with the capability for generating realistic realizations of porous formations with very complex channels, as well as features that are mainly a barrier to fluid flow. One group of such models consists of pattern-based methods that use a set of data points for generating stochastic realizations by which the large-scale structure and highly-connected features are reproduced accurately. The cross correlation-based simulation (CCSIM) algorithm, proposed previously by the authors, is a member of this group that has been shown to be capable of simulating multimillion cell models in a matter of a few CPU seconds. The method is, however, sensitive to pattern's specifications, such as boundaries and the number of replicates. In this paper the original CCSIM algorithm is reconsidered and two significant improvements are proposed for accurately reproducing large-scale patterns of heterogeneities in porous media. First, an effective boundary-correction method based on the graph theory is presented by which one identifies the optimal cutting path/surface for removing the patchiness and discontinuities in the realization of a porous medium. Next, a new pattern adjustment method is proposed that automatically transfers the features in a pattern to one that seamlessly matches the surrounding patterns. The original CCSIM algorithm is then combined with the two methods and is tested using various complex two- and three-dimensional examples. It should, however, be emphasized that the methods that we propose in this paper are applicable to other pattern-based geostatistical simulation methods. [ABSTRACT FROM AUTHOR]

A seepage face is a nonlinear dynamic boundary that strongly affects pressure head distributions, water table fluctuations, and flow patterns. Its handling in hydrological models, especially under complex conditions such as heterogeneity and coupled surface/subsurface flow, has not been extensively studied. In this paper, we compare the treatment of the seepage face as a static (Dirichlet) versus dynamic boundary condition, we assess its resolution under conditions of layered heterogeneity, we examine its interaction with a catchment outlet boundary, and we investigate the effects of surface/subsurface exchanges on seepage faces forming at the land surface. The analyses are carried out with an integrated catchment hydrological model. Numerical simulations are performed for a synthetic rectangular sloping aquifer and for an experimental hillslope from the Landscape Evolution Observatory. The results show that the static boundary condition is not always an adequate stand-in for a dynamic seepage face boundary condition, especially under conditions of high rainfall, steep slope, or heterogeneity; that hillslopes with layered heterogeneity give rise to multiple seepage faces that can be highly dynamic; that seepage face and outlet boundaries can coexist in an integrated hydrological model and both play an important role; and that seepage faces at the land surface are not always controlled by subsurface flow. The paper also presents a generalized algorithm for resolving seepage face outflow that handles heterogeneity in a simple way, is applicable to unstructured grids, and is shown experimentally to be equivalent to the treatment of atmospheric boundary conditions in subsurface flow models. [ABSTRACT FROM AUTHOR]

Training image-based geostatistical methods are increasingly popular in groundwater hydrology even if existing algorithms present limitations that often make real-world applications difficult. These limitations include a computational cost that can be prohibitive for high-resolution 3-D applications, the presence of visual artifacts in the model realizations, and a low variability between model realizations due to the limited pool of patterns available in a finite-size training image. In this paper, we address these issues by proposing an iterative patch-based algorithm which adapts a graph cuts methodology that is widely used in computer graphics. Our adapted graph cuts method optimally cuts patches of pixel values borrowed from the training image and assembles them successively, each time accounting for the information of previously stitched patches. The initial simulation result might display artifacts, which are identified as regions of high cost. These artifacts are reduced by iteratively placing new patches in high-cost regions. In contrast to most patch-based algorithms, the proposed scheme can also efficiently address point conditioning. An advantage of the method is that the cut process results in the creation of new patterns that are not present in the training image, thereby increasing pattern variability. To quantify this effect, a new measure of variability is developed, the merging index, quantifies the pattern variability in the realizations with respect to the training image. A series of sensitivity analyses demonstrates the stability of the proposed graph cuts approach, which produces satisfying simulations for a wide range of parameters values. Applications to 2-D and 3-D cases are compared to state-of-the-art multiple-point methods. The results show that the proposed approach obtains significant speedups and increases variability between realizations. Connectivity functions applied to 2-D models transport simulations in 3-D models are used to demonstrate that pattern continuity is preserved. [ABSTRACT FROM AUTHOR]

This paper presents the fundamental theory and laboratory test results on a new device that is deployed in boreholes in fractured rock aquifers to characterize vertical distributions of water and contaminant fluxes, aquifer hydraulic properties, and fracture network properties (e.g., active fracture density and orientation). The device, a fractured rock passive flux meter (FRPFM), consists of an inflatable core assembled with upper and lower packers that isolate the zone of interest from vertical gradients within the borehole. The outer layer of the core consists of an elastic fabric mesh equilibrated with a visible dye which is used to provide visual indications of active fractures and measures of fracture location, orientation, groundwater flux, and the direction of that flux. Beneath the outer layer is a permeable sorbent that is preloaded with known amounts of water soluble tracers which are eluted at rates proportional to groundwater flow. This sorbent also captures target contaminants present in intercepted groundwater. The mass of contaminant sorbed is used to quantify cumulative contaminant flux; whereas, the mass fractions of resident tracers lost are used to provide measures of water flux. In this paper, the FRPFM is bench tested over a range of fracture velocities (2-20 m/day) using a single fracture flow apparatus (fracture aperture = 0.5 mm). Test results show a discoloration in visible dye corresponding to the location of the active fracture. The geometry of the discoloration can be used to discern fracture orientation as well as direction and magnitude of flow in the fracture. Average contaminant fluxes were measured within 16% and water fluxes within 25% of known imposed fluxes. [ABSTRACT FROM AUTHOR]

Abstract: Hydraulic tomography (HT) is a recently developed technology for characterizing high‐resolution, site‐specific heterogeneity using hydraulic data (nd) from a series of cross‐hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (ny), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (ny × ny) in these models are prodigious for large‐scale 3‐D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (ny forward runs). Although employment of the adjoint method can reduce the cost to nd forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced‐Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen‐Loeve Expansion (KLE) truncated to nkl order, and it calculates the directional sensitivities (in the directions of nkl eigenvectors) to form the covariance and cross‐covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3‐D transient HT analysis of data from a highly heterogeneous field site. [ABSTRACT FROM AUTHOR]

Abstract: Relative permeability is a critical parameter characterizing multiphase flow in porous media and it is strongly dependent on the wettability. In many situations, the porous media are nonuniformly wet. To investigate the effect of wettability heterogeneity on relative permeability of two‐phase flow in porous media, a multi‐relaxation‐time color‐gradient lattice Boltzmann model is adopted to simulate oil/water two‐phase flow in porous media with different oil‐wet solid fractions. For the water phase, when the water saturation is high, the relative permeability of water increases with the increase of oil‐wet solid fraction under a constant water saturation. However, as the water saturation decreases to an intermediate value (about 0.4–0.7), the relative permeability of water in fractionally wet porous media could be lower than that in purely water‐wet porous media, meaning additional flow resistance exists in the fractionally wet porous media. For the oil phase, similar phenomenon is observed. This phenomenon is mainly caused by the wettability‐related microscale fluid distribution. According to both our simulation results and theoretical analysis, it is found that the relative permeability of two‐phase flow in porous media is strongly related to three parameters: the fluid saturation, the specific interfacial length of fluid, and the fluid tortuosity in the flow direction. The relationship between the relative permeability and these parameters under different capillary numbers is explored in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present a hydrochemical model that can be used to generate plausible karstic conduit networks that honor what is known about geology, hydrology, and topography of a karst system. To make the model applicable to a range of natural karst systems, we introduce a flexible and physically realistic flow boundary condition along the land surface. Moreover, whereas comparable existing speleogenesis models use an explicit reactive-transport scheme, we propose an implicit reactive-transport scheme to permit a coarser spatial discretization of the conduit cells. An application to a real karst system illustrates that the model can generate a realistic karstic network that reproduces observed hydrologic behavior in terms of current spring flow rates, regional hydraulic head field as well as average groundwater residence times. Our model provides a useful tool to generate ensembles of possible karstic conduit networks that may be used within a stochastic framework to analyze flow and transport prediction uncertainty associated with a lack of knowledge about network geometry. [ABSTRACT FROM AUTHOR]

This work advances a unified approach to process-based hydrologic modeling, which we term the 'Structure for Unifying Multiple Modeling Alternatives (SUMMA).' The modeling framework, introduced in the companion paper, uses a general set of conservation equations with flexibility in the choice of process parameterizations (closure relationships) and spatial architecture. This second paper specifies the model equations and their spatial approximations, describes the hydrologic and biophysical process parameterizations currently supported within the framework, and illustrates how the framework can be used in conjunction with multivariate observations to identify model improvements and future research and data needs. The case studies illustrate the use of SUMMA to select among competing modeling approaches based on both observed data and theoretical considerations. Specific examples of preferable modeling approaches include the use of physiological methods to estimate stomatal resistance, careful specification of the shape of the within-canopy and below-canopy wind profile, explicitly accounting for dust concentrations within the snowpack, and explicitly representing distributed lateral flow processes. Results also demonstrate that changes in parameter values can make as much or more difference to the model predictions than changes in the process representation. This emphasizes that improvements in model fidelity require a sagacious choice of both process parameterizations and model parameters. In conclusion, we envisage that SUMMA can facilitate ongoing model development efforts, the diagnosis and correction of model structural errors, and improved characterization of model uncertainty. [ABSTRACT FROM AUTHOR]

Parameter specification is an important source of uncertainty in large, complex geophysical models. These models generally have multiple model outputs that require multiobjective optimization algorithms. Although such algorithms have long been available, they usually require a large number of model runs and are therefore computationally expensive for large, complex dynamic models. In this paper, a multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) algorithm is introduced that aims to reduce computational cost while maintaining optimization effectiveness. Geophysical dynamic models usually have a prior parameterization scheme derived from the physical processes involved, and our goal is to improve all of the objectives by parameter calibration. In this study, we developed a method for directing the search processes toward the region that can improve all of the objectives simultaneously. We tested the MO-ASMO algorithm against NSGA-II and SUMO with 13 test functions and a land surface model - the Common Land Model (CoLM). The results demonstrated the effectiveness and efficiency of MO-ASMO. [ABSTRACT FROM AUTHOR]