Evaluation of an upscaled model for DNAPL dissolution kinetics in heterogeneous aquifers

Estimates of contaminant fluxes from DNAPL sources as a function of time and DNAPL mass reduction are important to assess the long-term sustainability and costs of monitored natural attenuation and to determine the benefits of partial source removal. We investigate the accuracy of the upscaled mass transfer function (MTF) proposed by Parker and Park [Parker JC, Park E. Modeling field-scale dense nonaqueous phase liquid dissolution kinetics in heterogeneous aquifers. WRR 2004;40:W05109] to describe field-scale dissolved phase fluxes from DNAPL sources for a range of scenarios generated using high-resolution 3-D numerical simulations of DNAPL infiltration and long-term dissolved phase transport. The results indicate the upscaled MTF is capable of accurately describing field-scale DNAPL dissolution rates as a function of time. For finger-dominated source regions, an empirical mass depletion exponent in the MTF takes on values greater than one which results in predicted mass flux rates that decrease continuously with diminishing DNAPL mass over time. Lens-dominated regions exhibit depletion exponents less than one, which results in more step-function like mass flux versus time behavior. Mass fluxes from DNAPL sources exhibiting both lens- and finger-dominated subregions were less accurately described by the simple MTF, but were well described by a dual-continuum model of the same form for each subregion. The practicality of calibrating a dual-continuum model will likely depend on the feasibility of obtaining spatially resolved field measurements of contaminant fluxes or concentrations associated with the subregions using multilevel sampling or some other means.     

Effect of NAPL exposure on the wettability and two‐phase flow in a single rock fracture

Surface‐wetting properties are an important cause of changing the groundwater and two‐phase fluid flows. Various factors affecting the surface wettability were investigated in a parallel‐walled glass fracture with non‐aqueous phase liquid (NAPL) (gasoline, diesel, trichloroethylene, and creosote) wetted surfaces. First, the effect of the duration of NAPL exposure on wettability change was considered at pre‐wet fracture surfaces using the various NAPL species, and the result showed that the surface became hydrophobic after the exposure time of NAPL exceeded 2000 min. Second, the initial wetting state of the surface affected the timing when the wettability change begins as well as the extent of the wettability change in an NAPL‐wetted rock fractures. Under the dry condition, the wettability change was completed within a very short time of exposure to NAPL (~5 min), and then it finally reached the intermediate and weakly NAPL wetting (contact angle of 118°). Under the pre‐wet condition, a relatively long time of exposure (~5000 min) was needed to observe the obvious change of the surface wettability, which was changed up to strongly NAPL wetting (contact angle of 142°). Third, the wettability changed by NAPL exposure was stable and maintained for a long time, regardless of water flushing rate and temperature. Finally, the wettability change by the exposure of NAPL on parallel fracture surfaces was evaluated at various groundwater flow velocities. Result showed that groundwater flow velocity has an important impact upon measured contact angle. Although fracture surfaces were exposed to NAPL at the low groundwater flow velocity, the wettability was not changed from hydrophilic to hydrophobic when the contact time between NAPL and mineral surfaces was not sufficient owing to the pulse‐type movement of NAPL. This implies that the variation of exposure pattern due to groundwater flow on the wettability change can be an important factor affecting the wettability change of fracture surface and migration behaviour at natural fractured rock aquifers in case of NAPL spill. Copyright © 2015 John Wiley & Sons, Ltd.     

Effect of NAPL film stability on the dissolution of residual wetting NAPL in porous media: A pore-scale modeling study

Wettability profoundly affects not only the initial distribution of residual NAPL contaminants in natural soils, but also their subsequent dissolution in a flowing aqueous phase. Under conditions of preferential NAPL wettability, the residual NAPL phase is found within the smaller pores and in the form of continuous corner filaments and thick films on pore walls. Such films expose a much greater interfacial area for mass transfer than would be exposed by the same amount of non-wetting NAPL. Importantly, capillary and hydraulic continuity of NAPL filaments and thick films is essential for sustaining NAPL–water counterflow during the course of NAPL dissolution in flowing groundwater—a mechanism which maintains and even increases the interfacial area for mass transfer. Continued dissolution results in gradual thinning of the NAPL films, which may become unstable and rupture causing disconnection of the residual NAPL in the form of clusters. Using a pore network simulator, we demonstrate that NAPL film instability drastically modifies the microscopic configuration of residual NAPL, and hence the local hydrodynamic conditions and interfacial area for mass transfer, with concomitant effects on macroscopically observable quantities, such as the aqueous effluent concentration and the fractional NAPL recovery with time. These results strongly suggest that the disjoining pressure of NAPL films may exert an important, and hitherto unaccounted, control on the dissolution behaviour of a residual NAPL phase in oil wet systems.     

Pore-scale simulation of entrapped non-aqueous phase liquid dissolution

We investigated the dissolution of non-aqueous phase liquids (NAPLs) in a three-dimensional random sphere-pack medium using a pore-scale modeling approach to advance fundamental understanding and connect rigorously to microscale processes. Residual NAPL distributions were generated using a morphological approach and the entrapped non-wetting phase was quantitatively characterized by calculating volume, orientation, interfacial area, and shape of isolated NAPL regions. With a detailed aqueous-phase flow field obtained by a multiple-relaxation time lattice Boltzmann approach, we solved the advective–diffusive equation in the pore space using a high-resolution, adaptive-stencil finite-volume scheme and an operator-splitting algorithm. We show good agreement between the mass transfer rates predicted in the computational approach and previously published experimental observations. The pore-scale simulations presented in this work provide the first three-dimensional comparison to the considerable experimental work that has been performed to derive constitutive relations to quantify mass transfer from a residual NAPL to a flowing aqueous phase.     

Comparison of theory and experiment for solute transport in weakly heterogeneous bimodal porous media

In this work, the influence of non-equilibrium effects on solute transport in a weakly heterogeneous medium is discussed. Three macro-scale models (upscaled via the volume averaging technique) are investigated: (i) the two-equation non-equilibrium model, (ii) the one-equation asymptotic model and (iii) the one-equation local equilibrium model. The relevance of each of these models to the experimental system conditions (duration of the pulse injection, dispersivity values…) is analyzed. The numerical results predicted by these macroscale models are compared directly with the experimental data (breakthrough curves). Our results suggest that the preasymptotic zone (for which a non-Fickian model is required) increases as the solute input pulse time decreases. Beyond this limit, the asymptotic regime is recovered. A comparison with the results issued from the stochastic theory for this regime is performed. Results predicted by both approaches (volume averaging method and stochastic analysis) are found to be consistent.     

Binary upscaling—the role of connectivity and a new formula

Although recognized as important, measures of connectivity (i.e. the existence of high-conductivity paths that increase flow and allow for early solute arrival) have not yet been incorporated into methods for upscaling hydraulic conductivities of porous media. We present and evaluate a binary upscaling formula that utilizes connectivity information. The upscaled hydraulic conductivity (K) of binary media is determined as a function of the proportions and conductivities of the two materials, the geometry of the inclusions, and the mean distance between them. The use of a phase interchange theorem renders the formula equally applicable to two-dimensional media with inclusions of low K and high K as compared with the matrix. The new upscaling formula is tested on two-dimensional binary random fields spanning a broad range of spatial correlation structures and conductivity contrasts. The computed effective conductivities are compared to what is obtained using self-consistent effective medium theory, the coated ellipsoids approximation, and to a streamline approach. It is shown that, although simple, the proposed formula performs better than available methods for binary upscaling. The use of connectivity information leads to significantly improved behavior close to the percolation threshold. The proposed upscaling formula depends exclusively on parameters that are obtainable from field investigations.     

The influence of biogeochemical conditions and level of model complexity when simulating cometabolic biodegradation in sorbent-water systems

Eighteen models with different levels of complexity for representing sorption, mass transfer, and biodegradation are used to simulate the biodegradation of toluene (primary substrate) and TCE (cometabolic substrate). The simulations are conducted for hypothetical completely mixed systems of various scenarios with regard to sorbent, microbial composition, and solute concentrations. The purpose of the suite of simulations is to investigate the sensitivity of different modeling approaches in simulating the bio-attenuation of co-existing solutes in sorbent-water systems. The sensitivity of results to the modeling approach depends on the biogeochemical conditions of the system. For example, the results are insensitive to the type of sorption model in systems with low sorption strength and slow biodegradation rates, and insensitive to the biodegradation rate model if mass transfer controlled. Differences among model results are generally greater when evaluated in terms of total mass removal rather than aqueous phase concentration reduction. The fate of the cometabolite is more sensitive to the proper consideration of co-solute effects than is the fate of the primary substrate. For a given system, graphical comparison of a characteristic mass transfer rate coefficient (α_mt) versus a characteristic biodegradation rate coefficient (α_bio) provides an indication of how sensitivity to the different processes may be expected to change with time and can guide the selection of an appropriate level of model complexity.     

Impact of capillary hysteresis and trapping on vertically integrated models for CO2 storage

Vertically integrated models are frequently applied to study subsurface flow related to CO₂ storage scenarios in saline aquifers. In this paper, we study the impact of capillary-pressure hysteresis and CO₂ trapping on the integrated constitutive parameter functions. Our results show that for the initial drainage and a subsequent imbibition, trapping is the dominant contributor to hysteresis in integrated models. We also find that for advective processes like injection and plume migration in a sloped aquifer the correct treatment of the hysteretic nature of the capillary fringe is likely of secondary importance. However, for diffusive/dispersive processes such as a redistribution of the CO₂ plume due to buoyancy and capillary forces, the hysteretic nature of the capillary fringe may significantly impact the final distribution of the fluids and the timescale of the redistribution.     

Structure of residual oil as a function of wettability using pore-network modelling

In the water flooding of mixed-wet porous media, oil may drain down to relatively low residual oil saturations (S_or). Various studies have indicated that such low saturations can only be reached when oil layers in pore corners are included in the pore-scale modelling. These processes within a macroscopic porous medium can be modelled at the pore-scale by incorporating the fundamental physics of capillary dominated displacement within idealised pore network models. Recently, the authors have developed thermodynamic criteria for oil layer existence in pores with non-uniform wettability which takes as input geometrically and topologically representative networks, to calculate realistic S_or values for mixed-wet and oil-wet sandstones [16, 21]. This previous work is developed in this paper to include (i) the visualisation of the 3D structure of this residual oil, and (ii) a statistical analysis of this “residual/remaining” oil. Both the visualisation and the statistical analysis are done under a wide range of wettability conditions, which is reported for the first time in this paper.The structure of residual oil for strongly water wet systems is well known (where residual = remaining oil) and our model agrees with this but this structure changes radically for mixed wet systems (where residual ≠ remaining) and this has not yet been visualised experimentally. We find that for more water-wet systems high final residual oil saturations are reached at relatively small amounts of water injected and this oil is present in the pores as bulk oil. On the other hand, for more oil-wet systems we find a slow decrease of the amount of remaining oil with increasing amounts of injected water. During the process, the remaining connectivity of the oil phase is increasingly provided by oil layers only, hence the slow drainage. The final residual oil saturation, only reached in the theoretical limit of an infinite amount of injected water, is almost entirely contained in large number of (relatively low volume) oil layers, which are present in pores of most radius sizes.     

From slots to tubes: The influence of dimensionality on fracture dissolution models

We briefly review the models of fracture dissolution process, discussing the experimental and numerical evidence showing that this phenomenon is inherently two-dimensional and hence cannot be accurately described by one-dimensional models. The physical reason for this incompatibility is that a dissolution front in a single rock fracture is potentially unstable to small variations in local permeability, leading to spontaneous formation of dissolution channels in the rock. This leads to a dramatic increase of fissure opening rates, which must be taken into account not only in the estimation of karstification times but also in the assessment of ground subsidence, dam collapse or toxic seepage risks.     

Effects of wettability and pore-level displacement on hydrocarbon trapping

We use a three-dimensional mixed-wet random network model representing Berea sandstone to extend our previous work on relative permeability hysteresis during water-alternating-gas (WAG) injection cycles [Suicmez, VS, Piri, M, Blunt, MJ, 2007, Pore-scale simulation of water alternate gas injection, Transport Porous Med 66(3), 259–86]. We compute the trapped hydrocarbon saturation for tertiary water-flooding, which is water injection into different initial gas saturations, S_gi, established by secondary gas injection after primary drainage. Tertiary water-flooding is continued until all the gas and oil is trapped. We study four different wettability conditions: water-wet, weakly water-wet, weakly oil-wet and oil-wet. We demonstrate that the amounts of oil and gas that are trapped show surprising trends with wettability that cannot be captured using previously developed empirical trapping models. We show that the amount of oil that is trapped by water in the presence of gas increases as the medium becomes more oil-wet, which is opposite from that seen for two-phase flow. It is only through a careful analysis of displacement statistics and fluid configurations that these results can be explained. This illustrates the need to have detailed models of the displacement processes that represent the three-phase displacement physics as carefully as possible. Further work is needed to explore the full range of behavior as a function of wettability and displacement path.     

Direct simulations of two-phase flow on micro-CT images of porous media and upscaling of pore-scale forces

Pore-scale forces have a significant effect on the macroscopic behaviour of multiphase flow through porous media. This paper studies the effect of these forces using a new volume-of-fluid based finite volume method developed for simulating two-phase flow directly on micro-CT images of porous media. An analytical analysis of the relationship between the pore-scale forces and the Darcy-scale pressure drops is presented. We use this analysis to propose unambiguous definitions of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each phase, and then use them to obtain the relative permeability curves. We show that this definition is consistent with conventional laboratory/field measurements by comparing our predictions with experimental relative permeability. We present single and two-phase flow simulations for primary oil injection followed by water injection on a sandpack and a Berea sandstone. The two-phase flow simulations are presented at different capillary numbers which cover the transition from capillary fingering at low capillary numbers to a more viscous fingering displacement pattern at higher capillary numbers, and the effect of capillary number on the relative permeability curves is investigated. Overall, this paper presents a new finite volume-based methodology for the detailed analysis of two-phase flow directly on micro-CT images of porous media and upscaling of the results to the Darcy scale.     

三维竖向断层场地对地面运动的影响

实际工程场地中的断层通常具有三维尺寸,应进行三维分析。本文考虑均匀弹性半空间内存在不同长度、深度的三维断层,由下向上垂直入射一个脉冲波,主要采用三维时域显式有限元结合透射人工边界的方法及相应编写的三维显示有限元波动程序DSI3,计算断层附近地震地面运动的时程反应,研究含有三维断层场地地面运动的一些特点,并与自由场反应对比,以说明三维竖向断层对地震波传播的特点和对断层附近地面运动的影响。     

裂隙展布特征对EGS采热影响的理论数值模拟研究

增强型地热系统(EGS)储层的裂隙展布特征决定了热开采的效果.基于EGS储层压裂得到的裂隙网络呈现出较强的非均匀性,本文构建EGS平行多裂隙非均匀展布模型研究裂隙展布特征对EGS采热影响.为表征裂隙展布的非均匀性,创新地引入了优势流动比的概念.研究结果表明:在体积为500 m×600 m×600 m,初始温度200℃,均匀激发热储层7条裂隙展布,流量为30 kg/s时,储层产出温度可保持储层初始温度15年,并在热开采进行50年后仍能保持较高产出温度192.3℃,电功率为2.88～3.10 MW,电功率的降幅仅为7.1%.非均匀激发热储层的采热性能受到裂隙数量和裂隙展布特征的共同影响.产出温度与裂隙数量呈不严格的正相关性,并与优势裂隙比呈负相关性.非均匀压裂的热储层中,通过封堵优势裂隙或增强储层压裂使裂隙宽度均匀化,均可增强系统的采热性能.综合来看,裂隙数目越多,裂隙宽度分布越均匀,流体产出温度越高,采热效果越好.本文对EGS地热田的储层激发,和人工热储层的构建有一定的指导意义.     

竖向断层对场地地面运动的影响

本文采用二维显式有限元结合透射边界的数值方法,考虑均匀弹性半空间内存在着不同宽度及深度的断层,由下向上分别垂直和斜(30°)入射一个脉冲波,研究非发震断层地面运动的一些特点。通过计算断层内外地震地面运动传递函数的幅值谱,并与自由场反应对比,以说明竖向断层对地震波传播和附近地面运动的影响,在此基础上进一步对断层周边一般结构抗震设计是否要考虑断层影响提出了几点建议。     

含水层渗透性能变化对水位影响的数值模拟研究

应用有限差分法,对弹性孔隙介质在无水平应力作用情况下的充水过程和充水稳定后部分区域阻塞情况下水头调整过程进行了分析。研究结果显示:就含水层内某一点而言,其水头除与位置和含水层的边界条件有关外,还与它本身及其周围区域的压力传导系数有关;含水层不同程度的阻塞会引起给定点的水位变化,而且不同的阻塞范围对含水层的水头分布和给定点的水头变化有很大的影响。     

Upscaling hydraulic conductivity based on the topology of the sub-scale structure

The hydraulic conductivity of heterogeneous porous media depends on the distribution function and the geometry of local conductivities at the smaller scale. There are various approaches to estimate the effective conductivity K_eff at the larger scale based on information about the small scale heterogeneity. A critical geometric property in this ‘upscaling’ procedure is the spatial connectivity of the small-scale conductivities. We present an approach based on the Euler-number to quantify the topological properties of heterogeneous conductivity fields, and we derive two key parameters which are used to estimate K_eff. The required coefficients for the upscaling formula are obtained by regression based on numerical simulations of various heterogeneous fields. They are found to be generally valid for various different isotropic structures. The effective unsaturated conductivity function K_eff (ψ_m) could be predicted satisfactorily. We compare our approach with an alternative based on percolation theory and critical path analysis which yield the same type of topological parameters. An advantage of using the Euler-number in comparison to percolation theory is the fact that it can be obtained from local measurements without the need to analyze the entire structure. We found that for the heterogeneous field used in this study both methods are equivalent.     

Upscaling of CO2 vertical migration through a periodic layered porous medium: The capillary-free and capillary-dominant cases

We present an upscaled model for the vertical migration of a CO₂ plume through a vertical column filled with a periodic layered porous medium. This model may describe the vertical migration of a CO₂ plume in a perfectly layered horizontal aquifer. Capillarity and buoyancy are taken into account and semi-explicit upscaled flux functions are proposed in the two following cases: (i) capillarity is the main driving force and (ii) buoyancy is the only driving force. In both cases, we show that the upscaled buoyant flux is a bell-shaped function of the saturation, as in the case of a homogeneous porous medium. In the capillary-dominant case, we show that the upscaled buoyant flux is the harmonic mean of the buoyant fluxes in each layer. The upscaled saturation is governed by the continuity of the capillary pressure at the interface between layers. In the capillary-free case, the upscaled buoyant flux and upscaled saturation are determined by the flux continuity condition at the interface. As the flux is not continuous over the entire range of saturation, the upscaled saturation is only defined where continuity is verified, i.e. in two saturation domains. As a consequence, the upscaled buoyant flux is described by a piecewise continuous function. Two analytical approximations of this flux are proposed and this capillary-free upscaled model is validated for two cases of heterogeneity. Upscaled and cell averaged saturations are in good agreement. Furthermore, the proposed analytical upscaled fluxes provide satisfactory approximations as long as the saturation set at the inlet of the column is in a range where analytical and numerical upscaled fluxes are close.