Mixed formulation for an easy and robust numerical computation of sorptivity

Sorptivity is one of the most important parameters for the quantification of water infiltration into soils. Parlange (1975) proposed a specific formulation to derive sorptivity as a function of the soil water retention and hydraulic conductivity functions, as well as initial and final soil water contents. However, this formulation requires the integration of a function involving the hydraulic diffusivity, which may be undefined or present numerical difficulties that cause numerical misestimations. In this study, we propose a mixed formulation that scales sorptivity and splits the integrals into two parts: the first term involves the scaled degree of saturation while the second involves the scaled water pressure head. The new mixed formulation is shown to be robust and well-suited to any type of hydraulic functions - even with infinite hydraulic diffusivity or positive air-entry water pressure heads - and any boundary condition, including infinite initial water pressure head, h → −∞.

Hydraulic conductivity and diffusivity of an Oxisol cultivated with sugarcane fertigated with nitrogen and potassium

This study had the objective to evaluate the effect of irrigation and fertigation (NK) in the hydraulic conductivity and diffusivity of an Oxisol cultivated with sugarcane. The experimental design comprised randomized blocks in a 5 × 2 factorial scheme, with four replications. Treatments consisted of five levels of water replacement (100, 75, 50, 25 and 0%), with and without fertirrigation (NK). The planting of sugarcane, cultivar RB85-5453, was performed in a double row (W-shaped), 8 m long, with 1.80 m spacing between the double rows, the distance between the crops in the double row was 0.40 m, with a total area of 52,8 m2 in each paddock. For treatments with water, replacement (WR) a drip tube was placed in the ground at a depth of 0.20 m among the furrows of the double row. The drip tube (DRIPNET PC 16150) comprised a thin wall, 1.0 bar pressure, nominal discharge 1.0 L h-1, and 0.50 m spacing between drippers. Nitrogen was applied by fertirrigation at a dose of 100 Kg ha-1, at 30-day intervals, with 10 applications throughout the development of the sugarcane culture. Potassium fertilization was done partially, in 30% of the furrows, and the remaining part was treated with the irrigation water. Nitrogen and potassium were spread only in the treatment with 0% water replacement. Was evaluated hydraulic conductivity and diffusivity versus logarithmic pressure head, at a depth of 10 cm, using RETC software. The hydraulic diffusivity for water replacement of 25 and 50% with fertigation was 160.3 and 14.9 cm2 days-1 for the lower values of the logarithm of the pressure head.

Earthquake rupture properties in presence of thermal -pressurization of pore fluids

<p>Frictional heat generated in the fault core during earthquake rupture can raise the fluid pressure in the slip zone. Such increase of fluid pressure decreases the effective normal stress and thereby lowers the frictional strength of the fault. Therefore, thermal pressurization (TP) of pore fluid affects earthquake rupture processes including nucleation, propagation, and arrest. While the effects of pore pressure and fluid flow rate on dynamic weakening of faults are qualitatively understood, a detailed analysis of how TP affects  earthquake rupture parameters is needed to further deepen our understanding. </p><p>In this study, we investigate the role of two key TP parameters -- hydraulic diffusivity and shear-zone half-width -- earthquake dynamics and kinematic source properties (slip, peak slip-rate, rupture speed and rise time). We conduct  a suite of 3D dynamic rupture simulations applying a rate-and-state dependent friction law (with strong velocity weakening) coupled with thermal-pressurization of pore fluids. Simulations are carried out with the open source software SeisSol (www.seissol.org). The temporal evolution of rupture parameters over ~1’000 randomly  distributed on-fault receivers is statistically analyzed in terms of  mean variations of rupture parameters and correlations among rupture parameters. </p><p>Our simulations reveal that mean slip decreases with increasing hydraulic diffusivity, whereas mean peak slip-rate and rupture speed remain nearly constant. On the other hand, we observe only a slight decrease of mean slip with increasing shear-zone half-width, whereas mean peak slip-rate and rupture speed show clear decrease. The faster diffusion of pore pressure as hydraulic diffusivity increases promotes faster increase of the effective normal stress (and fault strength) behind the main rupture front, reducing the rise time and, therefore also affecting mean slip. An increase in shear-zone half- width represents a heat source distributed over larger fault normal distance causing a second-order effect on mean slip. Additionally, our simulations reveal correlations among rupture parameters: 1) slip has weak negative correlation with peak slip-rate and negligible correlation with rupture speed, but a positive correlation with rise time, 2) peak slip-rate has a strong positive correlation with rupture speed, but a strong negative correlation with rise time, 3) rupture speed has strong negative correlation with rise time. We observe little or negligible effects of variations of hydraulic diffusivity and shear-zone half- width on the correlations between rupture parameters. Overall, our study builds a fundamental understanding on how thermal pressurization of pore fluids affects dynamic and thereby kinematic earthquake rupture properties. Our findings are thus important for the earthquake source modeling community, and particularly, for assessing seismic hazard due to induced events in geo-reservoirs.</p>

Fault’s hydraulic diffusivity enhancement during injection induced fault reactivation: application of pore pressure diffusion inversions to laboratory injection experiments

SUMMARY In situ observations of fluid induced fault slip reactivation, as well as the analysis of induced seismicity have demonstrated the complexity of fluid–fault interactions under geological conditions. If fluid flow commonly reactivates faults in the form of aseismic slip or earthquakes, the resulting shear deformation causes strong modifications of the hydraulic properties. In this context, the relationship between slip front and fluid front on deep faults remains not fully understood. In this study, we investigate shear induced fluid flow and hydraulic diffusivity enhancement during fracture shearing in the laboratory. We use a series of injection reactivation tests, conducted under triaxial conditions, at different confining pressures (30, 60 and 95 MPa). The evolution of the fluid pressure along the saw-cut Andesite rock sample was monitored by two pressure sensors, at two opposite locations of the experimental fault. We estimate the history of the effective hydraulic diffusivity (and its associated uncertainties) governing the experimental fault, using the pressure history at two points on the fault. For this, we develop a deterministic and a probabilistic inversion procedure, which is able to reproduce the experimental data for a wide time range of the different experiments. In this study, the hydraulic diffusivity increases by one order of magnitude through the injection experiment. Hydraulic diffusivity changes are mainly governed by the reduction of the effective normal stress acting on the fault plane, with a second-order effect of the shear slip.

Induced Fault Reactivation and Hydraulic Diffusivity Enhancement : Insights from Pressure Diffusion Inversion in Laboratory Injection Tests

<p>Understanding how the permeability of a fault evolves during injection induced fault reactivation process is of great interest. The interactions between fluids and faults can be complex, as the confining pressure, effective stress and shear slip can affect the hydro-mechanical properties of the fault. The relationship between induced slip (reactivation) front and fluid front requires a better understanding of what controls hydraulic diffusivity as well. <br>In this study, we investigate shear induced fluid flow and permeability enhancement during fracture shearing. We used a series of laboratory injection reactivation tests on saw cut Andesite rock sample, under triaxial conditions, at different confining pressures (30, 60 and 95 MPa). The sample was connected to two pressure sensors, at two opposite locations of the fault, and equipped by strain gauges along strike. <br>We thus propose a numerical method, in the context of deterministic and probabilistic inversion approaches, that allows to estimate the temporal evolution of the effective hydraulic diffusivity (and its associated uncertainties) of an experimental fault throughout an injection test, using the pressure history at two points on the fault. <br>The numerical method was able to reproduce the experimental data for a wide time range of the different experiments. The hydraulic diffusivity was found to largely depend on the confining pressure and to increase (by one order of magnitude) throughout the injection experiment with the reduction of the mean effective stress acting along the fault plane. As well, the shear slip was observed to have an effect on the hydraulic diffusivity evolution. Instantaneous short term diffusivity enhancement accompanied slip events with large slip velocities, while long term increases accompanied slow slip events.</p>

Utilizing time-lapse hydraulic tomography to characterize the subsurface changes during methane and heat injection experiments

<p>Storage options for the energy storage in the subsurface includes the injection and storage of the “energy gas” (e.g., methane, hydrogen, compressed air) or thermal water into the underground formations. The heterogeneous structure of the storage formations could play a crucial role on the potential storage capacity, as well as the formulation of post treatment strategy. Hence, innovative techniques are required for characterizing the high-resolution formation heterogeneity and monitoring the gas or heat plume distribution in the subsurface after their injections.  Previous studies have shown that flow properties can vary as the gas or thermal water being injected into the aquifer. In this study, we propose a time-lapse hydraulic tomography (HT) method for characterizing the baseline hydraulic information and depicting the hydraulic property changes through a series of cross-well pumping tests. These tests were implemented in two pilot sites for methane and hot water injection tests at Wittstock, Germany. In order to generate a three-dimensional tomographical configuration, each pumping test was conducted at certain depth in a testing well, accompanying with multiple observation points at other wells. Depth-variant pumping and observation segments were formed by the double-packer system. As a result, we achieved 198 and 135 baseline drawdown curves for the methane and heat sites, respectively. For these measured data, we initially evaluated the effective hydraulic conductivity and specific storage of the aquifer according to certain analytical fitting methods. Furthermore, the vertical anisotropy of the hydraulic conductivity was also estimated. Sequentially, the fitted hydraulic parameters and analytical drawdown curves were utilized for correcting the well skin effects on hydraulic traveltimes and attenuations, as they have an unneglectable impact on them.  The corrected hydraulic traveltimes and attenuations were used for the inversion of the baseline hydraulic diffusivity and specific storage, respectively. Hydraulic conductivity distribution was then estimated through these two parameters. After we achieved the baseline information, HT was executed again by repeating the tomographical pumping tests after methane and hot water injections. The same data processing and inversion techniques were applied to the drawdown curves derived from the post-injection period. Inverted hydraulic diffusivity, specific storage, and hydraulic conductivity were compared to the baseline inversion results. Changes on these hydraulic properties could provide the information of the spatial distribution of methane or heat plume.</p>

Fluid flow along a rough fracture: impact on hydraulic diffusivity

<p>Fluid flow along fractures or in fractured rock is of great importance in Enhanced Geothermal System, since natural fracture networks generally affect the permeability of the reservoir rocks and therefore the hydraulic performance. The cubic law commonly estimates the permeability of a single fracture, which is only valid for the flow through two smooth parallel plates. In fact, the flow performance is strongly influenced by the aperture fluctuations, which are related to the fracture surface roughness, the fluid-rock interaction process, and the amount of flow exchange between the matrix and the fracture itself, etc.</p><p>To quantify the hydraulic performance and get the better knowledge of the more real fracture flow, we conduct numerical simulations of fluid flow in a fracture-rock system hosting one single rough fracture from laboratory to field scales. As an example, a 2D self-affine rough surface is synthetically generated (Candela et al, 2012), with two anisotropic roughness exponents H<sub>//</sub> = 0.6 along the slip direction, H<sub>perp</sub> = 0.8 in the perpendicular direction and a RMS amplitude of 0.1m at the 512m scale. Based on this surface generation, the opening geometry of a rough fracture is obtained as an input structure for finite element mesh generation. On one hand, we apply a lubrication approximation and limit the fracture opening to spatially variable 2D features with lower-dimensional element embedded in a saturated porous. On the other hand, we consider the full 3D features of the fracture opening as the space between two surfaces symmetrical about the mean fracture plane. The simulations are performed in the framework of the Mutiphysics Object Oriented Simulation Environment (MOOSE) combined with a MOOSE-based application GOLEM dedicated to modeling coupled Thermal-Hydraulic-Mechanical (THM) process in fractured geothermal reservoirs.</p><p>For the lubrication case, the mass balance equation for a saturated porous medium is described in terms of volumetric averaged mass conservation equations for the fluid phase, with Darcy’s law governing the momentum conservation equation. For the 3D fracture case, the incompressible Navier-Stokes equation is solved for the dynamic pressure and the velocity field inside the fracture only.</p><p>We compare the 2D and 3D cases and assess the effects of the nonlinear inertial term (<strong>u</strong>•∇)<strong>u</strong> in 3D case especially when the Reynolds number is high. The objective is to evaluate the large-scale hydraulic diffusivity of the fractured domain and its anisotropy owing to the strong contrast between the fluctuating fracture opening, and the homogeneous bulk porosity. The results show that the long-range aperture variations significantly affect the fluid flow, like the channeling effect and the hydraulic diffusivity anisotropy (i.e., along and perpendicular to the fault), which may have strong implications on the spatial distribution of fluid-induced seismic events in faulted reservoir.</p>

The Cause and Statistical Analysis of the River Valley Contractions at the Xiluodu Hydropower Station, China

The Xiluodu Dam is a concrete double-curvature arch dam with a crest elevation of 610 m and a height of 285.5 m. Since the impoundment of the Xiluodu reservoir, remarkable river valley contractions (RVCs) have been observed upstream and downstream of the reservoir, potentially threatening the safety of the dam. However, the cause of these RVCs remains unclear. Based on an analysis of hydrogeological conditions, the RVCs were determined a result of the expansion of the aquifer, within which the effective stress decreased due to an increase in the hydraulic head after reservoir impoundment. Referring to the hydrostatic seasonal time (HST) model, a groundwater hydrostatic seasonal (GHS) model is proposed for simulating and predicting the development of the RVCs. Unlike the HST model, the GHS model can provide information on aquifer hydraulic diffusivity. The calibration results illustrate that the GHS model can accurately fit the observed RVCs data. The calculation results revealed that the RVCs were mainly affected by the hydraulic head of the confined aquifer, and that seasonal effects gave rise to less than 10% of the total RVCs. Finally, the development of RVCs were predicted using the GHS model. The prediction results demonstrated that the RVCs of most monitoring lines in the Xiluodu reservoir would gradually approach a convergence condition after 6 February 2021. Until the deadline of the prediction on 1 May 2035, there is still one monitoring line that has not reached a convergence condition (whose RVCs are 157.6 mm, and where the RVC growth rate will decrease to 0.005 mm/d by that time). Considering the large amount of RVCs, we think the safety of the dam requires closer consideration.