The simulation of unstable invasion patterns in porous media flow is very challenging because small perturbations are amplified, so that slight differences in geometry or initial conditions result in significantly different invasion structures at later times. We present a detailed comparison of pore-scale simulations and experiments for unstable primary drainage in porous micromodels. The porous media consist of HeleShaw cells containing cylindrical obstacles. By means of soft lithography, we have constructed two experimental flow cells, with different degrees of heterogeneity in the grain size distribution. As the defending (wetting) fluid is the most viscous, the interface is destabilized by viscous forces, which promote the formation of preferential flow paths in the form of a branched finger structure. We model the experiments by solving the NavierStokes equations for mass and momentum conservation in the discretized pore space and employ the Volume of Fluid (VOF) method to track the evolution of the interface. We test different numerical models (a 2-D vertical integrated model and a full-3-D model) and different initial conditions, studying their impact on the simulated spatial distributions of the fluid phases. To assess the ability of the numerical model to reproduce unstable displacement, we compare several statistical and deterministic indicators. We demonstrate the impact of three main sources of error: (i) the uncertainty on the pore space geometry, (ii) the fact that the initial phase configuration cannot be known with an arbitrarily small accuracy, and (iii) three-dimensional effects. Although the unstable nature of the flow regime leads to different invasion structures due to small discrepancies between the experimental setup and the numerical model, a pore-by-pore comparison shows an overall satisfactory match between simulations and experiments. Moreover, all statistical indicators used to characterize the invasion structures are in excellent agreement. This validates the modeling approach, which can be used to complement experimental observations with information about quantities that are difficult or impossible to measure, such as the pressure and velocity fields in the two fluid phases.

[1] Accurate estimates of water losses by evaporation from shallow water tables are important for hydrological, agricultural, and climatic purposes. An experiment was conducted in a weighing lysimeter to characterize the diurnal dynamics of evaporation under natural conditions. Sampling revealed a completely dry surface sand layer after 5 days of evaporation. Its thickness was <1 cm early in the morning, increasing to reach 4-5 cm in the evening. This evidence points out fundamental limitations of the approaches that assume hydraulic connectivity from the water table up to the surface, as well as those that suppose monotonic drying when unsteady conditions prevail. The computed vapor phase diffusion rates from the apparent drying front based on Fick's law failed to reproduce the measured cumulative evaporation during the sampling day. We propose that two processes rule natural evaporation resulting from daily fluctuations of climatic variables: (i) evaporation of water, stored during nighttime due to redistribution and vapor condensation, directly into the atmosphere from the soil surface during the early morning hours, that could be simulated using a mass transfer approach and (ii) subsurface evaporation limited by Fickian diffusion, afterward. For the conditions prevailing during the sampling day, the amount of water stored at the vicinity of the soil surface was 0.3 mm and was depleted before 11:00. Combining evaporation from the surface before 11:00 and subsurface evaporation limited by Fickian diffusion after that time, the agreement between the estimated and measured cumulative evaporation was significantly improved.

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An Ac vely Heated Fiber Op cs (AHFO) method to es mate soil moisture is tested and the analysis technique improved on. The measurements were performed in a lysimeter uniformly packed with loam soil with variable water content profi les. In the fi rst meter of the soil profi le, 30 m of fi ber op c cable were installed in a 12 loops coil. The metal sheath armoring the fi ber cable was used as an electrical resistance heater to generate a heat pulse, and the soil response was monitored with a Distributed Temperature Sensing (DTS) system. We study the cooling following three con nuous heat pulses of 120 s at 36 W m −1 by means of longme approxima on of radial heat conduc on. The soil volumetric water contents were then inferred from the es mated thermal conduc vi es through a specifi cally calibrated model rela ng thermal conduc vity and volumetric water content. To use the pre-asympto c data we employed a me correc on that allowed the volumetric water content to be esmated with a precision of 0.01-0.035 (m 3 m −3 ). A comparison of the AHFO measurements with soil-moisture measurements obtained with calibrated capacitance-based probes gave good agreement for we er soils [discrepancy between the two methods was less than 0.04 (m 3 m −3 )]. In the shallow drier soils, the AHFO method underes mated the volumetric water content due to the longer me required for the temperature increment to become asympto c in less thermally conduc ve media [discrepancy between the two methods was larger than 0.1 (m 3 m −3 )]. The present work suggests that future applica ons of the AHFO method should include longer heat pulses, that longer hea ng and cooling events are analyzed, and, temperature increments ideally be measured with higher frequency.