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We present an experimental study of foam-flow characterization inside a 3D granular medium packed in a cell. The foam is formed by coinjecting a surfactant solution and gas inside a cell filled with silica grains. The porous medium is initially saturated with dodecane and water before the gas-surfactant coinjection. To simplify the interpretation of the measurements, a contrast matching methodology has been applied in order to obtain a two phase system regarding the scattering length density values. The combination of transmission and incoherent scattering allows us to estimate the volume fractions of each phase, whereas the coherent scattering is used to estimate the surface to volume ratio S/V related to water-oil and water-gas interfaces. Considering the evolution of S/V ratio, volume fractions and pressure difference, we infer some mechanisms of foam generation and transportation as well as oil removal.

The performance of bicontinuous microemulsions is usually assessed on the characteristics of the middle phase at equilibrium. However, applied to Enhanced Oil Recovery, such an evaluation would not be representative of the structure and composition of fluids in reservoir rocks. Studies on the properties of non-equilibrated microemulsions are still needed to better understand the formation of such complex systems, in particular to optimize input parameters of process simulation tools.For this purpose, we monitored the formation of a microemulsion from contact with the oil to equilibrium when no mixing or convection is provided. Non-destructive methods such as Nuclear Magnetic Resonance, Micro-Computed Tomography, Dynamic Light Scattering and Small Angle X-ray scattering were used to extract the compositions, phase thicknesses, dynamics and structures of the system over time.We found that the system gets structured into several layers over time that include the transient presence of an oriented semi-crystalline phase. The growth of the bicontinuous middle phase results from a progressive reorganization of the liquid crystal. The compositional and structural gradients, observed along the sample height, are correlated and linked to the corresponding structures of the phase diagram of the quaternary system. Equilibrium is reached after the total transfer of the liquid crystal into the bicontinuous phase.

International audience; We present a general novel technique to monitor saturation changes on small rock samples of only 15 mm in diameter and 20 mm in length for the purpose of assessing the kinetics of spontaneous imbibition processes. With a fully-3D imbibition configuration involving counter-current flows through all faces of the sample, the method is based on a NMR technique in which the sole oil phase present within the sample is monitored. The experimental method is fast for two reasons that are i) the possibility to perform accurate measurements on tiny samples, ii) the adoption of a 3D flow geometry. The kinetics of oil desaturation during spontaneous imbibition is analyzed with the help of an analytical 3D diffusion model, according to which the kinetics is proportional to the value of a "capillary" diffusion coefficient. For the purpose of demonstrating our methodology, we used this technique to compare the spontaneous imbibition of restored sandstone miniplugs from a sandstone reservoir, with and without alkali in the imbibing brine. The imbibition kinetics was quantified as capillary diffusion coefficient values. The studied case results revealed mixed impacts of alkali on the spontaneous imbibition kinetics, involving both a brine-oil interfacial tension change and a wettability alteration of the rock, the latter requiring further investigation beyond the scope of this article. List of symbols EOR Enhanced oil recovery IFT Interfacial tension [N/m] NMR Nuclear magnetic resonance D, 2r Diameter of the core (r: radius) [m] D c Capillary diffusion coefficient [m 2 /s] D e Effective molecular diffusion coefficient [m 2 /s] D m Molecular diffusion coefficient [m 2 /s] K Single-phase permeability [m²] k rw , k ro Relative permeabilities to water (w) and oil (o) L, 2l Length of the core (l: half length) [m]  w,  o Relative mobility for water (w) and oil (o) [Pa-1 .s-1 ]  w ,  o Viscosities of water (w) and oil (o) [Pa.s] Pc Capillary pressure [Pa]  Porosity of the core S w , S o Water (w) and oil (o) saturation S w *, S o * Scaled water (w) and oil (o) saturation (cf eq (3)) S wi , S oi Initial water (w) and oil (o) saturation S of Final oil saturation T 2 Transverse relaxation time [s] V Bulk volume of the sample [m 3 ] V p Porous volume [m 3 ] V o Oil volume in the core [m 3 ] V oi Initial oil volume in the core [m 3 ] ACKNOWLEDGEMENTS We thank OMV for allowing us to publish the results. Wolfgang Hujer is also acknowledged for providing laboratory data and rock description.

Applied to Enhanced Oil Recovery, microemulsions are valuable systems for extracting the crude oil trapped by capillary forces in the porous reservoir rocks. The performances of the injected formulations are often assessed by quantifying oil composition in model systems that contain relatively high amount of surfactant/co-surfactant. Recently, the question of representativity of such systems was raised because kinetics aspects and complexity of crude were neglected in model systems and are likely to impact the process efficiency. The current quantification techniques limit the characterization of representative model systems as they are destructive, time consuming and not often applicable to dark or opaque systems. In the original aim to provide a quantitative kinetic study of such microemulsions, we propose a high resolution T

The sinuosity of a porous microstructure may be quantified by geometric tortuosity characterization, namely the ratio of geodesic and euclidean distances. The assessment of geometric tortuosity, among other descriptors, is of importance for rigorous characterization of complex materials. This paper proposes a new way of calculation, based on a graph structure, of the topological descriptor M-tortuosity introduced in [3]. The original M-tortuosity descriptor is based on a geodesic distance computation algorithm. A pore network partition [7] method is used to extract pores and construct a graph from the void of a porous microstructure. Through this scheme, pores are the nodes, distances between pores are the arcs between nodes and the goal boils down to the determination of the shortest paths between nodes. Solving this on a graph requires a tree search formulation of the problem. Our results have shown a drastic time complexity decrease while preserving good agreement with the original results. The added value of our method consists in its simplicity of implementation and its reduced execution time.

Digital twins of materials allow to achieve accurate predictions that help creating novel and tailor-made materials with higher standards. In this paper, we are interested in the characterization of porous media. Our attention is drawn to develop a method to describe accurately the pore network microstructure of porous materials as presented in [7]. This work proposes an efficient algorithm based on the distance transform method [12] which is a widely used method in image processing. The followed approach suggests that a distance transform map, obtained from a microstructure image, passes through different steps. Starting from local maxima extraction and filtering operation, to end up with another distance transform with source propagation. We illustrate our algorithm with the well-known Pore Network Model of the literature [13], which supposes that the pore structure is either a network of connected cylinders or cylinders and spheres. Our approach is also applied on multi-scale Boolean random models modelling complex porous media microstructures [11]. The porous media morphological characteristics extracted could be used to simulate complex phenomena as the physisorption isotherms or other experimental techniques.

International audience; In this work, we studied experimentally and numerically the pressure–flow rate relationship for yield stress fluids in porous media. We developed and validated 3D numerical simulations of the velocity field via a lattice Boltzmann method based on the TRT scheme, and a specific experimental setup allowing yield stress fluids to flow in a closed-loop system to obtain stable rheological properties over a wide range of flow rates (4 decades). The porous medium studied experimentally is a sandstone. The flow properties were also simulated on a regular sphere packing and a random sphere packing as well as on a 3D geometry of a sandstone obtained by x-ray tomography. These different geometries allow highlighting the role of the heterogeneity of the pore structure on the flow properties. All results are expressed as the flow rate ˜Q versus the difference of the pressure gradient to the critical pressure (Δ˜P−Δ˜Pc); Pc defines the pressure below which there is no flow. We observed both numerically and experimentally three specific scaling regimes, already identified by Talon and Bauer [Eur. Phys. J. E 36, 139 (2013)] for a Bingham fluid in 2D porous media. We also evidenced the existence of two critical pressures: the “true” critical pressure ˜Pc defined as the pressure below which there is no flow and the “pseudo” critical pressure threshold ˜P∞c determined by fitting the data in the high-flow-rate regime. We show that the “true” critical pressure is always lower than the “pseudo” one in heterogeneous porous media and can be equal only in the case of regular porous structures. We explain these observations using an energy minimization principle.

We study non-inertial flows of single-phase yield stress fluids along uneven/rough-walled channels, e.g. approximating a fracture, with two main objectives. First, we re-examine the usual approaches to providing a (nonlinear) Darcy-type flow law and show that significant errors arise due to self-selection of the flowing region/fouling of the walls. This is a new type of non-Darcy effect not previously explored in depth. Second, we study the details of flow as the limiting pressure gradient is approached, deriving approximate expressions for the limiting pressure gradient valid over a range of different geometries. Our approach is computational, solving the two-dimensional Stokes problem along the fracture, then upscaling. The computations also reveal interesting features of the flow for more complex fracture geometries, providing hints about how to extend Darcy-type approaches effectively.

We propose a deuterium diffusion tracer approach to measure diffusion coefficient in the case of very short NMR relaxation times, too short for NMR pulsed field gradient sequences (T1 or T2 below 1 ms). We also treat the case of porous media containing metallic fibers (such as reinforced concrete) strongly disturbing the magnetic field, and the case of inhomogeneous porous media containing large non porous granulates. For the latter, we propose a hollow geometry maximizing the investigated volume and minimizing the experimental time. The method is a 3D diffusion technique in which samples are immersed in deuterium and the water content inside the sample is monitored as a function of time. Water diffusing outside the sample with very long relaxation times can be subtracted either from T2 relaxation time distribution or not polarizing these components using a short repeat delay. Using analytical formulations describing the concentration of a tracer diffusing out of a cylinder or a hollow cylinder, we can calculate the corresponding pore diffusion coefficient.

The sustained lower oil price for the last three years has shifted tight oil industry interest from an intensive drilling and completion based approach to more cost effective methods aimed at maximizing rates and ultimate recovery from existing wells. In that framework, application of conventional EOR methods to unconventional tight oil well has gained momentum in the recent period, with theoretical and experimental evaluation of approaches ranking from water and CO2 flooding to huff'n puff with chemicals. For that purpose, usual EOR experiments used for conventional rock cannot always be applied due to the extremely low volumes and permeability of tight reservoir rocks. This can lead to inaccurate results or extremely long experimental times. Here, we present a novel method for rapidly evaluating oil production by EOR methods in micro-Darcy permeability reservoir rock, and apply it to evaluate various chemical EOR approaches for unconventional tight oil wells. Our method relies on a fast screening and a continuous NMR monitoring of fluid saturations during imbibition experiments at reservoir temperature in miniaturized plugs. This permits to evaluate oil and water saturations in the rock samples as a function of time without having to interrupt the experiment for carrying out measurements. We validate this method by evaluating recovery from 10 μD sandstones and carbonates during imbibition of LowIFT formulations with various chemical additives. Despite the extremely low permeability, oil production from plugs using various chemicals can be evaluated and compared in less than 72 hours. Our new protocol shall be of interest to all laboratories trying to adapt EOR techniques to unconventional reservoirs, by permitting a real-time accurate and quantitative evaluation of various EOR options. In addition, the data we generated using various chemical EOR techniques support the interest of using low-IFT inspired chemical EOR methods to improve the ultimate recovery from tight reservoirs.

International audience; Spontaneous imbibition processes can play an important role in oil production. It can be enhanced or influenced by wettability changes generated by properly designed chemicals or by the natural surfactants resulting from reactive crude oils in the presence of alkaline solutions. The reaction of basic salts with some components of oil can, indeed, lead to the formation of natural soaps that reduces the interfacial tension between oil and brine. The latter scenario is studied herein on samples and oil from the St Ulrich oil field in the Vienna basin. To that end, spontaneous imbibition experiments were performed with two brines differing by the absence or presence of alkali. We first present a general novel technique to monitor saturation changes on small rock samples for the purpose of assessing the efficiency of a given recovery process. Samples of only 15 mm in diameter and 20 mm in length and set at irreducible saturation were fully immersed in the solution of interest, and the evolution of the samples' saturation with time was monitored thanks to a dedicated NMR technique involving the quantification of the sole oil phase present within the sample. A fully-3D imbibition configuration was adopted, involving counter-current flows through all faces of the sample. The experimental method is fast for two reasons: (i) the kinetics of capillary imbibition process is proportional to the square of sample size, i.e. very rapid if accurate measurements can be acquired on tiny samples, (ii) the present 3D situation also involves faster kinetics than the 1D configuration often used. The NMR technique was crucial to achieve such conditions that cannot be satisfied with conventional volumetric methods. The kinetics of oil desaturation during spontaneous imbibition is interpreted with the help of an analytical 3D diffusion model. For the alkaline solution, the diffusion coefficient is reduced by a factor of only two compared to the non-alkaline brine, although the interfacial tension between the oil and the imbibing solution is reduced by a factor of 10. Hence, a wettability change to a more water wet state has to be assumed when the alkaline solution replaces the non-alkaline solution in the imbibition process. However, no significant impact on the final saturation was observed.

This paper presents a plasticity/damage formulation in the context of the physically based micro-continuum theory for multiphase materials described in a companion paper (see Vernerey, A physically-based micro-continuum theory, Mech. Adv. Mater. Struct., 2012). Based on a micro-structurally motivated decomposition of the deformation, the presented inelastic formulation is capable of characterizing the independent plastic/damage processes occurring in different phases (such as fiber or inclusions) and predicting the overall material behavior. The inelastic constitutive relation can thus be cast in a simple, physically motivated form, compared to conventional models. Such a formulation is thus very attractive for establishing a link between materials structure and properties. To illustrate the presented framework, we apply the micro-continuum model to the tensile failure of fiber-reinforced composite and compare it to a “brute force” approach in which the microstructure is explicitly modeled. We show that the model captures accurately the evolution of various features that cannot be calculated with conventional methods such as the independent stress, strain, and damage in the matrix and fibers and the fiber/matrix interface. Moreover, the existence of a size effect during failure is accounted for correctly.

We present an experimental study of the flow of a liquid foam, composed of a monolayer of millimetric bubbles, forced to invade an inhomogeneous medium at a constant flow rate. To model the simplest heterogeneous fracture medium, we use a Hele-Shaw cell consisting of two glass plates separated by a millimetric gap, with a local constriction. This single defect localized in the middle of the cell reduces locally its gap thickness, and thus its local permeability. We investigate here the influence of the geometrical property of the defect, specifically its height, on the average steady-state flow of the foam. In the frame of the flowing foam, we can observe a clear recirculation around the obstacle, characterized by a quadrupolar velocity field with a negative wake downstream the obstacle, which intensity evolves systematically with the obstacle height.

In this article, we propose a simple model to understand the critical behavior of path opening during flow of a yield stress fluid in porous media as numerically observed by Chevalier and Talon (2015). This model can be mapped to the problem of a contact line moving in an heterogeneous field. Close to the critical point, this line presents an avalanche dynamic where the front advances by a succession of waiting time and large burst events. These burst events are then related to the non-flowing (i.e. unyielded) areas. Remarkably, the statistics of these areas reproduce the same properties as in the direct numerical simulations. Furthermore, even if our exponents seem to be close to the mean field universal exponents, we report an unusual bump in the distribution which depends on the disorder. Finally, we identify a scaling invariance of the cluster spatial shape that is well fit, to first order, by a self-affine parabola.

In this paper, we numerically investigate the statistical properties of the nonflowing areas of Bingham fluid in two-dimensional porous media. First, we demonstrate that the size probability distribution of the unyielded clusters follows a power-law decay with a large size cutoff. This cutoff is shown to diverge following a power law as the imposed pressure drop tends to a critical value. In addition, we observe that the exponents are almost identical for two different types of porous media. Finally, those scaling properties allow us to account for the quadratic relationship between the pressure gradient and velocity.

International audience; The present work addresses the problem of using Pulsed Field Gradient (PFG) experiments to measure velocity probability density functions and/or distributions in restricted flows, without being subjected to the blurring due to diffusive molecular motions. It especially focuses on two important classes of complex yield-stress fluids, i.e. water based colloidal suspensions or polymeric gels, and concentrated emulsions. Taking into account the many constraints owing to fluid diffusive properties, flow rate, hardware characteristics and pore size, it is found that the existence of suitable and optimised sequence parameters can be discussed in a graphical way. To do so, it also shown that Murday and Cotts formula describing diffusion inside emulsion droplets can be efficiently approximated by means of a set of asymptotic expressions. Different tuning regimes are identified for both kind of fluids, highlighting the influence of each of the various constraints on measuring possibilities. A method is given to build quantitative diagrams indicating pore sizes and flow rates allowing pure velocity assessment for a given fluid and Nuclear Magnetic Resonance (NMR) hardware. Measurements are found to be mainly constrained by fluid self-diffusivity and microstructure at low flow rates, and hardware characteristics at high flow rates. Although high gradient strengths can be made necessary to decrease achievable velocities and pore sizes in some specific cases, low gradient systems turn out suitable in many situations thanks to optimised sequence tuning. Due to their larger size, the latter also appear to offer the widest variety of workable experimental conditions. The use of these results is finally exemplified on the practical case of an emulsion flow in a model porous system. © 2014 Elsevier Inc. All rights reserved.

This study was aimed at the detection of potential differences in the osmoregulatory capacity of two cryptic species of gobies, Pomatoschistus microps (Kroyer, 1838) and P. marmoratus (Risso, 1810), that have different distributions in French Mediterranean lagoons characterised by different salinity regimes. Specimens of both species were experimentally exposed to different salinities, their salinity tolerance was evaluated and their blood osmolality was measured. Both species are strong osmoregulators over a wide range of salinities but P. microps showed higher performances of hyper-regulation at very low salinities (10 and 40 mosm/kg, i.e. freshwater 0.3 and 1.4) and of hypo-regulation at high salinities (1500 mosm/kg, 51). Only P. microps was able to tolerate freshwater exposure over 4 days. We conclude that the high osmoregulatory capacity found in P. microps is linked to its better survival at very low salinities and is a physiological requirement for living in areas such as the Mauguio lagoon where salinity is highly variable. In contrast, as osmoregulation of P. marmoratus is less efficient at extreme salinities, this species cannot colonise such environments and is restricted to habitats where salinity is more stable, such as the Thau lagoon.

International audience; We show that frustrated creep flows of yield stress fluids give rise to a boundary layer, which takes the form of a liquid region of uniform significant thickness separating two solid regions. In this boundary layer the shear rate is approximately constant for a given flow rate and the layer thickness varies extremely slowly with the flow rate.