Drainage in two-dimensional porous media: from capillary fingering to viscous flow

Characterization of dynamic interplay among different channels during immiscible displacement in porous media under different flow rates

Although immiscible displacement in porous media has been extensively studied, a more comprehensive analysis of the underlying dynamic behaviors is still necessary. In this work, we conducted experimental and theoretical analyses on the dynamic interplay among channels during immiscible displacement under varying flow rates. In a rock-structured microfluidic chip, we observed typical displacement patterns, including viscous fingering and capillary fingering, and analyzed their frontiers and efficiencies. Interestingly, we discovered a novel 'V'-shaped recovery rate pattern, which differs from the monotonic curve considered in previous research. The recovery rate reaches its lowest point at an injection rate of 1 μL/min (42%), increasing to 55 and 65% at rates of 16 and 0.1 μL/min, respectively. This increase may attribute to all-directional displacement at lower rates and multi-fingering displacement at higher rates, contrasting with primary fingering displacement observed at intermediate rates. Furthermore, we developed a dual-tube model to investigate the dynamic mechanisms between adjacent channels during the displacement process. At high injection rates, an increase in low-viscosity fluid rapidly reduces overall average viscosity of the channels, accelerating displacement while hindering the displacement process in neighboring channels. Conversely, at low injection rates, increased capillary forces at pore-throat junctions delay breakthrough in one channel, promoting simultaneous displacement in parallel channels and ensuring stability. These findings significantly enhance our understanding of the interplay between viscous and capillary forces in porous media during displacement processes.

Foam Generation Through a Single Pore with Rectangular Cross-Section: Hysteretic Behavior and Geometric Limitation of the Volume Fraction of Bubbles

We study foam production and destabilization through a flow-focusing geometry, namely a single pore of rectangular cross-section, by coinjecting gas and liquid at constant pressure, Pg, and constant flow rate, Qw. We observe that bubble production results from a Rayleigh-Plateau destabilization of the internal gas thread that occurs at the pore neck when its width becomes comparable to the height of the rectangular-section channel. Using a simple model and numerical approach, we (i) predict the shape of the gas jet and its stability range as a function of flow parameters and device geometry, which we successfully compare with our experimental results, and (ii) demonstrate the existence of a critical local pressure drop at the pore neck that determines whether or not a stable gas flow can form. We thus show that bubble foam generation exhibits hysteretic behavior due to hydrodynamic feedback and demonstrate that there is a maximum bubble volume fraction that the generated foam cannot exceed, the value of which is fixed by the geometry. Our results suggest that the foam collapse observed in porous media when the fractional gas flow becomes too large may result from hydrodynamic feedback inhibiting foam generation and not necessarily from coalescence between bubbles, as is usually claimed.

Liquid Repellence of Phobic Fiber Networks

The wetting behavior of fiber networks, which are central to many research and industrial applications, can be difficult to predict accurately owing to their complex, heterogeneous structure. The cylindrical pore model, widely used to interpret and predict the forced wetting of hydrophobic porous materials, often does not yield correct results when working with fibrous networks like paper substrates and non-woven fabrics. This is because these materials exhibit variation in pore size, fiber length, and fiber diameter, as well as a reentrant pore geometry. Quantitative prediction of the critical wetting resistance of hydrophobized papers to arbitrary entrant liquids requires a more sophisticated analytical approach that considers this unique fibrous structure and the effect of stochastic variations within the pore matrix. In this work, we directly measure the critical breakthrough pressure for different porous substrates across various wetting entrant liquids. To isolate the effects of the structure and stochastics on critical wetting behavior of fibrous networks, we analyze additional materials strategically chosen for their subsets of structural features. Ultimately, we formulate a method that demonstrates physical reasonableness, numerical accuracy, and the ability to elucidate the effects of pore size, pore size distribution, fiber diameter, fiber diameter distribution, surface wettability, and liquid surface tension on critical breakthrough pressure of liquids through hydrophobic fibrous networks.

Effect of Viscosity Action and Capillarity on Pore-Scale Oil–Water Flowing Behaviors in a Low-Permeability Sandstone Waterflood

Water flooding technology is an important measure to enhance oil recovery in oilfields. Understanding the pore-scale flow mechanism in the water flooding process is of great significance for the optimization of water flooding development schemes. Viscous action and capillarity are crucial factors in the determination of the oil recovery rate of water flooding. In this paper, a direct numerical simulation (DNS) method based on a Navier–Stokes equation and a volume of fluid (VOF) method is employed to investigate the dynamic behavior of the oil–water flow in the pore structure of a low-permeability sandstone reservoir in depth, and the influencing mechanism of viscous action and capillarity on the oil–water flow is explored. The results show that the inhomogeneity variation of viscous action resulted from the viscosity difference of oil and water, and the complex pore-scale oil–water two-phase flow dynamic behaviors exhibited by capillarity play a decisive role in determining the spatial sweep region and the final oil recovery rate. The larger the viscosity ratio is, the stronger the dynamic inhomogeneity will be as the displacement process proceeds, and the greater the difference in distribution of the volumetric flow rate in different channels, which will lead to the formation of a growing viscous fingering phenomenon, thus lowering the oil recovery rate. Under the same viscosity ratio, the absolute viscosity of the oil and water will also have an essential impact on the oil recovery rate by adjusting the relative importance between viscous action and capillarity. Capillarity is the direct cause of the rapid change of the flow velocity, the flow path diversion, and the formation of residual oil in the pore space. Furthermore, influenced by the wettability of the channel and the pore structure’s characteristics, the pore-scale behaviors of capillary force—including the capillary barrier induced by the abrupt change of pore channel positions, the inhibiting effect of capillary imbibition on the flow of parallel channels, and the blockage effect induced by the newly formed oil–water interface—play a vital role in determining the pore-scale oil–water flow dynamics, and influence the final oil recovery rate of the water flooding.

Asymmetric invasion in anisotropic porous media

We report and discuss, by means of pore-scale numerical simulations, the possibility of achieving a directional-dependent two-phase flow behavior during the process of invasion of a viscous fluid into anisotropic porous media with controlled design. By customising the pore-scale morphology and heterogeneities with the adoption of anisotropic triangular pillars distributed with quenched disorder, we observe a substantially different invasion dynamics according to the direction of fluid injection relative to the medium orientation, that is depending if the triangular pillars have their apex oriented (flow aligned) or opposed (flow opposing) to the main flow direction. Three flow regimes can be observed: (i) for low values of the ratio between the macroscopic pressure drop and the characteristic pore-scale capillary threshold, i.e., for Δp_{0}/p_{c}≤1, the fluid invasion dynamics is strongly impeded and the viscous fluid is unable to reach the outlet of the medium, irrespective of the direction of injection; (ii) for intermediate values, 1<Δp_{0}/p_{c}≤2, the viscous fluid reaches the outlet only when the triangular pillars are flow-opposing oriented; (iii) for larger values, i.e., for Δp_{0}/p_{c}>2, the outlet is again reached irrespective of the direction of injection. The porous medium anisotropy induces a lower effective resistance when the pillars are flow-opposing oriented, suppressing front roughening and capillary fingering. We thus argue that the invasion process occurs as long as the pressure drop is larger then the macroscopic capillary pressure determined by the front roughness, which in the case of flow-opposing pillars is halved. We present a simple approximated model, based on Darcy's assumptions, that links the macroscopic effective permeability with the directional-dependent front roughening, to predict the asymmetric invasion dynamics. This peculiar behavior opens up the possibility of fabrication of porous capillary valves to control the flow along certain specific directions.

Can unmixed complex forming polymer surfactant formulations be injected into oil reservoirs or aquifers without clogging them?

In the context of enhanced oil recovery or soil remediation, we study the role of interactions between polymers and surfactants on the injectivity of formulations containing mixtures of polymers and surfactants. We show that contrary to the first intuition, the formation of aggregates in polymers surfactants formulations is not necessarily a hindrance to the injection of these formulations into pores. It is important above all to compare the size of aggregates according to the applied shear rate and the pore size to find the formulations that may induce clogging. We highlight a new positive and unexpected phenomenon. The small aggregates that do not lead to clogging ensure the transport of the surfactant vesicles in the porous medium and limit the adsorption of the latter.

Modelling foam improved oil recovery: towards a formulation of pressure-driven growth with flow reversal

The pressure-driven growth model that describes the two-dimensional (2-D) propagation of a foam through an oil reservoir is considered as a model for surfactant-alternating-gas improved oil recovery. The model assumes a region of low mobility, finely textured foam at the foam front where injected gas meets liquid. The net pressure driving the foam is assumed to reduce suddenly at a specific time. Parts of the foam front, deep down near the bottom of the front, must then backtrack, reversing their flow direction. Equations for one-dimensional fractional flow, underlying 2-D pressure-driven growth, are solved via the method of characteristics. In a diagram of position versus time, the backtracking front has a complex double fan structure, with two distinct characteristic fans interacting. One of these characteristic fans is a reflection of a fan already present in forward flow mode. The second fan however only appears upon flow reversal. Both fans contribute to the flow's Darcy pressure drop, the balance of the pressure drop shifting over time from the first fan to the second. The implications for 2-D pressure-driven growth are that the foam front has even lower mobility in reverse flow mode than it had in the original forward flow case.

Pore-Scale Transport and Two-Phase Fluid Structures in Fibrous Porous Layers: Application to Fuel Cells and Beyond

We present pore-scale simulations of two-phase flows in a reconstructed fibrous porous layer. The three-dimensional microstructure of the material, a fuel cell gas diffusion layer, is acquired via X-ray computed tomography and used as input for lattice Boltzmann simulations. We perform a quantitative analysis of the multiphase pore-scale dynamics, and we identify the dominant fluid structures governing mass transport. The results show the existence of three different regimes of transport: a fast inertial dynamics at short times, characterised by a compact uniform front, a viscous-capillary regime at intermediate times, where liquid is transported along a gradually increasing number of preferential flow paths of the size of one–two pores, and a third regime at longer times, where liquid, after having reached the outlet, is exclusively flowing along such flow paths and the two-phase fluid structures are stabilised. We observe that the fibrous layer presents significant variations in its microscopic morphology, which have an important effect on the pore invasion dynamics, and counteract the stabilising viscous force. Liquid transport is indeed affected by the presence of microstructure-induced capillary pressures acting adversely to the flow, leading to capillary fingering transport mechanism and unstable front displacement, even in the absence of hydrophobic treatments of the porous material. We propose a macroscopic model based on an effective contact angle that mimics the effects of the such a dynamic capillary pressure. Finally, we underline the significance of the results for the optimal design of face masks in an effort to mitigate the current COVID-19 pandemic.

Studying key processes related to CO2 underground storage at the pore scale using high pressure micromodels

Micromodels experimentation for studying and understanding CO₂ geological storage mechanisms at the pore scale.

An Experimental Investigation of Flow Regimes in Imbibition and Drainage Using a Microfluidic Platform

Instabilities in immiscible displacement along fluid−fluid displacement fronts in porous media are undesirable in many natural and engineered displacement processes such as geological carbon sequestration and enhanced oil recovery. In this study, a series of immiscible displacement experiments are conducted using a microfluidic platform across a wide range of capillary numbers and viscosity ratios. The microfluidic device features a water-wet porous medium, which is a two-dimensional representation of a Berea sandstone. Data is captured using a high-resolution camera, enabling visualization of the entire domain, while being able to resolve features as small as 10 µm. The study reports a correlation between fractal dimensions of displacement fronts and displacement front patterns in the medium. Results are mapped on a two-dimensional parameter space of log M and log Ca, and stability diagrams proposed in literature for drainage processes are superimposed for comparison. Compared to recent reports in the literature, the results in this work suggest that transition regimes may constitute a slightly larger portion of the overall flow regime diagram. This two-phase immiscible displacement study helps elucidate macroscopic processes at the continuum scale and provides insights relevant to enhanced oil recovery processes and the design of engineered porous media such as exchange columns and membranes.

Pore-scale characteristics of multiphase flow in heterogeneous porous media using the lattice Boltzmann method

This study provides a pore-scale investigation of two-phase flow dynamics during primary drainage in a realistic heterogeneous rock sample. Using the lattice Boltzmann (LB) method, a series of three-dimensional (3D) immiscible displacement simulations are conducted and three typical flow patterns are identified and mapped on the capillary number (Ca)-viscosity ratio(M) phase diagram. We then investigate the effect of the viscosity ratio and capillary number on fluid saturation patterns and displacement stability in Tuscaloosa sandstone, which is taken from the Cranfield site. The dependence of the evolution of saturation, location of the displacement front, 3D displacement patterns and length of the center of mass of the invading fluid on the viscosity ratio and capillary number have been delineated. To gain a quantitative insight into the characteristics of the invasion morphology in 3D porous media, the fractal dimension D_f of the non-wetting phase displacement patterns during drainage has been computed for various viscosity ratios and capillary numbers. The logarithmic dependence of D_f on invading phase saturation appears to be the same for various capillary numbers and viscosity ratios and follows a universal relation.

The impact of drainage displacement patterns and Haines jumps on CO2 storage efficiency

Injection of CO₂ deep underground into porous rocks, such as saline aquifers, appears to be a promising tool for reducing CO₂ emissions and the consequent climate change. During this process CO₂ displaces brine from individual pores and the sequence in which this happens determines the efficiency with which the rock is filled with CO₂ at the large scale. At the pore scale, displacements are controlled by the balance of capillary, viscous and inertial forces. We simulate this process by a numerical technique, multi-GPU Lattice Boltzmann, using X-ray images of the rock pores. The simulations show the three types of fluid displacement patterns, at the larger scale, that have been previously observed in both experiments and simulations: viscous fingering, capillary fingering and stable displacement. Here we examine the impact of the patterns on storage efficiency and then focus on slow flows, where displacements at the pore scale typically happen by sudden jumps in the position of the interface between brine and CO₂, Haines jumps. During these jumps, the fluid in surrounding pores can rearrange in a way that prevent later displacements in nearby pores, potentially reducing the efficiency with which the CO₂ fills the total available volume in the rock.

Liquid-liquid displacement in slippery liquid-infused membranes (SLIMs)

Liquid-infused membranes inspired by slippery liquid-infused porous surfaces (SLIPS) have been recently introduced to membrane technology. The gating mechanism of these membranes is expected to give rise to anti-fouling properties and multi-phase transport capabilities. However, the long-term retention of the infusion liquid has not yet been explored. To address this issue, we investigate the retention of the infusion liquid in slippery liquid-infused membranes (SLIMs) via liquid-liquid displacement porometry (LLDP) experiments combined with microscopic observations of the displacement mechanism. Our results reveal that pores will be opened corresponding to the capillary pressure, leading to preferential flow pathways for water transport. The LLDP results further suggest the presence of liquid-lined pores in SLIM. This hypothesis is analyzed theoretically using an interfacial pore flow model. We find that the displacement patterns correspond to capillary fingering in immiscible displacement in porous media. The related physics regarding two-phase flow in porous media is used to confirm the permeation mechanism appearing in SLIMs. In order to experimentally observe liquid-liquid displacement, a microfluidic chip mimicking a porous medium is designed and a highly ramified structure with trapped infusion liquid is observed. The remaining infusion liquid is retained as pools, bridges and thin films around pillar structures in the chip, which further confirms liquid-lining. Fractal dimension analysis, along with evaluation of the fluid (non-wetting phase) saturation, further confirms that the fractal patterns correspond to capillary fingering, which is consistent with an invasion percolation with trapping (IPT) model.

The Role of Local Instabilities in Fluid Invasion into Permeable Media

Wettability is an important factor which controls the displacement of immiscible fluids in permeable media, with far reaching implications for storage of CO₂ in deep saline aquifers, fuel cells, oil recovery, and for the remediation of oil contaminated soils. Considering the paradigmatic case of random piles of spherical beads, fluid front morphologies emerging during slow immiscible displacement are investigated in real time by X-ray micro-tomography and quantitatively compared with model predictions. Controlled by the wettability of the bead matrix two distinct displacement patterns are found. A compact front morphology emerges if the invading fluid wets the beads while a fingered morphology is found for non-wetting invading fluids, causing the residual amount of defending fluid to differ by one order of magnitude. The corresponding crossover between these two regimes in terms of the advancing contact angle is governed by an interplay of wettability and pore geometry and can be predicted on the basis of a purely quasi-static consideration of local instabilities that control the progression of the invading interface.

Monitoring CO2 invasion processes at the pore scale using geological labs on chip

In order to investigate at the pore scale the mechanisms involved during CO2 injection in a water saturated pore network, a series of displacement experiments is reported using high pressure micromodels (geological labs on chip - GLoCs) working under real geological conditions (25 < T (°C) < 75 and 4.5 < p (MPa) < 8). The experiments were focused on the influence of three experimental parameters: (i) the p, T conditions, (ii) the injection flow rates and (iii) the pore network characteristics. By using on-chip optical characterization and imaging approaches, the CO2 saturation curves as a function of either time or the number of pore volume injected were determined. Three main mechanisms were observed during CO2 injection, namely, invasion, percolation and drying, which are discussed in this paper. Interestingly, besides conventional mechanisms, two counterintuitive situations were observed during the invasion and drying processes.

Large scale flow visualization and anemometry applied to lab-on-a-chip models of porous media

The following is a report on an experimental technique that allows one to quantify and map the velocity field with very high resolution and simple equipment in large 2D devices. Illumination through a grid is proposed to reinforce the contrast in the images and allow one to detect seeded particles that are pixel-sized or even smaller. The velocimetry technique that we have reported is based on the auto-correlation functions of the pixel intensity, which we have shown are directly related to the magnitude of the local average velocity. The characteristic time involved in the decorrelation of the signal is proportional to the tracer size and inversely proportional to the average velocity. We have reported on a detailed discussion about the optimization of relevant involved parameters, the spatial resolution and the accuracy of the method. The technique is then applied to a model porous medium made of a random channel network. We show that it is highly efficient to determine the magnitude of the flow in each of the channels of the network, opening the door to the fundamental study of the flows of complex fluids. The latter is illustrated with a yield stress fluid, in which the flow becomes highly heterogeneous at small flow rates.

Extra dissipation and flow uniformization due to elastic instabilities of shear-thinning polymer solutions in model porous media

We study flows of hydrolized polyacrylamide solutions in two dimensional porous media made using microfluidics, for which elastic effects are dominant. We focus on semi-dilute solutions (0.1%-0.4%) which exhibit a strong shear thinning behavior. We systematically measure the pressure drop and find that the effective permeability is dramatically higher than predicted when the Weissenberg number is greater than about 10. Observations of the streamlines of the flow reveal that this effect coincides with the onset of elastic instabilities. Moreover, and importantly for applications, we show using local measurements that the mean flow is modified: it appears to be more uniform at high Weissenberg number than for Newtonian fluids. These observations are compared and discussed using pore network simulations, which account for the effect of disorder and shear thinning on the flow properties.

CO2/water two-phase flow in a two-dimensional micromodel of heterogeneous pores and throats

Small capillary fingerings can be collapsed by capillary pressure in the beginning of displacement. Larger fingerings tend to form with developing displacement and cannot be overcome anymore.

Lattice Boltzmann simulations of supercritical CO2-water drainage displacement in porous media: CO2 saturation and displacement mechanism

CO2 geosequestration in deep aquifers requires the displacement of water (wetting phase) from the porous media by supercritical CO2 (nonwetting phase). However, the interfacial instabilities, such as viscous and capillary fingerings, develop during the drainage displacement. Moreover, the burstlike Haines jump often occurs under conditions of low capillary number. To study these interfacial instabilities, we performed lattice Boltzmann simulations of CO2-water drainage displacement in a 3D synthetic granular rock model at a fixed viscosity ratio and at various capillary numbers. The capillary numbers are varied by changing injection pressure, which induces changes in flow velocity. It was observed that the viscous fingering was dominant at high injection pressures, whereas the crossover of viscous and capillary fingerings was observed, accompanied by Haines jumps, at low injection pressures. The Haines jumps flowing forward caused a significant drop of CO2 saturation, whereas Haines jumps flowing backward caused an increase of CO2 saturation (per injection depth). We demonstrated that the pore-scale Haines jumps remarkably influenced the flow path and therefore equilibrium CO2 saturation in crossover domain, which is in turn related to the storage efficiency in the field-scale geosequestration. The results can improve our understandings of the storage efficiency by the effects of pore-scale displacement phenomena.

Two-phase flow in a chemically active porous medium

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the species, in a one-dimensional macroscopic description, identify the relevant dimensionless numbers, and provide simple models for capillary pressure and relative permeabilities, which are quantities of crucial importance when tackling multiphase flows in porous media. We set the domain of validity of our models and discuss the importance of viscous coupling terms in the extended Darcy's law. We investigate numerically the steady regime and demonstrate that the spatial transformation rate of the species along the reactor is non-monotonous, as testified by the existence of an inflection point in the volume fraction profiles. We obtain the scaling of the location of this inflection point with the dimensionless lengths of the problem. Eventually, we provide key elements for optimization of the reactor.

Experimental study of crossover from capillary to viscous fingering for supercritical CO2-water displacement in a homogeneous pore network

Carbon sequestration in saline aquifers involves displacing brine from the pore space by supercritical CO(2) (scCO(2)). The displacement process is considered unstable due to the unfavorable viscosity ratio between the invading scCO(2) and the resident brine. The mechanisms that affect scCO(2)-water displacement under reservoir conditions (41 °C, 9 MPa) were investigated in a homogeneous micromodel. A large range of injection rates, expressed as the dimensionless capillary number (Ca), was studied in two sets of experiments: discontinuous-rate injection, where the micromodel was saturated with water before each injection rate was imposed, and continuous-rate injection, where the rate was increased after quasi-steady conditions were reached for a certain rate. For the discontinuous-rate experiments, capillary fingering and viscous fingering are the dominant mechanisms for low (logCa ≤ -6.61) and high injection rates (logCa ≥ -5.21), respectively. Crossover from capillary to viscous fingering was observed for logCa = -5.91 to -5.21, resulting in a large decrease in scCO(2) saturation. The discontinuous-rate experimental results confirmed the decrease in nonwetting fluid saturation during crossover from capillary to viscous fingering predicted by numerical simulations by Lenormand et al. (J. Fluid Mech.1988, 189, 165-187). Capillary fingering was the dominant mechanism for all injection rates in the continuous-rate experiment, resulting in monotonic increase in scCO(2) saturation.

A web of streamers: biofilm formation in a porous microfluidic device

Using a microfabricated porous media mimic platform, we investigated how fluid flow influences the formation of filamentous structures, known as streamers, between porous media structures. We demonstrate how hydrodynamics govern the formation, morphology and the distribution of these biofilm streamers in the device. Our work establishes that, under favorable hydrodynamic conditions, streamers can often act as precursors to mature microbial structures found in complex geometries, such as those involved in porous media.

Strong influence of geometrical heterogeneity on drainage in porous media

We present an experimental study of drainage in two-dimensional porous media exhibiting bimodal pore size distributions. The role of the pore size heterogeneity is investigated by measuring separately the desaturation curves of the two pore populations. The displaced wetting fluid remains trapped in small pores at low capillary numbers and is swept only above a critical capillary number proportional to the permeability of the big pores network. Based on this observation, we derive a simple criterion for phase trapping based on the balance of viscous to capillary forces. Numerical implementation of this theory in a pore network model quantitatively fits our experimental results. This combination of approaches demonstrates quantitatively the influence of geometrical heterogeneities on drainage in porous media.

Liquid CO2 displacement of water in a dual-permeability pore network micromodel

Permeability contrasts exist in multilayer geological formations under consideration for carbon sequestration. To improve our understanding of heterogeneous pore-scale displacements, liquid CO(2) (LCO(2))-water displacement was evaluated in a pore network micromodel with two distinct permeability zones. Due to the low viscosity ratio (logM = -1.1), unstable displacement occurred at all injection rates over 2 orders of magnitude. LCO(2) displaced water only in the high permeability zone at low injection rates with the mechanism shifting from capillary fingering to viscous fingering with increasing flow rate. At high injection rates, LCO(2) displaced water in the low permeability zone with capillary fingering as the dominant mechanism. LCO(2) saturation (S(LCO2)) as a function of injection rate was quantified using fluorescent microscopy. In all experiments, more than 50% of LCO(2) resided in the active flowpaths, and this fraction increased as displacement transitioned from capillary to viscous fingering. A continuum-scale two-phase flow model with independently determined fluid and hydraulic parameters was used to predict S(LCO2) in the dual-permeability field. Agreement with the micromodel experiments was obtained for low injection rates. However, the numerical model does not account for the unstable viscous fingering processes observed experimentally at higher rates and hence overestimated S(LCO2).

Influence of wetting conditions on drainage in porous media: a microfluidic study

This paper presents some experimental results on two-phase flows in model two-dimensional (2D) porous media with different wetting properties. Standard microfluidic techniques are used to fabricate the 2D micromodels that consist of a network of straight microchannels having heterogeneous sizes. The invasion mechanism is analyzed quantitatively for partial and total wetting conditions, and for various stable viscosity ratios and capillary pressure heterogeneity. For capillary numbers ranging from 10(-7) to 10(-2), we observe a transition between capillary fingering and a stable front. The capillary fingering regime exhibits differences between partial and complete wetting systems: The front width in complete wetting is larger. Simple models are proposed to account for these regimes and indicate that the differences between the systems are likely to be due to the flow of the displaced fluid in the complete wetting situation.