Volume 56, Issue 7 e2019WR026944
Research Article
Free Access

Microfluidic Diagnostics of the Impact of Local Microfracture Connectivity on Hydrocarbon Recovery Following Water Injection

Yujing Du

Yujing Du

Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, USA

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Ayaz Mehmani

Corresponding Author

Ayaz Mehmani

Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, USA

Correspondence to: A. Mehmani,

[email protected]

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Ke Xu

Ke Xu

Department of Energy and Resources Engineering, Peking University, Beijing, China

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Shaina Kelly

Shaina Kelly

ConocoPhillips Company, Houston, TX, USA

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Matthew Balhoff

Matthew Balhoff

Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, USA

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Carlos Torres-Verdín

Carlos Torres-Verdín

Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX, USA

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First published: 16 April 2020
Citations: 18


Microfractures originate in hydrocarbon reservoirs and groundwater aquifers either in the form of pore-scale authigenic apertures or secondary openings during well stimulation. Microfractures are often difficult to detect and can act as an invisible impediment when predicting hydrocarbon recovery. We use microfluidics to identify the flow conditions at which microfracture connectivity with macrofractures becomes impactful. The analysis focuses on fluid displacements at unfavorable mobility ratios, which are difficult to capture with high-order numerical methods. Two configurations of microfracture type with the porous matrix, either dead-end (only connected to one macrofracture) or connecting two macrofractures, were investigated as case examples for both water and oil-wet conditions. Our findings confirm that improvements in hydrocarbon recovery are not universal due to the presence of microfractures but rather are a function of capillary number, wettability, and microfracture connectivity. We find that, regardless of wettability, a capillary number threshold for a connected microfractured system exists beyond which the effects of microfractures on recovery, fluid dendrite morphology, and oil ganglia number diminish considerably. However, substantial geometry-dependent differences in recovery are observed below this threshold. A connected microfracture generally decreases hydrocarbon recovery and suppresses coalescence of viscous fingering dendrites regardless of wettability. In contrast, a dead-end microfracture causes wettability-dependent effects with (1) minimal impact on hydrocarbon recovery at water-wet conditions and (2) both decreasing and increasing recovery effects at oil-wet conditions. Furthermore, dead-end microfractures become somewhat impactful to the divergence of viscous dendrites when capillary number increases but are overall ineffective to the trapped ganglia numbers.

Key Points

  • Microfractured systems present three distinct viscous fingering generation mechanisms
  • Capillary number and microfracture connectivity are more impactful in creating a viscous fingering generation mechanism than wettability
  • Although dead-end microfractures adopt unique dendrite generation mechanisms, their impacts on recovery are minimal at water-wet conditions

1 Introduction

Microfractures, which we define as openings with aperture sizes similar to matrix pores, occur in the subsurface due to various chemical and mechanical processes related to weathering, tectonic activity, diagenesis, or reactivation of dormant natural fractures during hydraulic fracturing (Gale et al., 2014; Landry et al., 2014; Maréchal et al., 2004). Their presence between macrofractures (those with apertures orders of magnitude larger than matrix pores) can contribute to overall fracture connectivity, which has been identified as having significant impact on subsurface flow (Wilke et al., 1985). However, much uncertainty regarding their in situ presence and aperture size exists such that seismic and borehole measurements need to be supplemented with transmitted light and scanning electron microscopy to achieve accurate fracture maps (Andres et al., 2014; Landry et al., 2014). In addition, the extent to which this uncertainty is relevant for oil production and NAPL recovery is not clear because predicting transport phenomena, in particular multiphase flow, in fractured rocks is not well established (Berkowitz, 2002). Predictive and conceptual pictures of fracture connectivity and fluid flow are critical for optimizing production (Faulkner et al., 2009; Matthäi, & Belayneh, 2004; Odling et al., 1999).

Unstable immiscible flow (viscous and capillary fingering) (Lenormand et al., 1988; Saffman & Taylor, 1958) may occur in fractured formations during invasion of a less viscous flow (such as fracture fluid) or when performing waterflooding of a dense nonaqueous phase liquid (DNAPL). Previous work on unstable two-phase flow, however, has generally focused on either the competition between viscous and capillary forces, described by capillary number (Ca = μiv/γ), or the viscosity ratio between the displacing and displaced fluid, quantified by the viscosity ratio (M = μi/μd). Pore-scale geometrical effects, such as fracture connectivity, are typically not included when predicting viscous/capillary fingering behavior. In addition to capillary number and viscosity ratio, wettability effects on fingering patterns were recently investigated as a third dimension for a phase diagram in 2D flow cells (Zhao et al., 2016). The investigated pore-scale geometries have generally been 2D (Lenormand et al., 1988), 2.5D (Christensen et al., 2019), or 3D homogeneous porous matrices (Islam et al., 2014) or a single planar rough fracture (Chen et al., 2017). Whether and to what extent the existence of microfractures, connected or dead-end, can affect unstable flow is not yet well-known.

Investigating unstable immiscible flow in fractured rocks through numerical modeling is challenging. Direct numerical simulation methods, such as the lattice Boltzmann method (Tsuji et al., 2016), are promising but can be computationally costly in two-scale systems such as those of fractured rocks. Reduced-order methods, such as the dielectric breakdown model (Doorwar & Mohanty, 2014), rely on a priori rules for fluid movement that are derived from experimental observations. Although core flooding has been used to provide measurements within fractured rocks (Lu et al., 2014; Mirzaei et al., 2016; Rangel-German & Kovscek, 2002), visualization of pore-level fluid flow behavior in cores (e.g., computerized topography) is difficult, especially in tight rock samples where pore sizes can be smaller than voxel resolution (Akbarabadi et al., 2017; Mehmani, Kelly, & Torres-Verdín, 2020; Wildenschild & Sheppard, 2013). Given that pore sizes in unconventional formations can fall into the nanometer range, nanofluidics and nanomodels are appealing to mimic tight rocks and probe their flow behavior at the subpore (single pores/channels) and pore scales (ensemble of pores) (He et al., 2014; Kelly et al., 2016b; Zhong et al., 2018). However, despite their capacity to provide valuable information about nanoconfinement effects on fluid transport, challenges in nanofluidics fabrication and fluid flow visualization are considerable obstacles (Kelly et al., 2016a). Given the complexity of nanoporous systems (which is a result of coupled nanoconfinement and geometrical effects) such as mudrocks, decoupling their pore-space geometrical impacts on fluid transport properties with microfluidics can reduce uncertainties associated with measurements acquired with nanofluidics.

Microfluidic systems have been used to investigate multiphase flow and transport phenomena from subpore-scale features to more complex porous media, as extensively discussed in recent review papers by Lifton (2016) and Anbari et al. (2018). Their capacity for direct visualization of fluid movement in repeatable and controlled environments has allowed the investigation of fundamental physics concepts with simplified geometries. Microfluidics is also an effective screening tool for petroleum applications (Ma et al., 2012; Xu et al., 2015). However, microfluidics studies generally have focused on geometries containing an intact (not fractured) porous matrix or a porous matrix with a single connected fracture (Er et al., 2010; Mejia et al., 2019; Wan et al., 1996), where the impact of fracture connectivity on flow was not systematically investigated. The two dimensionality of micromodels may limit their quantitative discoveries to rocks with uniform geometries in the vertical direction or thin geological layers. However, 2D micromodels can capture qualitative two-phase flow trends associated with 3D porous media (Avraam et al., 1994), providing useful observations on pertinent functional relationships. With regard to unstable flow, microfluidics work has generally been performed for probing fingering dendrites in matrix pores (Aminah Setu et al., 2013; Wang et al., 2013; Xu et al., 2014; Zhao et al., 2016) wherein the concept of coupled impacts of microfractures and an adjacent porous matrix were not investigated.

In this paper, we utilize diagnostic microfluidics to investigate the effects of microfracture/macrofracture connectivity on oil recovery and viscous/capillary fingering patterns. Direct experimental observations of two-phase flow in analogue media can assist in reducing the complexity of microfracture transport into several key independent geometrical and flow property variables. We performed water-flood experiments in three micromodel geometries: one with only a porous matrix, one with a connected microfracture (connecting two adjacent macrofractures), and one with a semiconnected (dead-end) microfracture (only connected to one macrofracture). Figure 1a shows a schematic of a hydraulic fracturing operation where microfractures intersect with macrofractures. Figure 1b shows the two cases studied in this paper (i.e., the presence of connected microfractures and dead-end microfractures). Figure 1c describes an analogues framework for formulating immiscible flow in a fractured vadose system for NAPL remediation (Faybishenko et al., 2000). Both water- and oil-wet conditions were designed and implemented to determine the impact of wettability on recovery and fingering patterns. Capillary numbers ranging from 10−7 (capillary forces are comparatively dominant) to 10−5 (viscous forces are comparatively dominant) were selected by changing the flow rate of the injection water. Figure 2 shows a schematic of fluid and geometrical contributors to the flow patterns within the scope of our work. In addition to other extensively investigated parameters (to the left of the chart), we propose that microfracture connectivity (to the right of the chart) can be regarded as an independent variable for both oil recovery and flow patterns.

Details are in the caption following the image
(a) Schematic of a hydraulically fractured horizontal well with microfractures. Macrofractures and microfractures are identified with blue and red, respectively. (b) Close-up schematic of connected and dead-end microfractures. (c) Example of a fracture network in the vadose zone (fracture network conceptualization taken from Faybishenko et al., 2000). Lateral fractures can be considered microfractures for the purpose of the conceptualization of immiscible flow in this paper. Schematics presented here are not to scale and only serve as an illustration for the fracture connectivity classification implemented in this research.
Details are in the caption following the image
Schematic chart of parameters that affect the behavior of unstable fluid displacement in porous media.

2 Methods

Three 2.5-dimensional (2.5D) glass micromodels were fabricated using the method developed by Xu et al. (2017) so that pore throats are shallower than pore bodies. In such 2.5D micromodels, important pore-scale flow phenomena such as the continuity of the wetting phase and capillary snap-off of the nonwetting phase can be captured by having pore-scale 3D features in the 2D pore arrays. This 2.5D feature is important for studying the unstable immiscible flow, where finger initiation has been shown to be sensitive to pore-scale geometries (Chen & Wilkinson, 1985). The three micromodels used in this work are denoted as M1, M2, and M3, with all having a domain size of 2.5 cm in length and 1.5 cm in width and the same porous matrix. M1 is only a homogenous matrix between the inlet and the outlet, M2 has a microfracture in the middle of the matrix connecting only to the inlet side, and M3 has a microfracture in the middle of the matrix connecting the inlet to the outlet (which connects the two macrofractures). In the microfractured micromodels, the microfractures are of comparable size to matrix pores (the depths are both ~21 μm). However, there are two key features that distinguish microfractures from matrix pores, therefore affecting the flow significantly. Firstly, microfractures are lacking in frequent diverging–converging structures, therefore posing little capillary barriers during drainage and serve as “highways” for imbibition along their flow path. Meanwhile, matrix pores have frequent diverging–converging structures, posing capillary barriers to fluid invasion. Secondly, matrix pores are approximately isotropic in average, while microfractures are directional. The photomask designs of the flow domain in M1, M2, and M3 are depicted in Figure 3a, where the boundary conditions are also specified. The inlet, outlet, and flow channels to/from the flow domain are shown in Figure 3b. Micromodels are made of soda-lime glass. The grains are cylinders with a near-square cross-section as seen from Figure 3c, and the surfaces are macroscopically smooth. The pore-scale geometric features are illustrated in two schematic sketches of the vertical cross-section from two angles (45° and 90° from horizontal direction) as shown in Figures 3d and 3e. Details regarding the fabrication and micromodel properties can also be found in the paper by Xu et al. (2017). Other relevant geometric properties of the three micromodels are summarized in Table 1.

Details are in the caption following the image
(a) Photomask design of the flow domains in micromodels 1, 2, and 3 denoted as M1, M2, and M3, respectively. (b) Photomask design schematic (M1) of inlet, outlet, flow channels to/from the flow domain. (c) Microscopic image of the micromodel after flow experiment with 45° and 90° cross-sections in planar view. (d) Cross-sectional schematic of micromodel pore body/grain at 45°. (e) Cross-sectional schematic of micromodel pore body/pore throat at 90°. Note that throats are etched shallower than pores as part of the 2.5D fabrication scheme.
Table 1. Summary of micromodel properties
Model Pore body width (μm) Pore body depth (μm) Pore throat width (μm) Pore throat depth (μm) Fracture length (cm) Fracture width (μm)
M1 200 ~21 25 ~5 N/A N/A
M2 200 ~21 25 ~5 2.2 600, 400, 200
M3 200 ~21 25 ~5 2.5 600

Mineral oil and a crude oil (undisclosed composition) were used as the displaced fluids with viscosities of 170 and 230 cp, respectively. The viscosities of water and both oils were measured using Rheometer DHR3 from TA Instrument at 20 °C, in the range of 0.1–100 s−1, which covers the shear rate range in the experiment. The viscosities of both oils stayed constant within the measurement range, confirming that both oils can be approximated as Newtonian fluids in the experiments. The displacing fluid is deionized (DI) water with a viscosity of 1 cp. Viscosity ratios of the displacing fluid (DI water) and the two displaced fluids (mineral oil and crude oil) are 5.8 × 10−3 and 4.3 × 10−3, respectively. Table 2 lists the properties of fluids used in this work including their density, viscosity, and interfacial tensions. The density of water was computed from the weight of water measured with a digital balance (Adam Equipment HCB123 Highland Digital Precision Balance, with a precision of 0.001 g). We measured the weight of 1–5 ml (1 ml interval) of water and calculated the density from the weight–volume slope. The equipment used for interfacial tension measurement is a spinning drop tensiometer (KRÜSS SDT). The crude oil was preequilibrated with deionized water before IFT measurements. We added equal volume of crude oil and deionized water in the same tube and agitated the mixture in an ultrasonic equipment (Branson 2800) for 50 minutes when the two fluids were completely mixed. After 1 week of resting at ambient conditions, oil and water separated into two layers with oil staying on the top layer; 70 and 27 measurements were conducted at 20 °C for crude oil—water IFT and mineral oil—water IFT, respectively. The average viscosity values along with the standard deviations were reported in Table 2. While having similar viscosity ratios, the two oils give rise to different wetting states with the glass surface. From the microscopic images shown in Figure 4, it is clear that the mineral oil–water-glass system is water wet, while the crude oil–water-glass system is oil wet. The crude oil-wet state was achieved by aging the micromodel for 24 hours prior to flow experiments. Surface reactions that cause the glass surfaces oil-wetting, such as the adsorption of polar components on the surface, were previously reported in literature (Du et al., 2019).

Table 2. Summary of fluid properties
Fluid Density (g/ml) Viscosity (cp) IFT with water (mN/m)
Crude oil 0.92 230 10 ± 0.82
Mineral oil 0.86 170 19 ± 0.97
Water 1.0 1 N/A
Details are in the caption following the image
Pore-scale images of (a) mineral oil (red) remaining after water injection in M2 and (b) crude oil (beige) remaining after water injection in M3. Mineral oil and crude oil are the nonwetting and wetting phase, respectively. Contact angles are obtained by measuring along the contact lines at multiple liquids/solid interfaces from corresponding cases.
A total of 18 experiments were performed with the three micromodels (M1, M2, and M3) by systematically varying the capillary number from 10−7 to 10−5 at two different wettability states (water wet and oil wet). To ensure the desired wettability for each experiment, we designed the experiment sequence so that we conducted mineral oil experiments in three new micromodels before crude oil experiments; therefore, the wettability can be confirmed to be water wet in three mineral oil experiments. The capillary number, Ca, was varied by changing the water flow rate from 4 to 400 μl/hr and is given by
where Qw is the injection rate, μw is water viscosity, W and D are the width and the etching depth of the micromodel, respectively, and γ is the water–oil interfacial tension. Table 3 summarizes the capillary number and other properties for each of the 18 experiments. Figure 5 shows an overlay of experiments conducted in this work in the context of a capillary number-viscosity ratio phase diagram. The viscosity ratio of our experiments is on the order of 5 × 10−3, and the capillary number is between 10−7 and 10−4. We note that according to two phase boundaries determined in the literature (Lenormand et al., 1988; Zhang et al., 2011), our experiments fall approximately into the capillary fingering to viscous fingering cross-over and viscous fingering regions. As is observed subsequently in the supporting information section 3.1.1., the dendrite propagations demonstrate characteristic viscous fingering behaviors by moving forward and not forming loops (Lenormand et al., 1988; Zhang et al., 2011). We classify each drainage and imbibition data point into low (~10−7), medium (~10−6), and high (~10−5) capillary number experiments.
Table 3. Summary of the microfluidics experiments considered in this paper
Model Oil Wettability Ca low ~ 10−7 Ca medium ~ 10−6 Ca high ~ 10−5
M1 Crude oil Oil wet Exp. 1, Ca = 3.5 × 10−7 Exp. 2, Ca = 3.5 × 10−6 Exp. 3, Ca = 3.5 × 10−5
Mineral oil Water wet Exp. 4, Ca = 1.9 × 10−7 Exp. 5, Ca = 1.9 × 10−6 Exp. 6, Ca = 1.9 × 10−5
M2 Crude oil Oil wet Exp. 7, Ca = 3.5 × 10−7 Exp. 8, Ca = 3.5 × 10−6 Exp. 9, Ca = 3.5 × 10−5
Mineral oil Water wet Exp. 10, Ca = 1.9 × 10−7 Exp. 11, Ca = 1.9 × 10−6 Exp. 12, Ca = 1.9 × 10−5
M3 Crude oil Oil wet Exp. 13, Ca = 3.5 × 10−7 Exp. 14, Ca = 3.5 × 10−6 Exp. 15, Ca = 3.5 × 10−5
Mineral oil Water wet Exp. 16, Ca = 1.9 × 10−7 Exp. 17, Ca = 1.9 × 10−6 Exp. 18, Ca = 1.9 × 10−5
Details are in the caption following the image
Flow pattern classification based on capillary number (Ca) and viscosity ratio (M). Boundary lines are determined by Lenormand et al. (1988) (shown in blue) and Zhang et al. (2011) (shown in red). Drainage (crude oil recovery) is identified with black squares while imbibition (mineral oil recovery) is identified with brown X's.

For each experiment, the micromodels were saturated with mineral oil or crude oil and aged for 24 hours for crude oil. The aging time needed to create an oil-wet condition is dependent on the type of the system as reviewed by Bartels et al., 2017. In previous microfluidic experiments, many different aging times, from days to weeks, were used to create an oil-wet condition (Bartels et al., 2017; Du et al., 2019; Song & Kovscek, 2015). For our system, we did not have connate water in the glass micromodels before oil invasion; therefore, the aging time was shorter as oil contacted the surface the moment it was injected in the micromodels. To expel air from the systems, we injected the oils at a high injection rate using a syringe pump (PHD 2000, Harvard Apparatus) for tens of pore volumes. After saturating micromodels with crude oil, we kept injecting crude oil at a flow rate of 1–2 μl/hrs during the aging process. Each of the micromodels was reused in three mineral oil and three crude oil experiments in order to eliminate the effects due to even small fabrication difference when using different micromodels. Between experiments, we cleaned the micromodels by injecting hexane, acetone, and DI water in sequence. Both organic and inorganic components can be efficiently removed from the system with this cleaning procedure. After cleaning, the micromodels were placed on a hot plate at 110 °C for drying. Micromodels were checked under the microscope (Olympus IX73) before each experiment to confirm cleanliness. During the water injection, the micromodels were placed horizontally on top of a light pad. A digital camera (Nikon D5500) was mounted on top of the micromodel to capture time-lapse images. Auto-exposure mode of the camera was enabled to ensure optimal imaging quality according to the background light intensity. Exposure time varied slightly among experiments in the range of 1/160–1/250 s. The image resolution is 300 × 300 dpi, and the image dimension is 6000 × 4000 pixels. Time intervals for the injection with low, medium, and high capillary number are 6 min, 1 min 12 s, and 9 s, respectively. Figure 6 shows the experimental system. Immediately after flow experiments, we checked the wettability under the microscope and documented the wettability. We have included pore-scale images captured immediately after flow experiments in the supporting information section S3.

Details are in the caption following the image
Experimental system, including a digital camera (Nikon D5500), a syringe pump (PHD 2000, Harvard Apparatus), a LED light pad, and a tripod.

Figure 7 demonstrates the image processing procedures we used in this work. Image stacks were cropped to the porous medium domain (2.5 × 1.5 cm—see Figure 3a) using ImageJ, which is an open-source image processing software (Cates et al., 2004). A set of images captured during each experiment were imported into ImageJ as an image stack. Each image was aligned to the same position using a function called “Linear Stack Alignment” (image registration). Subsequently, the images were cropped around the porous medium regions. The local contrast in each image was enhanced using the “Enhanced Local Contrast (CLAHE)” function. This step ensures that phase boundaries in the images are clear. The images were then binarized using the thresholding method “Otsu,” and in order to offset ambient light oscillations, thresholds for each image were set independently from others in the image stack. During color segmentation, the image stack was binarized into black (oil phase) and white (water and grains) for oil recovery curves and number of isolated oil ganglia (see Figure 7a). The area fraction of the black (oil) area (within both matrix pores and fractures) in each image was then measured. Oil saturation in each image was calculated as the area fraction in each image divided by the area fraction in the fully oil-saturated image (captured at zero pore volume). The gray scale distribution (measured using ImageJ's “histogram” function) of the raw and binarized image from a mineral oil experiment and a crude oil experiment (both conducted in M1 at low capillary number) is shown in Figure 7b. Number of ganglia were determined via a Forest Fire Algorithm (Mehmani, Kelly, Torres-Verdín, & Balhoff, 2019a) in which each oil pixel is designated as “unburned” initially. A “fire” is set at each pixel, which “burns” all the neighboring pixels until an oil/water interface is reached and isolated oil ganglia are identified. We find that images reveal whether pendular rings between grains can form and are sensitive enough to determine their contribution to fluid film connectivity. However, the nonbinary phase distributions within a single pore (which in our results is only the case at high capillary numbers in an unfractured medium) are not captured. We therefore consider the images in meso/Darcy-scale (in contrast to the pore scale where a nonbinary phase distribution within a single pore can be captured). For fractal dimension calculation, we focused on the morphology of the invading phase in the mesoscale as well. For this purpose, any influence of grains on fractal dimension values was removed by conducting erosion and dilation procedures on the binarized image (see similar examples by Islam et al. (2014), Ferer et al. (2014), and Chen et al. (2017)).

Details are in the caption following the image
(a) Image processing steps for binarizing each frame and subsequently determining isolated oil ganglia. Note that the steps for image analysis effectively capture wetting-phase pendular rings. (b) Gray scale distribution of the raw and binarized image from imbibition (left) and drainage (right) at low capillary number in M1.

Voxel resolution in our experiments is approximately 12 micrometers/pixel. Subresolution features, in particular film thickness and roughness size, are therefore not captured in our analysis. However, they can potentially impact fractal dimension and oil ganglia numbers/sizes if the image resolution were higher. Presence of film in the invaded zones can potentially reduce fractal dimension and increase the number of oil ganglia by fragmenting the invading phase at the subpore scale (Mehmani, Kelly, Torres-Verdín, & Balhoff, 2019a). In addition, when surface roughness is considerable, a two-dimensional quantification of the pore space for fractal analysis is potentially inadequate as the surface roughness generates subpore-scale dynamics, such as pinning and corner flow, which may not be captured at plan-view images such as our experiments. We selected smooth micromodels for our experiments that have surface roughness to pore depth ratios of less than 1%, which according to Mehmani, Kelly, Torres-Verdín, and Balhoff (2019b), subpore-scale dynamics are not enhanced in such surface conditions. Nevertheless, a thorough investigation of subresolution impacts is merited as future work. The fractal and ganglia analyses in our work therefore are restricted to the image resolution of experiments.

3 Results and Discussions

3.1 Sweep Patterns

3.1.1 Qualitative Observations

Experiments show that microfracture connectivity can significantly alter upscaled fingering morphology. In this article, we refer to “upscale” as the scale at which flow behavior is captured with the digital camera throughout the micromodel. Figures 8a and 8b show the sweep patterns for both imbibition and drainage at breakthrough and steady state. Figure 8c summarizes our observations in a conceptual picture for fluid–fluid displacement under unfavorable viscosity ratio in the presence of microfractures (discussed below).

Details are in the caption following the image
Patterns of invading phase for three capillary numbers at breakthrough and steady state during (a) imbibition, and (b) drainage. The matrix micromodels (M1) demonstrate characteristics that resembles viscous fingering behavior by moving toward the outlet and not forming loops. (c) Conceptual picture for fingering fluid dendrite propagation in the presence of a microfracture. Flow direction is from one macrofracture (inlet, not shown) to another (outlet, not shown). Main microfracture dendrites are confined inside the microfracture. Macrofracture dendrites originate from the macrofracture (inlet) and traverse within the matrix. Secondary microfracture dendrites originate from the microfrature and traverse within the matrix. Base Case (M1)

In the absence of microfractures, fingering is generated only from the macrofracture, as shown in Figures 8a and 8b. We refer to this finger type as macrofracture dendrite (Figure 8c). At the time of breakthrough, the initial macrofracture dendrites have penetrated from one macrofracture (inlet side) to the other (outlet side). Macrofractures are not shown in Figure 8. Dendrites become narrower as capillary number increases. At steady state, as capillary number increases (regardless of wettability), macrofracture dendrites become narrower but dispersed, which is consistent with observations made by Doorwar and Mohanty (2017). However, the divergence of macrofracture dendrites increases considerably at high capillary numbers in water-wet systems, while in oil-wet systems macrofracture dendrites become considerably dispersed starting from medium capillary numbers. Macrofracture dendrites are chaotic and do not indicate preferential displacement pathways regardless of capillary number and wettability condition. Dead-End Microfracture (M2)

A porous system with a dead-end (semiconnected) microfracture, demonstrates a fingering morphology that is qualitatively distinct from that of an unfractured system (M1), as shown in Figures 8a and 8b. Unlike an unfractured system, fingering dendrites do not exhibit a chaotic movement but a preferential one determined by the dead-end microfracture. In a dead-end microfractured system, fingering dendrites originate from the dead-end microfracture and are referred to as main microfracture dendrites in Figure 8c. At breakthrough, the single main microfracture dendrite has penetrated along the dead-end microfracture while several secondary microfracture dendrites invade the porous matrices. The dendrite patterns are qualitatively similar at low to high capillary numbers for both imbibition and drainage, while secondary microfracture dendrites become narrower as the capillary number increases. At steady state, macrofracture dendrites only emerge at high capillary numbers but are less dominant than secondary microfracture dendrites. Once the secondary microfracture dendrites develop from the microfracture, they do not traverse backward, causing poor sweep near the upstream end (near the inlet macrofracture). At the tip of the dead-end microfracture, dendrites coalesce more readily and result in a higher sweep compared to the matrix adjacent to the microfracture. Dendrite patterns are qualitatively similar for both imbibition and drainage, highlighting the dominant role played by the dead-end microfracture compared to wettability. Microfracture Connecting Macrofractures (M3)

A connected microfractured system demonstrates a distinctly different unstable flow pattern than unfractured (M1) or dead-end microfractured (M2) systems. At low to medium capillary numbers, the displacing phase traverses mainly through the microfracture and is referred to as main microfracture dendrite in Figure 8c. At breakthrough, a main microfracture dendrite prevents the invading phase from entering the matrix, which suppresses oil recovery at all capillary numbers. The suppression of fingering is stronger for drainage than imbibition, as a small amount of secondary microfracture dendrites develop during imbibition and in particular at low capillary numbers. After breakthrough, when the capillary number reaches a threshold value (between 10−5 and 10−4), macrofracture and secondary microfracture dendrites begin to form, which results in an increase in oil recovery, as observed in the steady state images in Figures 8a and 8b. Although additional data points are required to determine the exact threshold capillary number, our results indicate that the threshold is between the viscous fingering and transient regions, as shown in Figure 5. The capillary number threshold is furthermore likely to depend on the flow capacity contrast (e.g., permeability contrast) between the microfracture and matrix for which additional experiments are needed. Interestingly, a capillary number threshold for fingering dendrite development is not observed for a dead-end microfractured system (M2). Invasion of secondary microfracture dendrites is more prominent for imbibition at low to medium capillary number, while the generation of macrofracture dendrites widens for drainage at high capillary number.

3.1.2 Quantitative Analysis

Fractal dimension (Df) is used to describe and quantify two-phase flow sweep patterns into capillary fingering or viscous fingering regimes (Chen et al., 2017; Islam et al., 2014; Lenormand & Zarcone, 1984; Lenormand et al., 1988; Zhang et al., 2011). The fractal dimension varies from 1 to 2, with higher values indicating a coalescent dendrite evolution. Quantifying sweep patterns can have other applications as well, such as determining functional relationships for a chemical's dissipation rate at the evolving immiscible interface. We therefore utilize fractal dimension to investigate the impact of dead-end and connected microfractures on unstable flow morphology. Figure 9a, adapted from Chen et al. (2017), compares the visual morphology of fingering patterns and fractal dimension. The fractal dimension of an immiscible front has generally been investigated as a function of capillary number and viscosity ratio, while (as discussed in the Introduction) geological effects, such as connectivity of microfractures, are typically not considered when studying their variability. For the computation details of the fractal dimensions, an example of the box-counting method is described in the supporting information section S1.

Details are in the caption following the image
(a) Reference fractal dimension values for capillary and viscous fingering. The higher the fractal dimension, the more coalescent the immiscible front becomes (Chen et al., 2017). (b) Steady-state fractal dimension values calculated for the micromodels at all capillary numbers for the two wettability conditions. (c) Fractal dimension for micromodels throughout their water-flood experiments (top) imbibition and (bottom) drainage. We note that fractal dimension is a function of capillary trapped oil saturation. Error bars are the maximum range of values obtained when values of capillary trapped oil saturation were altered by ±5%.

Figure 9b shows the fractal dimension of the micromodels at steady state. We observe that the lowest fractal dimension belongs to the connected microfractured system at oil-wet conditions and low capillary numbers. As is revealed in Figure 8, a connected microfractured system predominantly displays a main microfracture dendrite pattern prior to reaching a capillary number threshold. We also observe that changing the wettability from oil wet to water wet slightly increases the fractal dimension. This behavior is partly due to the presence of secondary microfracture dendrites, which give rise to a more coalescent fingering pattern. At low capillary number and regardless of wettability, a dead-end microfracture reduces the front fractal dimension as well, even though its impact is less than due to a connected microfracture. The effects of a dead-end microfracture on fractal dimension are consistent with our observation in Figures 8a and 8b; the microfracture decreases the chaotic movements of the dendrites by providing a preferential pathway in the middle of the porous domain. Similar to a connected microfractured system, the main microfracture dendrite traverses through the microfracture itself and effectively develops a Saffman finger with low dendrite divergence. At medium capillary numbers, the impact of a connected microfracture is similar to low capillary numbers in reducing the front fractal dimension. However, the ability of a dead-end microfracture to confine dendrite divergence decreases at medium capillary numbers while secondary microfracture dendrites increase the fractal dimension compared to the unfractured system. At high capillary numbers, differences between fractal dimension for the three micromodel types and two wettability conditions decrease considerably. This reduction is due to the inefficacy of microfractures, dead end or connected, from influencing the sweep patterns of the invading phase beyond a capillary number threshold.

Figure 9c illustrates the fractal dimension of the dendrites throughout the evolution of the invading front. We notice that as capillary trapped oil saturation decreases, fractal dimension generally increases. This increase is due to the evolution of fingering dendrites as they become more likely to coalescence and decrease the capillary trapped oil saturation. However, at equal oil recovery values, only a connected microfracture (M3) at high capillary numbers (regardless of wettability) suppresses the divergence of fingering dendrites. This contrast in microfracture connectivity effects with the steady-state values shown in Figure 9b highlights the importance of capillary trapped saturation in properly assessing dendrite morphology. In other words, if a recovery operation is conducted at low and medium capillary numbers, the recovered oil saturation is sufficient information for monitoring its performance, while connectivity effects of microfractures on sweep patterns become negligible. This assumption is valid for both water- and oil-wet systems but becomes invalid at high capillary numbers where microfracture connectivity is a relevant parameter in determining flow patterns when monitoring recovery.

3.2 Oil Recovery

Figure 10 shows the oil saturation versus pore volumes injected for each microfractured system at three capillary numbers and both wettability conditions. Figure 11 shows functional relationships for ultimate oil recovery and pore volumes required to reach steady state as functions of capillary number. The recovery and pore volume values shown in Figures 10 and 11 are also summarized in Tables 4 and 5.

Details are in the caption following the image
Capillary trapped saturation curves for each micromodel at three capillary numbers during imbibition (top) and drainage (bottom).
Details are in the caption following the image
(a) Oil recovery and (b) pore volume injected at 95% recovery for each micromodel at three capillary numbers for imbibition and drainage processes.
Table 4. Summary of measured oil recovery for different geometries
Ca* M1imb M2imb M3imb M1dra M2dra M3dra
~10−7 0.35 0.36 0.28 0.47 0.33 0.09
~10−6 0.38 0.43 0.15 0.34 0.51 0.10
~10−5 0.40 0.42 0.39 0.52 0.53 0.65
  • * Capillary numbers are 3.5 × 10−7, 3.5 × 10−6, and 3.5 × 10−5 for imbibition and 1.9 × 10−7, 1.9 × 10−6, and 1.9 × 10−5 for drainage.
Table 5. Pore volume injected at 95% recovery in different geometries
Ca* M1imb M2imb M3imb M1dra M2dra M3dra
~10−7 0.8 4 0.1 9 7 0.1
~10−6 5 14 0.14 1 14 0.1
~10−5 8 25 28 5 54 53
  • * Capillary numbers are 3.5 × 10−7, 3.5 × 10−6, and 3.5 × 10−5 for imbibition and 1.9 × 10−7, 1.9 × 10−6, and 1.9 × 10−5 for drainage.

3.2.1 Base Case (M1)

The analysis in Figures 10 and 11a shows that recovery slightly increases with capillary number by up to 5% in water-wet systems, where fingers become more dispersed and sweep larger areas. During drainage, however, recovery at medium capillary number is the lowest while recovery at high capillary number is highest. The largest recovery difference is 18%. As shown qualitatively in Figure 8, fingers become more dispersed but narrower with the increase in capillary number. The two effects compete with each other, resulting in a nonmonotonic trend in recovery versus capillary number.

3.2.2 Dead-End Microfracture (M2)

Dead-end microfractures in water-wet systems, despite changes in dendrite generation mechanism, do not alter ultimate recovery significantly regardless of capillary number (see Figures 10 and 11a). In fact, recovery differences due to presence of a dead-end microfracture are less than 5%. In oil-wet dead-end microfractured systems, recovery discrepancies can increase up to 17% but unlike water-wet systems, oil recovery can both increase or decrease depending on the capillary number. This higher dependence on capillary number for drainage can be due to the dominance of pore-scale bulk velocities (in contrast to the presence of corner films for imbibition) on immiscible flow (Zhao et al., 2016). However, additional numerical simulations (Alpak et al., 2018) or particle image velocimetry experiments (Kazemifar et al., 2015) are needed to determine the precise impact of wettability on capillary number dependence for oil recovery. Figure 11b and Table 5 show that dead-end microfractures, at almost all capillary numbers, delay oil recovery by increasing the amount of injected pore volumes required to reach 95% recovery. This delay is most significant in oil-wet systems and high capillary numbers. In an unfractured system (M1), oil recovery reaches steady state rapidly once preferential pathways are established at the early stages of injection and leave oil ganglia trapped in the remaining regions. By contrast, in a dead-end microfractured system after the early stage pathways are formed, water continues to sweep into the remaining regions, resulting in long tails of up to tens of pore volumes in the recovery curves shown in Figure 10.

3.2.3 Microfracture Connecting Macrofractures (M3)

As shown in Figures 10 and 11, prior to reaching a capillary number threshold, a connected microfracture decreases oil recovery significantly. The decrease in recovery is more prominent in oil-wet systems because water can enter the matrix from the microfracture during imbibition (secondary microfracture dendrites as shown in Figure 8c). However, at high capillary numbers, ultimate recovery in a connected microfractured system is similar to (1% lower in in water-wet systems) or higher (12% in oil-wet systems) than for an unfractured system. The increase of oil recovery could indicate that the pressure difference from upstream to downstream in porous matrices in the connected microfracture system overcomes the largest capillary pressure pinning the oil between two macrofractures. As observed in Figure 11b, similar to a dead-end microfracture, a connected microfracture can delay oil recovery but only beyond a capillary number threshold (i.e., high capillary numbers). The long tail in capillary trapped saturation curves indicates that water continues to sweep into the matrix after breakthrough along the microfracture. The tail lengths for M3 are comparable to those of M2 because the pore volumes injected at 95% oil recovery are similar. From Figure 11a, we find that an increase of capillary number improves oil recovery for unfractured and dead-end microfractured systems regardless of wettability. In a connected microfractured system, however, oil recovery can significantly improve (up to 56% in drainage and up to 24% in imbibition) at high capillary numbers, especially during drainage. From observing the immiscible phase distributions in Figure 8, we interpret that the connected microfracture establishes hydraulic connectivity for the invading phase between the two macrofractures at breakthrough. Given (1) the narrow cross-section of the microfracture compared to the domain cross-section, and (2) the constant flow rate condition, the pressure difference for the invading phase between the two macrofractures becomes highest compared to those of the dead-end and matrix systems. The heightened pressure difference gives rise to a higher imposed “global” capillary pressure, which drives the oil-in place considerably to the outlet.

As discussed by Tanino and Christensen (2019), capillary end effects can become considerable for water invasion in oil-wet media that are conducted in micromodels with domain sizes similar to this work. Our predictions of oil recovery with those cases are therefore smaller than what would be expected if capillary end effects did not exist. However, in fractured tight reservoirs, capillary end effect can be naturally present due to extreme small matrix pore sizes (two to three orders of magnitude smaller than in micromodels) and frequent microfractures, where the increased capillary end effective length would become comparable to fracture spacing. Our designs can therefore serve as analogues for investigating recovery in the presence of naturally occurring capillary end effects in the subsurface, where the results are quantitatively significant. In addition, our aim is to capture the invasion patterns qualitatively and parameterize them quantitatively, even though the precise values presented in this work may not translate to subsurface conditions. In qualitative aspect, as presented in Figuress 8a and 8b, the invasion patterns are mostly determined at an early stage prior to breakthrough conditions when end effects are not yet effective (i.e., the invading phase has not yet sensed the domain end). Finally, given that similar domain sizes were used in this work, conclusions based on comparing flow patterns at various capillary numbers for each wettability condition, even though capillary end effects are potentially present, are still valuable for our understanding of microfracture effects during unstable flow.

We aimed to provide a straightforward, semiquantitative comprehension of the interplay between the microfractures and the porous matrix and their effects on unstable two-phase flow. A comprehensive reproducibility study is not within the scope of this work, but from several replicate experiments performed in the three micromodels, the trend of the water invasion patterns in all three geometries are qualitatively reproducible. Quantitatively, we were also able to obtain good reproducibility as the remaining saturations are comparable with 5% variations in recovery, which agrees with the literature on the reproducibility of micromodels' study on unstable two-phase flow (Ferrari et al., 2015). All replicated experiments are included in the supporting information section S2.

3.3 Oil Ganglia Analysis

3.3.1 Ganglia Distribution Postwater-flooding

Figure 12 depicts the distribution of oil ganglion size at steady state for our experiments. We define oil ganglion size as the actual size of each ganglion divided by the size of one pore. Ganglion sizes are divided into 10 size groups with the calculated areal percentage of remaining oil for each group.

Details are in the caption following the image
Distribution of oil ganglia at steady state for each micromodel at three capillary numbers during imbibition (top) and drainage (bottom). Oil ganglion size is defined as the actual ganglion size divided by a single pore size. Oil ganglion percentage is defined as the area of a single oil ganglion as percentage of the total remaining oil in each size group. Base Case (M1)

In both imbibition and drainage processes, oil ganglion size decreases with an increase in capillary number as the plot shifts to the right (smaller size groups). During imbibition, oil ganglia larger than 500 take 62% of the total remaining oil at low capillary numbers and decrease to 46% at medium capillary numbers and 0% at high capillary numbers. During drainage, the percentage of oil ganglia larger than 500 decreases from 42% to 19% and 0% as the capillary number increases. This discrepancy due to wettability alteration agrees with the qualitative observation made from Figures 8 that the fingers are narrower under oil-wet conditions, resulting in overall smaller ganglion sizes.

As was shown in Figure 11a, oil recovery increases with capillary number; therefore, smaller oil ganglia correspond to higher recovery factors. However, the increase in oil recovery is less significant than the decrease in oil ganglion size because the increase of oil recovery is only 5–15% under both wetting conditions. As shown in Figure 12, although the percentage of the biggest oil ganglia decreases, the distribution tail containing smaller oil ganglia widens. For a given capillary trapped saturation, smaller oil ganglia can result in a higher spread of the injected phase, which is advantageous in chemical treatments. However, we observe that smaller remaining oil ganglia at the earlier stages are more difficult to recover compared to larger ones during continuous water flooding. Dead-End Microfracture (M2)

In a dead-end microfractured system, oil ganglion sizes decrease with capillary number but not as considerably as in an unfractured system. The decrease in the percentage of the largest oil ganglion group (>500) is 27% and 29% for imbibition and drainage processes which is much lower than the 62% and 42% decrease observed in an unfractured system. In contrast to M1, oil ganglia in the porous matrix in M2 are more difficult to mobilize even at high capillary numbers, as shown in Figure 8. Number of fingers that are generated in the porous matrix from the inlet (macrofracture) and microfracture increases with capillary number. The finger generation phenomenon decreases the size of large oil ganglia (>500) and contributes to the increase in oil recovery. Compared to M1, we found that the fragmentation of the large ganglion may not be efficient for improving recovery because smaller oil ganglia are harder to mobilize than larger ones at later stages. Microfracture Connecting Macrofractures (M3)

Recovery from the porous matrix is low at low to medium capillary numbers, leaving large oil ganglia (occupying >1,000 pores) trapped in the porous matrix. Figure 12 shows that approximately 99% of the remaining oil is in the largest size group (>500 pores). At high capillary numbers ~10−5, the oil ganglion size decreases significantly compared to unfractured and dead-end microfractured systems. In a connected microfractured system, the largest oil ganglia is 100 to 500 times the pore volume when water wet and 10 to 25 times the pore volume when oil wet. This sharp decrease of oil ganglion size in the porous matrix is consistent with the significant increase of oil recovery observed at high capillary numbers. At low to medium capillary numbers, water flows primarily through the microfracture, leaving large oil ganglia trapped in the matrix. At high capillary numbers, however, water dendrites enter into the matrix from the macrofracture and shrink the oil ganglia into smaller and more scattered oil ganglia. The fragmentation of the large oil ganglia contributes to the significant increase of oil recovery as capillary number increases.

3.3.2 Ganglia Generation During Displacement Processes

Figure 13a shows the number of generated oil ganglia as a function of capillary trapped oil saturation. We notice that the presence of a connected microfracture suppresses oil ganglia generation significantly. This reduction in oil ganglia number is for all capillary numbers and wettability conditions as long as fingering dendrites other than the main dendrite type shown in Figure 8c is generated. Flow patterns shown in Figures 8a and 8b verify that a connected microfracture can act as a point of convergence for fingering dendrites such that they are precluded from entering the matrix. In addition, given its higher hydraulic conductivity, a connected microfracture decreases the local velocity of the invading phase inside the matrix. A reduction in local velocity can enhance the coalescence of fingering dendrites. In contrast to a connected microfracture, a dead-end microfracture does not suppress oil ganglia generation significantly. This difference in oil ganglia generation is due to the ability of the invading dendrites to enter the matrix from the microfracture. Such a behavior results in front divergence similar to that of an unfractured system. As discussed in section 3.1.2, capillary trapped oil saturation may not be sufficient information for monitoring an enhanced oil recovery operation because it does not capture the spatial distributions of two immiscible phases. In Figure 13a, we observe that capillary trapped oil saturation alone cannot predict the total number of oil ganglia at a particular oil recovery step. Whether a microfracture is present and is connecting two macrofractures needs to be determined when predicting oil ganglia generation. Information about oil ganglia number can in fact become critical information during the development of a tertiary recovery operation. Figures 13b and 13c show aggregate depictions of all the data into a single plot for both imbibition and drainage. The plots clarify that the highest number of ganglia form in the absence of microfractures and at high capillary numbers. Furthermore, we find that variations between each ganglia generation plots are more prominent during drainage than imbibition. The increase in variation indicates a higher sensitivity to capillary number for oil ganglia generation in oil-wet systems. This difference is likely due to the absence of corner film percolation during drainage, which results in the bulk flow within channels becoming the main displacing mechanism. The higher sensitivity to capillary numbers at oil-wet conditions is consistent with measurements made in micromodels for immiscible displacement with varying wettability (Zhao et al., 2016).

Details are in the caption following the image
(a) Number of oil ganglia as a function of capillary trapped oil saturation (Soil) for (top) imbibition and (bottom) drainage. Aggregate plots of oil ganglia versus capillary trapped saturation are shown for (b) imbibition and (c) drainage.

3.4 Implications and Limitations

Fractures are ubiquitous in subsurface systems, potentially influencing the outcome of many hydrocarbon recovery and environmental remediation projects. Although fractures are recognized to affect transport phenomena, quantifying the various uncertainties about their impact on two-phase immiscible flow is still an important and open research topic. This is largely due to the technical challenge of quantifying fluid transport in fractured systems, which takes place through multiple length scales. The need for experimental data that visualize fluid transport in fractured rocks is also necessary to verify multiscale numerical models. However, the majority of experimental research has currently focused on single fractures to understand the impact of fracture surface rugosity and aperture distribution. Our work provides direct observations of fluid transport in macrofracture/microfracture ensembles. These observations can guide the development and verification of numerical algorithms for immiscible fluid dynamics with near-wellbore reservoir simulators for hydraulically fractured formations (Wang & Leung, 2015) and remediation projects in the vadose zone (Faybishenko et al., 2000). For instance, our results indicate using geological markers to determine if natural fracture presence or healing is relevant only below a critical capillary number threshold. Furthermore, we find that formation wettability is an irrelevant parameter when determining the implications of natural fracture openness based on geological investigations. Although not pursued in this article, a hybrid numerical-experimental approach based on our framework can be a next step in investigating transport properties of fractured rocks during unstable flow. This approach would follow the approach by Li et al. (2020) and Berg et al. (2016) and can potentially determine several key functional relationships such as that between relative permeability (krw) and water saturation (Sw). A hybrid numerical-experimental approach can furthermore be used to assess the viability of cost-effective computational fluid dynamics within a broad capillary number/wettability parameter space.

While capturing the essential features of fracture rock systems, our experimental models have certain simplifications, especially concerning geometrical design. More specifically,
  1. The porous matrices in the three micromodels are artificially designed as homogeneous pore arrays. Such homogeneity, when coupled with fractures, may affect the flow behavior. This limitation could be improved by replicating the patterns observed in thin sections of fractured rocks.
  2. Although the 2.5D pore models have pore-scale 3D features by having pore-to-pore connections in the third dimension, they are still insufficient to quantify the effects of connectivity in true 3D space. However, two-dimensional micromodels are still capable of serving as diagnostic tools for identifying multiphase flow dynamics phenomena and providing conceptual pictures of them (Armstrong & Berg, 2013; Avraam et al., 1994). The qualitative findings of our work, such as the viscous fingering generation mechanisms shown in Figure 8c are likely applicable for three-dimensional fractured formations. In contrast, our quantitative observations (and microfluidics research in general) are more useful for concluding trends and providing first order approximations for characterizing two-phase flow dynamics. A review of utility of microfluidics (and nanofluidics) in improving predictions of subsurface operations are provided in Mehmani, Kelly, and Torres-Verdín (2019c).
  3. Measurements are all acquired at the inch-long scale restricted by the size of the models. Upscaling by experimental or numerical methods is needed before applying our results to the spatial scales of actual subsurface operations.
  4. The microfracture-porous matrix system is simplified because the fractures are designed to be straight and symmetric through the porous matrices, constant in depth, and to exhibit rectangular cross-sections. Such basic designs could be modified for examining different rock conditions and consequences on multiphase fluid flow.
  5. This work explores phenomena at various macroscopic capillary numbers which is linked to the competition between the length scale of the capillary dispersion zone and the length scale of the observed domain (Armstrong et al., 2014; Berg & Ott, 2012) while the viscosity ratio was kept constant. It is also of great interest to systematically change the viscosity ratio and study the corresponding effects on fluid flow for various fracture rock systems. Future work may consider a wider capillary number, viscosity ratio, and wettability parameter space to provide insight into the validity of both macroscopic and microscopic dimensionless parameters in fractured systems. The onset of front instability and capillary desaturation (which has been computed for homogenous rocks by Oughanem et al. (2015) and Hilfer et al. (2015)) can be determined thereafter when channeling due to microfractures is present. Whether the presence of microfractures is of great influence in the competition of the two length scales (capillary and viscous length scales), and whether microfractures introduce a critical third length scale, remain in question and require additional work.
  6. Micromodels were chosen instead of nanomodels due to their low cost, tractable fabrication steps, and strong visualization ability to complete the systematic experimental research effort described in this paper (18 flooding experiments in total). Results obtained from our investigation are therefore suitable for formations with micrometer-scale pores (such as aquifers and certain multiscale tight formations). However, our results can be extended to nanoporous systems such as mudrocks, in order to decouple the impact of pore topology from nanoconfinement effects on fluid phase distributions and oil/NAPL recovery.

4 Conclusions

While relatively large conduits such as fractures enhance single-phase flow in rocks, the impact of their properties on multiphase flow (a more common subsurface condition) remains unclear. Controlled microfluidic experiments yielded the following insights concerning the combined effect of microfracture connectivity, wettability, and capillary number on oil recovery:
  1. Three distinct viscous fingering generation mechanisms in the presence of microfractures were identified. The dominance of each mechanism depends on both microfracture connectivity and capillary number. Wettability does not affect the conceptual pictures for the generation of fingering dendrites.
  2. Each dendrite generation mechanism affects front morphology, oil ganglia number, and, ultimately, oil recovery depending on capillary number and wettability conditions.
  3. A connected microfracture has the most influence in (1) suppressing oil recovery, (2) dendrite coalescence, and (3) oil ganglia generation. However, this influence decreases beyond a threshold capillary number between 10−5 and 10−4.
  4. Despite confirming a unique dendrite generation mechanism, dead-end microfractures have only minor impact on oil recovery under water-wet conditions.

Overall, our experimental observations (1) challenge the single-phase conceptual picture that microfracture connectivity necessarily improves recovery, and (2) highlight the complexity of multiphase transport within microfractures. The systematic experimental data presented in this paper provide benchmarking opportunities for mechanistic models and shed valuable insight for the development of reliable conceptual pictures of two-phase flow in spatially complex fractured rocks.


  • (D)NAPL
  • (dense) nonaqueous phase liquid
  • Ca
  • capillary number
  • M
  • viscosity ratio
  • So
  • oil saturation
  • 2D
  • two dimensional
  • 2.5D
  • two and a half dimensional: throats are shallower than pores in the micromodel
  • 3D
  • three dimensional
  • Qw
  • injection rate (μL/hr)
  • μw
  • water viscosity (cp)
  • W
  • micromodel width (cm)
  • D
  • pore depth (μm)
  • γ
  • interfacial tension (mN/m)
  • krw
  • water relative permeability
  • Sw
  • water saturation
  • c
  • Darcy velocity (m/s)
  • µi
  • viscosity of invading phase (cp)
  • µd
  • viscosity of displaced phase (cp)
  • Df
  • fractal dimension
  • Acknowledgments

    Use of The University of Texas at Austin's Center for Nano and Molecular Science cleanroom was vital to this work, and we thank the Welch Foundation for supporting those facilities. We would like to thank the sponsors of the Chemical EOR Industrial Affiliates Research Project at the University of Texas at Austin for their support. This research was furthermore supported by the University of Texas at Austin's Research Consortium on Formation Evaluation, sponsored by Anadarko, Aramco, Baker Hughes, BHP Billiton, BP, Chevron, ConocoPhillips, COSL, DEA, ENI, Equinor ASA, Exxonmobil, Halliburton, INPEX, Lundin-Norway, Nexen-CNOOC, Oil Search Alaska, OXY, Petrobras, Repsol, Schlumberger, Shell, Southwestern Energy, TOTAL, Woodside, and Wintershall. Carlos Torres-Verdín is thankful for the financial support provided by the Brian James Jennings Memorial Endowed Chair in Petroleum and Geosystems Engineering. Data generated for this paper can be accessed from Texas Data Repository (https://dataverse.tdl.org/dataverse/Du_Mehmani_et_al_WRR_2020).