Calvin Lumban
Gaol
*a,
Jonas
Wegner
b and
Leonhard
Ganzer
a
aInstitute of Subsurface Energy Systems, TU Clausthal, Agricolastrasse 10, 38678, Clausthal-Zellerfeld, Germany. E-mail: calvin.lumban.gaol@tu-clausthal.de; leonhard.ganzer@tu-clausthal.de; Fax: +49 5323 72 99 3910; Tel: +495323722449
bHOT Microfluidics GmbH, Am Stollen 19, 38640, Goslar, Germany. E-mail: jwegner@reservoirsolutions.com; Tel: +4915142440739
First published on 11th May 2020
Although the application of microfluidics is not new in the petroleum industry, the upscaling of fluid flow behavior from micromodels to reservoir rocks is still challenging. In this work, an attempt to close the gaps between micromodels and reservoir rocks was performed by constructing micromodels based on the X-ray micro-computed tomography (μCT) images of a Bentheimer core plug. The goal of this work was to build a digital 3D model of reservoir rocks and transfer its rock properties and morphological features such as porosity, permeability, pore and grain size distribution into a 2D microfluidics chip. The workflow consists of several steps which are (1) rock property extraction from a μCT image stack of the core plug, (2) micromodel pore structure design, (3) lithographic mask construction and (4) fabrication. Flooding experiments, including single- and two-phase flow experiments, were performed to confirm the micromodel design. As a result, the real structure micromodels show similar rock properties, as well as a comparable fluid flow behavior, to those of the Bentheimer core plug during typical water flooding and EOR polymer application. This framework demonstrates the potential for the general applicability of micromodels to support EOR studies on a larger scale, such as those on sandpacks or core plugs before field implementation.
The pore structure and surface characteristics of microfluidic chips or micromodels need to be analogous to those of real rocks so that a relationship between them can be established. Reservoir rocks typically contain various minerals, and until now, micromodels have been generally fabricated with homogeneous materials (i.e., silicon, glass, or polymers). Several studies have investigated surface modification techniques for micromodels to mimic the surface characteristics of reservoir rocks.20,21 Wang et al. (2017) and Yun et al. (2020) developed a nanofabrication process to homogeneously cover the original surface (silica) of micromodels with calcium carbonate (CaCO3). Their result showed that the modified chips could be used to investigate EOR methods for carbonate reservoirs. Moreover, the pore structure is one main factor that governs fluid flow behavior in reservoir rocks. The pore structure is generally quantified with several properties such as porosity and permeability as well as pore and grain size distribution. It is crucial to design micromodels that have the same rock properties as reservoir rocks. Therefore, this paper focuses on constructing a digital 3D image of reservoir rocks and transferring its properties/morphology into micromodels. However, modifications of the surface characteristics of the micromodels are not covered in this work.
Karadimitriou and Hassanizadeh (2012)22 classified micromodel pore structures into regular models (entirely and partially), irregular patterns and fractal patterns. Regular micromodels are generally constructed with identical grains where they can be distributed randomly or in specific patterns.5 Gunda et al. (2011)23 and Wu et al. (2012)24 used Delaunay triangulation and Voronoi tessellations, respectively, to generate an irregular network for the micromodels. Additionally, Cheng et al. (2004)25 and Nolte et al. (1989)26 designed and constructed micromodels based on flow area fractions (fractal geometry) of SEM micrographs. All of these patterns can be designed to reproduce the basic properties of reservoir rocks, such as porosity and permeability. However, little attention has been paid to the direct comparison between all rock properties of micromodels and reservoir rocks. Therefore, in this work, the pore structure of micromodels was designed based on μCT images of a Bentheimer core plug; thus, their rock properties can be compared before the fabrication process.
Conventionally, the properties of reservoir rocks can be measured directly in laboratories. Nowadays, with the availability of high-resolution imaging techniques such as microscale X-ray computed tomography (μCT), focused ion beam scanning electron microscopy (FIB-SEM) or nuclear magnetic resonance (NMR), the rock properties can be computed by using the digital rock physics (DRP) methodology.27 In this work, the DRP approach was used to extract rock property information from μCT images of a Bentheimer core plug; subsequently, these properties were used to design the pore structure of micromodels. This pore structure was then etched on a silicon material sealed with glass layers to enable direct optical visualization during experiments. Several studies have reported the advantages of glass–silicon–glass micromodels for enhanced oil recovery (EOR) experimental studies.5,28,29
It is generally accepted that a high degree of heterogeneity in reservoirs can cause poor oil displacement efficiency. When the permeability of the rocks is significantly different, the displacing fluid only flows through the high-permeability zone while the low permeability zone remains unswept. To mimic this condition, we constructed heterogeneous micromodels with two different permeability zones (low and high permeability). Afterward, we performed single- and two-phase flooding experiments to confirm the capability of the micromodels. Furthermore, one example of EOR application (polymer flooding) was performed to investigate the oil sweep efficiency improvement in heterogeneous porous media.
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Fig. 1 (a) An image of the Bentheimer sandstone core plug; (b) a 2D cross-section μCT image of the same sample with a resolution of 5 μm (c) a 3D μCT image stack after binary segmentation. |
Pore and grain size distributions are critical parameters that affect fluid flow in porous media. A maximal ball algorithm was used to estimate the pore and grain size distribution of the image stack. This approach was performed by assigning virtual spheres to all voxels and calculating the maximum radii of the spheres. The radii of the spheres were estimated based on the distance from the sphere's center to the closest grain points.32
Another main rock property that also influences the fluid flow behavior in porous media is tortuosity. This property describes the ratio of the shortest geometric flow path to the actual straight-line length of the porous media.33 In this study, a percolation path algorithm was used (Math2Market GmbH) to estimate the tortuosity of the image stack. By defining a sphere with a specific diameter, the shortest path length for the sphere to pass through the porous media can be estimated. Furthermore, pore-network modeling also enables the calculation of fluid transport properties such as permeability. Since the fluid flow in oil reservoirs is typically in the laminar regime, therefore, the Stokes–Brinkman approach was used (eqn (1)). A constant pressure drop and no-slip boundary applied on the grain surface of the porous media were used as boundary conditions.
−μΔu + μK−1u + ∇p = f | (1) |
The number and size of pore throats are primary factors that govern the pore size distribution of micromodels. Fig. 3 shows the medial axis extraction from the grain density map with two different structure elements, which resulted in two different amounts of pore throats. As illustrated in this figure, the white areas indicate the local maxima of the grain density map and the medial axis is the watershed ridge-line between them. The number of local maxima depends on the size of structural elements used in the morphology operations. By using a smaller structural element (size = 5 pixels), more maxima were detected (Fig. 3a and c); thus, more pore throats could be extracted compared to the larger structural element (size = 7 pixels, Fig. 3b and d). Furthermore, as indicated in this image, the extracted medial axis has the same dimensions (uniform) at each position in the matrix. This medial axis does not reflect real reservoir rocks where the pore throat size is non-uniform. Therefore, in the next step, the width of the medial axis was adjusted based on the actual distance between the center of the medial axis to the nearest grain pixels.
The algorithm developed in this work enables the design of several micromodel realizations while still accommodating the pore morphology of real rocks. With this algorithm, pore structures with different permeabilities can be easily generated by adjusting the pore throat size. In this work, a total of five ROC realizations were generated, which consist of three homogeneous and two heterogeneous pore structures. The three homogeneous structures, namely “Structure-1, Structure-2 and Structure-3,” have an average permeability of 3.5, 2.0 and 0.8 Darcy, respectively (Fig. 4b–d). Additionally, to facilitate the investigation of oil displacement efficiency, two heterogeneous structures, namely “Structure-A and Structure-B,” were designed with two different zones: low permeability zones at the sides of the micromodels and a high permeability zone in the middle. The difference between these two structures was the permeability in the high-permeability zone. The high-permeability zone of Structure-A and Structure-B was designed to be 2 Darcy and 3.5 Darcy, respectively. For both structures, the low-permeability zones have a permeability of 0.8 Darcy.
After the etching process was finished, the remaining photo-resist material was removed. Afterward, an anodic bonding process was performed to seal the silicon substrate with two transparent glass layers that enable visual access to the porous structure. In this work, Borofloat 33, with a thickness of 0.5 mm and a high degree of flatness, was used. The anodic bonding was performed separately; the first glass was bonded on the top side of the silicon, followed by the second glass, in which two boreholes were powder blasted. Since the grain size of the micromodels was relatively small, there was not enough bonding surface between the silicon and glass materials. Therefore to avoid the contact problem between the materials, the micromodels were baked in an oven at 400 °C and an electric field of 400 V was applied for 9 hours.
The wetting fluid phase used in this study is scientific-subsea-water (SSW) brine, which has a salinity of 35 g l−1 TDS. The oil (non-wetting) is original crude oil from a Romanian oil field which has a viscosity of 14 mPa s at a shear rate of 10 s−1. The interfacial tension (IFT) of the oil and brine is 14.3 mN m−1, which was measured in the laboratory using the Du Noüy ring method. For the EOR application, a commercial polymer (Flopaam 3530) with a molecular weight of 8 million Daltons was used. The concentration of the polymer of 1500 ppm was designed to obtain a mobility ratio close to one. The details of the fluid properties can be seen in Table 1.
Properties at room temperature | Fluids | ||
---|---|---|---|
Crude oil | Brine | Polymer solution | |
Density (kg m−3) | 869 | 1013 | — |
Viscosity at 10 s−1 (mpa s) | 13.82 | 1.1 | 14.02 |
IFT between oil and brine (mN m−1) | 14.29 | — | |
Salinity (ppm) | — | 35![]() |
— |
Polymer concentration (ppm) | — | — | 1500 |
Before the experiments started, the micromodel was saturated with N2 or CO2 to avoid gas bubble formation during the experiments. Injection of distilled water was performed to displace all the gas bubbles, followed by the injection of brine. During this injection, the pressure drop across the micromodel was measured to estimate the absolute permeability. This value will be used to validate the computed permeability of the micromodels. Then, the crude oil was injected into the brine-saturated micromodel at an injection rate of 0.1 μl min−1 equivalent to 1 ft per day Darcy velocity. The oil initialization was conducted until the differential pressure across the micromodel stabilized, followed by higher injection rates (bump rates, e.g., 10–50 ft per day). As the initial oil saturation (Soi) condition was reached, a standard secondary mode of brine flooding was performed to investigate the oil displacement efficiency in the micromodels. The brine was injected at an injection rate of 0.1 μl min−1 into the micromodel. During the brine injection, images of the micromodel were obtained using a camera. The images were then used to estimate fluid saturations inside the chip by using an image processing tool developed in MATLAB. Furthermore, 5 PV of the polymer solution was then injected into the micromodel (tertiary mode) at a similar injection rate (0.1 μl min−1) to investigate the sweep efficiency improvement.
Additionally, all flooding experiments were performed at room temperature and 1 bar(g) backpressure. This backpressure was established to avoid gas bubble formation in the micromodel during the experiments. Based on the pressure test, the fabricated micromodels could operate at a maximum of 25–30 bar differential pressure under atmospheric conditions.
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Fig. 7 (a) Lithographic mask of the heterogenous micromodel Structure-A. (b) Image of the micromodel acquired using a high-resolution camera after fabrication. |
The results of the rock property computations of the Bentheimer core plug are summarized in Table 2. As can be observed in this table, the calculated median pore size of the 3D μCT image stack was about 46.42 μm, with 10% of all the pores having a diameter less than 18.55 μm (D10) while 90% were below 94.46 μm (D90). This result was comparable to the pore size distribution of Bentheimer sandstone that was found in the literature.39–41 Maloney et al. (1990) reported that Bentheimer sandstone might have a broad range of pore size values ranging from 1–140 μm.41 Their results showed that using a visual microscopy technique and an image analysis technique, the median pore diameter of Bentheimer sandstone was in the range of 60 to 140 μm while smaller pore diameter values were obtained based on the mercury intrusion method, which were in the range of 1–60 μm.
Properties | Value | Unit |
---|---|---|
D10/50/90 mean that 10%/50%/90% of all pores have a diameter smaller than the values shown. | ||
Porosity | 0.2341 | [—] |
Pore size | ||
D10 | 18.55 | μm |
D50 | 46.42 | μm |
D90 | 94.46 | μm |
Grain size | ||
D10 | 68.46 | μm |
D50 | 124.10 | μm |
D90 | 180.01 | μm |
Tortuosity in the X direction | 1.11 | [—] |
Tortuosity in the Y direction | 1.12 | [—] |
Permeability, X direction | 3106 | mD |
Permeability, Y direction | 3491 | mD |
Based on the computation, 90% of the grains of the Bentheimer image stack have a diameter less than 180 μm (D90) while the median value was approximately 124 μm (D50). These values were slightly lower than the results reported by Peksa et al. (2015).40 Their results, based on the analysis of 20 thin sections, showed that the median grain size of Bentheimer sandstone was 235 μm while it was 320 μm based on μCT scans.40 Moreover, the calculated tortuosity of the image stack was about 1.11 and 1.12 in the X and Y directions, respectively. These values were comparable with those from the study reported by Kahl et al. (2013) that investigated the pathways of elastic waves through Bentheimer sandstone for the tortuosity estimation. Their result showed a tortuosity of 1.05 both in the X and Y directions.42
As outlined in the methodology, the absolute water permeability of the Bentheimer image stack was calculated based on the Stokes–Brinkman approach. The permeability values of the image stack were 3.1 and 3.5 Darcy in the X and Y directions, respectively. These values were similar to data from the literature.40,43 According to Peksa et al. (2015), the absolute permeability of Bentheimer sandstone can be in the range of 1.4 to 3.09 Darcy based on laboratory measurement techniques such as measurements using a Ruska gas and liquid permeameter or core flooding experiments.40 However, some literature studies also reported variations of Bentheimer sandstone permeability.43 The permeability of Bentheimer sandstone could vary, depending on the environmental conditions during the deposition of the rocks. An extensive study of Bentheimer sandstone with different sedimentation environments was reported by Traska et al. (2013), which showed that the permeability of Bentheimer sandstone could vary in the range of 0.1 to 4.1 Darcy.43
Rock properties | Homogeneous | Heterogeneous | |||
---|---|---|---|---|---|
1 | 2 | 3 | A | B | |
D10/50/90 mean that 10%/50%/90% of all pores have a diameter smaller than the values shown. | |||||
Porosity (—) | 0.245 | 0.212 | 0.177 | 0.192 | 0.202 |
Pore size (μm) | |||||
D10 | 16.97 | 14.32 | 11.52 | 12.21 | 12.66 |
D50 | 40.86 | 34.98 | 28.08 | 31.50 | 35.12 |
D90 | 107.91 | 108.85 | 105.12 | 112.52 | 112.39 |
Grain size (μm) | |||||
D10 | 98.93 | 98.47 | 97.28 | 99.34 | 99.44 |
D50 | 174.13 | 176.48 | 176.86 | 178.15 | 177.39 |
D90 | 240.30 | 244.31 | 249.67 | 254.78 | 253.64 |
Tortuosity in the X-dir. [—] | 1.11 | 1.12 | 1.13 | 1.13 | 1.12 |
Tortuosity in the Y-dir. [—] | 1.09 | 1.09 | 1.11 | 1.10 | 1.10 |
Permeability in the X-dir. (mD) | 3200 | 1762 | 803 | 1123 | 1605 |
Permeability in the Y-dir. (mD) | 3563 | 1974 | 869 | 1237 | 1767 |
Table 3 also shows the properties of heterogeneous Structure-A and Structure-B. As predicted, the rock properties of these structures lie between the properties of the low and high permeability zones. For example, the calculated average permeability of the micromodel Structure-A was ∼1.2 Darcy (Y-direction), where the permeability of the low and high-permeability zones was ∼0.86 and 1.9 Darcy, respectively.
The rock properties of the micromodels show a better relationship with the Bentheimer core plug than other methods from the literature.2,24,44,45 The approach presented in this study allows the construction of pore structures with realistic porosity while still maintaining the connections between pore bodies. Buchgraber et al. (2011) and Gauteplass et al. (2014) reported micromodels based on a thin section of sandstone with porosities close to 50%.2,44 The reason for these high porosity values was to provide flow connections across micromodels. A similar result was also described by Karadimitriou (2013), where the porosities of micromodels generated based on Delaunay triangulation were ∼50%.45
An irregular network micromodel based on Voronoi tessellations constructed by Wu et al. (2012) showed a porosity of 0.11–0.20 and a permeability of 0.42 to 0.55 Darcy.24 However, these micromodels were constructed with uniform pore throats, which were ∼10 μm to connect all the pore bodies. As described previously, this situation most likely does not occur in reservoir rocks; therefore, in this work, the size of pore throats in the micromodels was designed to be non-uniform. Fig. 8 shows the pore size comparison between the Bentheimer image stack and micromodels with uniform and non-uniform pore throats. As can be seen in this figure, the pore size distribution of the non-uniform micromodel Structure-1 was comparable to that of the image stack. The difference between their mean pore diameters was only ∼5 μm. As for the uniform pore throats, the difference from the image stack was noticeable, because the uniform pore throats dominated the distribution. Furthermore, the relationship between the local porosity and permeability of the micromodel was also compared to that of the Bentheimer image stack. As illustrated in Fig. 9, the local porosity–permeability relationship of the micromodel was in agreement with that of the Bentheimer core plug.
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Fig. 8 Comparison between the pore size distribution of the Bentheimer 3D image stack and micromodel structures with uniform and non-uniform pore throats. |
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Fig. 9 Porosity–permeability relationship of the Bentheimer image stack and the micromodel Structure-1. |
As can be observed in Fig. 10a, 100 images were stitched and synchronized to obtain the whole area of the micromodel. Fig. 10b and c show a section of the micromodel during the oil initialization at two different injection rates. As indicated in these images, not all the pores were filled with the oil since there was the presence of connate water (Swc) in the micromodel. Oil injection at a higher rate (0.5 μl min−1 equivalent to 5 ft per day Darcy velocity) was performed to minimize the connate water saturation (Swc). With this procedure, the typical initial oil saturation (Swc) was 79.0 ± 2%.
A standard secondary mode of brine flooding was performed to investigate the oil displacement efficiency in the micromodels. The brine was injected with an injection rate equivalent to 1 ft per day after the oil initialization. Fig. 11 shows a series of micromodel images during the brine flooding experiment. The images presented here were obtained by processing the raw images taken during the flooding experiment. Fig. 11a and b show the state after the oil initialization and at the brine breakthrough time. As illustrated in this image, the water-front in the high permeability zone, as predicted, was significantly ahead than that in the low permeability zones. The results show that the oil recovery factor at the breakthrough time was relatively low at 19.6 ± 4%. At this stage, most of the oil was produced from the high permeability zone and only small fractions were from the low permeability zones. However, even after breakthrough was already reached, oil displacement still can be observed in the low permeability zones (Fig. 11c). Typically, after a two pore-volume (PV) injection of the brine, no significant oil movement was observed anymore. In this study, the injection was performed until 10 PV to reduce the remaining oil saturation (ROS) to the smallest possible amount or close to residual oil saturation (Sor). The oil recovery factor measured after injection of 10 PV was 31.3 ± 2%.
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Fig. 11 Images of the micromodel during brine flooding. Images of the micromodel (a) under initial conditions, (b) at water breakthrough and (c) after ten pore volume injection of brine. |
As a continuation, three polymer flooding experiments were performed after brine flooding (tertiary mode). The oil recovery factor obtained from these experiments is depicted in Table 4. As indicated in this table, after the injection of a 5 PV polymer solution, an additional oil recovery of 4.7% was observed in the whole micromodel. The incremental oil was mainly produced from the low permeability zones (3% to 8%), with only 3% from the high permeability zone. This result indicated that the macroscopic conformance of the flooding process was improved during the polymer flooding.
Parameters | Micromodel area | |||
---|---|---|---|---|
Whole chip | Low perm 1 | High perm | Low perm 2 | |
Initial oil saturation [—] | 0.79 | 0.78 | 0.83 | 0.75 |
RF at breakthrough (%) | 19.65 | 9.02 | 41.78 | 3.56 |
RF after 10 PV brine flooding (%) | 31.34 | 25.60 | 44.48 | 20.87 |
RF after polymer flooding (%) | 36.01 | 29.08 | 47.38 | 28.92 |
ΔRF after polymer flooding (%) | 4.67 | 3.48 | 2.90 | 8.05 |
Fig. 12 shows the oil recovery factor and the differential pressure during brine (secondary mode) and polymer (tertiary mode) flooding experiments in the micromodels. From this figure, it can be seen that the trend of the oil recovery factor during polymer flooding is aligned with the increase in differential pressure. The differential pressure recorded across the micromodel was increased by 300%. This pressure increase was due to a change in the viscosity of the displacing fluid. Since the viscosity of the displacing fluids increased by 15 times (change from brine to polymer), the capillary number of the displacement process increased by only one order of magnitude. Based on the capillary desaturation curve (CDC) analysis, the increment of the capillary number should be higher than two orders of magnitude to mobilize the trapped oil significantly.
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Fig. 12 The oil recovery factor and the differential pressure during brine (secondary mode) and polymer (tertiary mode) flooding experiments in the micromodels. |
The results of flooding experiments show that the absolute permeability of the micromodel matched the simulated values. It was also found that during typical brine flooding experiments (secondary mode), most of the oil was produced from the high permeability zone and only small fractions were from the low permeability zones. This result suggested that the areal sweep efficiency of this micromodel during brine flooding was relatively low; therefore, it is excellent for an investigation of conformance improvement by using polymer, gel or microbial injection. An increase of the oil recovery factor was observed during polymer flooding (tertiary mode), where extra oil was mainly produced from the low permeability zones. This result indicates that an improvement of macroscopic conformance could be obtained in the heterogeneous micromodels.
Furthermore, the results demonstrate the benefits gained from the digital rock physics method for the construction of micromodels and could be used to support EOR studies on a larger scale, for example, sandpacks or core plugs or even for quick EOR screening before field application. Therefore, future work should focus on the direct comparison between the oil displacement efficiency of micromodels and the corresponding core plug to validate the construction workflow. By comparing these two approaches (core plug and micromodel), the differences between them could be quantitatively estimated and beneficial for improving the construction of micromodels.
An important question for future studies is to integrate the presented approach with surface modification techniques to mimic the surface heterogeneity of reservoir rocks. As previously described, several studies have investigated coating processes to cover the silicon materials of micromodels.20,21,46 Extensive research was reported by Saefken et al. (2019), where the surface wettability of silicon and glass micromodels could be altered by coating the silicon and glass materials with trichlorosilane.46 Furthermore, an in situ growing process of a calcium carbonate layer suggested by Wang et al. (2017) and Yun et al. (2020) could be beneficial to obtain micromodels that mimic carbonate reservoir rocks.20,21
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