Citation Alaamri, J., Chandra, V., Addassi, M., & Hoteit, H. (2023).
Experimental and Numerical Investigation of Spontaneous Imbibition in Multilayered Porous Systems. Energy & Fuels.
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DOI 10.1021/acs.energyfuels.3c01411 Publisher American Chemical Society (ACS) Journal Energy & Fuels
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Experimental and Numerical Investigation of Spontaneous Imbibition in Multilayered Porous Systems
Jamal Alaamri, Viswasanthi Chandra, Mouadh Addassi, and Hussein Hoteit *
Cite This:https://doi.org/10.1021/acs.energyfuels.3c01411 Read Online
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Metrics & More Article RecommendationsABSTRACT:
Spontaneous imbibition is a fundamental fluid flow mechanism that plays a significant role in various applications of multiphase fluid flow in porous media, including oil extraction from subsurface reservoirs and underground carbon dioxide storage.
Understanding the dynamics of imbibition, driven by capillary forces across multilayered systems, is essential for designing and optimizing field applications. Laboratory experiments with the traditional Amott cell, commonly used to quantify the imbibition performance by immersing an oil-saturated core plug in water and measuring the extracted oil, do not fully replicate actual reservoir conditions. Under reservoir conditions, imbibition occurs within
the porous formations across different rock types, while in the Amott cell, imbibition occurs between the rock and the open surrounding water medium. This misrepresentation of field conditions may not replicate the true potential of imbibition. In this study, we use micro-CT and dynamic pore-scale imaging as an alternative approach to visualize and quantify rock-to-rock imbibition within heterogeneous porous media, which cannot be achieved with traditional methods. This work aims at introducing a new concept to evaluate the imbibition mechanism across different porous formations, reflecting the conditions of multilayer systems in the subsurface.
1. INTRODUCTION
Despite recent and significant changes in the global energy portfolio, fossil energy remains the main contributor to energy resources worldwide.
1The current global oil and gas demand triggers searching for feasible recovery-enhancing methods and cost-effective and environmentally friendly practices.
2In addition to developing a new recovery technology, there is a need to revisit current practices to optimize subsurface flow and recovery processes.
In water-flooded oilfields, viscous, gravity, and capillary forces are often the dominant flow mechanisms of hydrocarbons in porous media.
3When developing hydrocarbon fields, each of these mechanisms is taken into consideration, with one mechanism being more important than the others depending on the reservoir conditions. For instance, viscous forces are often dominant in conventional reservoirs, while capillary forces could be pronounced in naturally fractured and layered reservoirs.
4,5The significance of these mechanisms is influenced by geological heterogeneity, which commonly arises from layers of different petrophysical properties influencing the reservoir’s multiphase flow behavior. Misrepresentation of heterogeneity in a reservoir may mislead the estimation of recovery factors and residual oil saturations, thereby resulting in suboptimal reservoir manage- ment decisions.
6,7Capturing the heterogeneity in the exper- imental and numerical models is essential to produce
representative and accurate petrophysical and multiphase flow data.
8,9The process of water flooding is commonly used as a secondary recovery mechanism, where water is injected into the reservoir through a network of injection/production wells developed according to the reservoir quality to displace oil.
10However, some areas remain unaffected due to the hetero- geneity in the reservoirs, which leads to poor sweep efficiency.
3These unswept zones are characterized by low permeability and porosity, where forced imbibition (viscous forces) are ineffective as high permeability zones provide easier pathways for fluid flow, resulting in significant bypassed oil. On the other hand, spontaneous imbibition may play a significant role in extracting oil from low-permeable zones, by acting on the capillarity contrast in the reservoir.
9,11−13Spontaneous imbibition is driven by capillarity relative to the interfacial forces between the immiscible fluids within the porous media.
12It occurs in water- and mixed-wet systems,
Received: April 23, 2023Revised: June 14, 2023
© XXXX The Authors. Published by American Chemical Society
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when the injected water (wetting phase) imbibes into the matrix and forces the oil (nonwetting phase) to expel. This mechanism is crucial to producing the oil from the rock matrix, specifically when the matrix permeability is low. Capillary pressure and relative permeability are the most influential parameters for multiphase flow in porous media. These macroscopic parame- ters are mainly controlled by pore geometry and interfacial forces. Understanding these processes at the pore-scale level is crucial to properly design and optimize the oil recovery scheme.
Many efforts have been dedicated in the literature to determining the capillary pressure and obtaining the relative permeability curves. However, further investigation is necessary to study the behavior of capillary forces at the pore scale in heterogeneous systems.
14−17Researchers have studied spontaneous imbibition exper- imentally, analytically, and through numerical simulation.
18−20Laboratory assessments and research, in general, are studied at different length scales, ranging from the molecular scale to the field scale (Figure 1). The importance of covering a wide range of scales while assessing various phenomena in physics and chemistry in different fields of study triggers more focus on improving the techniques and methodology driving these studies. Lucas and Gardner
21,22used a single-capillary tube experiment to establish an analytical solution for capillary rise.
The Lucas−Gardner equation correlates the height of liquid in the tube to the square root of time. The single capillary tube experiment demonstrates co-current spontaneous imbibition, where the wetting phase is expelled in the same direction as the nonwetting phase. In spontaneous counter-current imbibition, the wetting and nonwetting phases are imbibed and drained in the opposite direction.
18,23The Amott test
24is a commonly used laboratory method to quantify the oil recovery performance through spontaneous imbibition. With this experiment, the rock of interest is saturated with the nonwetting phase (oil) and placed in a glass bottle with a graduated cylinder. The bottle is then filled with the wetting phase (brine), resulting in counter-current flow, where the extracted oil from the rock is measured with time. This experiment is simple to conduct; however, it does not fully replicate the actual field conditions, where imbibition occurs within the porous media, i.e., from one rock type to another.
23,25This poor representation of field conditions may underestimate the full potential of the imbibition mechanism. Moreover, this method is inadequate to capture the micro-scale processes of the counter-current flow dynamics.
26Computed tomography (CT) is a well-known imaging technique that enables a 3D volume reconstruction of the
studied objects. CT scan is a powerful tool to image and extract pore space, which has been used for various industrial applications.
27−34The advancement of X-ray CT techniques has been widely used to uncover the physics of flow dynamics at the pore scale. For instance, Alhammadi et al.
35used the CT scan to describe the variation in imbibition between water-wet and mixed-wet systems. Garing et al.
36measured the capillary pressure and relative permeability curves of a mixed-wet system by X-ray imaging. Chakraborty et al.
37also worked with micro CT to analyze capillary pressure at the pore scale by computing the interface curvatures. David et al.
38studied spontaneous imbibition and its effect on the permeability of shale. David et al.
39tracked the capillary rise front using X-ray and ultrasonic methods and compared them to conventional methods. Gu et al.
40used a medical CT scan to investigate the capillary imbibition flow pattern under the influence of mechanical damage. Lee
41investigated spontaneous imbibition in extra-low permeability sandstone and quantified the effects of imbibition on oil micro-occurrence distribution. Issonov et al.
42inves- tigated the impacts of parametric factors such as flow rates, viscosity, and fracture orientation on capillary imbibition in fractured porous media with the use of the CT scan.
In this work, we propose a novel laboratory concept to study spontaneous imbibition, fully occurring within porous media from one porous formation to another, mimicking crossflow between reservoir layers. We use CT scan and time-lapse in situ imaging to visualize and quantify layer-to-layer imbibition within heterogeneous porous media, which cannot be achieved with traditional methods. We conducted two experiments to study spontaneous imbibition between a set of layers representing the reservoir system: the first experiment represents a homoge- neous-wettability two-layer system where each layer consists of a porous medium with different pore and pore-throat sizes. In the second experiment, we alter the system’s wettability to investigate the effect of wettability variation on imbibition.
Two-phase fluid flow simulations are then used to replicate the experimental results.
2. MATERIALS AND METHODS
2.1. Materials.The porous formation consisted of layers of glass beads with different mesh sizes, purchased from Karmer Industries, Inc.
The beads with various sizes, ranging from fine to extra coarse grades, represent porous media with different capillary pressure, which were used to induce spontaneous imbibition across layers. The glass-bead specifications are described inTable 1.
2.2. Experimental Procedure.We tested several combinations of porous formations initialized with different fluid saturations to evaluate the dynamics of spontaneous imbibition across layers. The setup is Figure 1.Various length scales controlling multiphase fluid flow in porous media.
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made of two layers of different glass-bead mesh sizes, fine and coarse.
The fine-bead layer (layer 1) contains the nonwetting fluid, while the coarse one (layer 2) contains the wetting phase, as illustrated inFigure 2. We also investigated the behavior of crossflow and spontaneous imbibition by altering the system’s wettability.Table 2summarizes the initial conditions and materials used in experiments.
2.2.1. Two-Layer Spontaneous Imbibition with Homogeneous Wettability.We used glass bottles of 1.85 cm internal diameters and 6.80 cm lengths as containers for the layered system. The dimensions of the glass bottle were selected to obtain high-resolution imaging based on the requirements of the X-ray CT scanner. To ensure that no air bubbles were trapped inside the pore space within the glass beads, we first poured the fluids and then added the glass beads.
We tested two combinations of glass beads to examine the effect of particle size in inducing crossflow imbibition between layers. In the first experiment, the difference in mesh sizes between the two layers is high, corresponding to 100/170 mesh size for layer 1 and 40/50 for layer 2. In the second one, the mesh size difference between the two layers was kept small, where layer 1 was 20/30 mesh size, and layer 2 was 40/50.
In both experiments 1 and 2, homogeneous wettability (water-wet) was set using glass in the system. To reduce the buoyancy effect, we modified the densities of the wetting and nonwetting phases to maintain equal densities of both fluids. Decane was diluted with 50 volume (v/v) % of iododecane to match the density of the deionized water. Iododecane also served as a contrasting agent to improve the
imaging resolution between the solid and fluid phases during the CT scan acquisition. Deionized water was doped with red color to visualize fluid redistribution during imbibition. The change in saturation was Table 1. Properties of the Used Glass Beads in This
Experiment
non-Mil grade Mil-Grade mesh size particle size
extra coarse Mil-3 20/30 540−650
coarse Mil-5 40/50 325−425
medium-fine Mil-10 100/170 90−150
Figure 2.Schematic of the experiment container where two layers of different mesh sizes and fluid saturations were set on top of each other.
Fluid imbibition spontaneously occurred across the interface.
Table 2. Summary of Experiments with the Used Materials and Fluids
# name wetting phase nonwetting phase layer 1 layer 2
1 two-layers with homogeneous wettability deionized water 50 v/v iododecane/decane 40/50 20/30
2 same as#1 same as#1 same as#1 40/50 100/170
3 two-layers with heterogeneous wettability 3.75 wt % cesium chloride solution decane 40/50 20/30
Table 3. Properties of the Wetting and Nonwetting Phases
material density, g/cm3 viscosity, mPa s 3.75 wt % cesium chloride solution 1.051 0.99
50 v/v iododecane/decane 0.991 1.60
decane 0.730 0.85
Table 4. Optimized CT Scan Parameters Used in the Three Experiments
experiment voxel size
(μm) exposure time (sec)
tube voltage
(kv) two-layer system with homogeneous
wettability (1 and 2) 25 60 70
two-layer with heterogeneous
wettability (3) 20 65 100
Figure 3.Global thresholding method based on histogram with (a) 2D segmented slice highlighting the four phases with different colors. (b) Histogram based on the fraction of gray value of each phase. The colors represent air (gray), water (blue), glass (yellow), and oil (green).
Global thresholding is based on the quality of the image histogram.
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recorded for 60 h with time-lapse scanning every 7 h to capture the dynamics of fluids in both layers.
2.2.2. Two-Layer Spontaneous Imbibition with Heterogeneous Wettability. In the third heterogeneous wettability experiment, we modified the system’s wall wettability by using a plastic bottle instead of glass. The modified experiment was set to investigate the wall effect on spontaneous imbibition. We used plastic bottles of 50 mL volume and glass beads of sizes 20/30 and 40/50 for layers 1 and 2, respectively. In this experiment, the gravity effect was captured by maintaining the
densities for the two fluids (seeTable 3), corresponding to 3.75 wt % cesium chloride in the aqueous phase and pure decane, as the nonwetting phase. The experiment lasted for 48 h, where CT-imaging data were collected every 7 h.
2.3. CT Scanning and Image Processing.We acquired X-ray CT scans using a TESCAN CoreTOM CT scanner. The scanner has a flat panel detector and an X-ray source, ranging from 30 to 180 kV. Several tube energies, voxel sizes, source-to-detector distances, and metal filters were examined during this study to optimize the CT scan parameters.
The optimized parameters for each experiment are summarized in Table 4.
Image post-processing is an essential step that should be performed before segmentation and data analysis.42Enhancement can be made by applying different filters to improve image quality and reduce artifacts produced during the acquisition and reconstruction processes. Some artifacts can lead to poor segmentation, such as the beam hardening effect. Most of the obtained CT images were of good quality, and the artifacts were insignificant. Some images, especially at smaller voxel sizes, were subjected to some filters. We tested different enhancement filters and found that the median filter fits our purpose better. The median filter replaces the voxel value of the window’s center with the neighboring median value, which preserves the edges and reduces the noise.
Some experiments observed beam hardening artifacts, specifically when a larger diameter holder was used. Beam hardening occurs because the X-ray beam comprises a wide range of photon energies. The dense material absorbs the lower energy photons of the X-ray beam and results in a higher X-ray beam mean value. We corrected some images for the beam hardening effect using the scientific image processing software package, Avizo.43Global thresholding segmentation was used throughout this study.
The global thresholding technique is based primarily on the obtained histogram distribution quality. The sharper separation between peaks Figure 4.Aerial view of the simulation model (left) and a vertical cross-section (right) of the simulation model showing the grid and initial water and oil initialization in the system.
Table 5. Input Parameters Used in the Simulation Model
property value/range unit
grid type 2D radial
grid dimensions 10×1×100
grid size (glass bottle radius) 1.0 cm
grid thickness (glass bottle height) 6.82 cm porosity (random distribution) 0.38−0.41
permeability in layer 1 3000 mD
permeability in layer 2 4000
rock compressibility 3.0×10−6 1/kPa
water compressibility 0.0 1/kPa
oil compressibility 0.0 1/kPa
water formation volume factor 1.0 cm3/cm3
reference pressure 101.325 kPa
oil viscosity 2.0 mPa s
water viscosity 1.0 mPa s
modified oil density 1.0 g/cm3
water density 1.0 g/cm3
initialSWin layer 1 0.0
initialSWin layer 2 1.0
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leads to more accurate thresholding. Using the optimized set of CT scan parameters, sufficient contrast between phases and better histogram distribution were obtained.44Figure 3illustrates the global thresholding for one of the experiments while different colors represent the phases:
air (gray), water (blue), glass (yellow), and oil (green).
Watershed segmentation was employed during image processing to further improve the segmentation results. Watershed segmentation is a region-based method applied to the image morphology.45 In this method, a gradient image is created to provide the topographic landscape of the original image. The landscape determines the minima of each phase and establishes a catchment basin.45In this study, we created gradient images and then identified different markers representing each estimated-phase gray value applied with the watershed algorithm in Avizo software.
2.4. CT-Data Analysis.The produced labeled CT images were further analyzed to estimate the petrophysical properties of the packed glass-bead layers and their corresponding time-varying fluid saturations.
Porosity and pore size distribution were computed to assess the performance of capillarity across the glass-bead layers. The porosity was calculated using the obtained CT scan images of the dry glass beads.
The porosity was calculated by dividing the pore’s labeled voxels by the total number of voxels. Different regions of interest, small to large sizes, were extracted as sub-volumes to identify the variation in porosity. Pore size distribution is calculated based on the equivalent diameter Deq
formula (built-in Avizo software)
= ·
D 6V
eq
3D
(1) whereV3Dis the computed 3D volume of each separated pore. The volume fraction of each phase is determined by dividing the volume of each labeled phase by the total volume. Oil and water saturations were
measured per slice along the domain based on the segmented images, resulting in constructing the time-dependent saturation curves versus length.
We used PerGeos software, from Thermo Fisher Scientific to extract the pore network model (PNM) from CT scan images of the glass beads. PNM is an effective approach used to elucidate the connectivity of the pores by representing them with equivalent geometry.46PNM was constructed in two steps: topological characterization and geometrical characterization.47Then, the extracted PNM was used in simulations to obtain various dynamic properties, including fluid velocity, relative permeabilities, and capillary pressure curves.27
Using the segmented images, we computed the in situ contact angle, θ, between the brine, oil, and solid using an image-processing open- source code.48The code extracts the contact line between the three phases: water, oil, and solid. Then, it defines two normal vectors perpendicular to the fluid/fluid nfluid/fluid and fluid/rock nfluid/rock
interfaces, respectively. The contact angle is then calculated between the two vectors following
= cos (1nfluid/fluid·nfluid/rock) (2) 2.5. Darcy-Scale Simulations. To assess the capillary-induced saturation dynamics in the two layers, we conducted two-phase fluid flow simulations using CMG-IMEX49using a 2D radial grid with 100 simulation cells in theZ-direction along the domain, as shown inFigure 4. We then divided the computational domain (grid) into two zones, corresponding to layers 1 and 2. Layer 1 consists of the fine glass beads, initially saturated in oil (i.e.,So= 1 in Layer 1), and layer 2 consists of the coarse glass beads, initially saturated in water saturation (i.e.,SW= 1 in layer 2).Table 5summarizes the input parameters for the Darcy-scale simulation.
Figure 5.Computed relative permeability curves for layer 1 (top left) and layer 2 (top right) and the corresponding J-function curves for layer 1 (bottom left) and layer 2 (bottom right).
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The relative permeability and capillary pressure curves of the porous layers were computed using the PNM, which are then used in the simulation model to capture the experimental saturation profile (Figure 5). We introduced a modified permeability zone at the layer 1−layer 2 interface to represent the mixing zone of the fine and coarse beads. We also scaled the initially obtainedJ-functions for the different layers using the following equation50,51
= P S
k J S
( ) 31.8316 cos ( )
c W W
(3)
where Pc(SW), in kPa, is the capillary pressure as a function of saturation,σis the interfacial tension in dyne/cm,θis the contact angle in degrees,φis the porosity, andkis the permeability in mD.
3. RESULTS AND DISCUSSION
3.1. Computed Petrophysical Properties.
To assess the variations of properties in the porous media, we considered several regions of interest (ROIs) and measured the change in static and dynamic property for each ROI.
Figure 6shows an example of the porosity measurement at different ROIs for the
Figure 6.Evaluation of the porosity of five different ROI in the 20/30 mesh size layer, showing almost invariant calculated porosity (top-right) for all ROIs.Figure 7.Constructed 3D image of an ROI showing the solid particles and the pore volume (left) and the corresponding PNM (right) representing the pore’s bodies and their interconnections for the 20/30 glass beads.
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layer with 20/30 mesh size. Results show that the porosity range for all the scanned glass beads varied between 35 and 43%, which is within the typical porosity of unconsolidated glass beads, as reported in the literature.
19,313.2. Pore Network Model.
The constructed PNM for the 20/30 mesh glass beads is shown in
Figure 7. The computedaverage pore and pore throat diameters are 144 and 79
μm,respectively.
Figure 8represents the pore equivalent diameter distribution. The average aspect ratio of the pore-to-throat diameter is around 1.8. Using the extracted PNMs, we computed the glass beads’ capillary pressure curves, which represent the driving mechanism for spontaneous imbibition.
52 Figure 9shows the obtained capillary pressure curves for layer 1 (fine beads) and layer 2 (coarse beads). The computed glass beads’
properties, based on the CT scan images, are summarized in
Table 6:3.3. In Situ Contact Angle Estimates.
We measured the in situ water−oil contact angle within different ROIs extracted from the glass bead layers with time.
Figure 10(left) shows an extracted ROI with red and blue labeling for oil and water, respectively.
Figure 10(right) shows the computed contact lines between the solid, oil, and water phases. The contact angle distribution through the contact line is plotted in
Figure 11.Results show that the observed average contact angle is around 72°, which indicates a water-wet system with a Gaussian distribution.
3.4. Two-Layer Spontaneous Imbibition with Homo- geneous Wettability Experiment.
In this experiment, the top layer (layer 1) consists of fine glass beads, resulting in higher capillarity compared to the bottom layer (layer 2), which consists of coarse beads. Driven by capillary forces, spontaneous imbibition took place immediately where the water phase initially saturating layer 1 imbibed into the upper oil-saturated layer, driving the oil to invade the water-saturated layer, following a counter-current flow behavior. As a result, the fluid saturations varied in time and space.
Figure 12shows fluid redistribution within the two layers at different times. One observes that the red-colored water ends in the top layer at the end of the imbibition process.
A segmentation sample with grayscale and colored labeling shows the solid and fluid phases, as presented in
Figure 13. CTscanning at different time lapses highlights the fluid redis- tribution across the two layers, which resulted from spontaneous imbibition, as shown in
Figure 14. We observed that initialimbibition started next to the container walls, which can be attributed to the packing process and the wall effect that might have triggered a distinct flow pathway (Figure 15). We were able to evaluate the saturation profile of the second layer using image segmentation. However, the saturation in the fine-grain layer was not produced at high resolution.
At the early stages, the oil phase imbibed into the lower layer following the percolation pathways corresponding to the large pore throats close to the bottle wall, while the counter-current flow of the water phase took the pore throats corresponding to the narrow pathways. The variations in pathways resulted from the packing process. The change in saturation with time shows that the oil continued to imbibe layer 2 (flowing from layer 1, top to bottom), where it exceeded the water saturation after 20 h.
Figure 16
illustrates the temporal evolution of the oil volume in the bottom layer.
Figure 17shows the average water and oil saturations versus distance in layer 2. We can observe that initially, the saturation of the wetting phase has an average of 0.9 along layer 2. The average saturation decreases with time, and the final saturation approaches 0.14.
3.5. Two-Layer Spontaneous Imbibition with Hetero- geneous Wettability Experiment.
In this experiment, we investigate the wall wettability effect by considering a plastic wall, which is an oil-wet material. Even though the difference in glass beads sizes in the two layers is not relatively significant,
Figure 8.Equivalent pore diameters distribution of 20/30 glass beadsbased on 3D CT images, resulting in an average diameter of 144μm.
Figure 9.Simulated mercury intrusion capillary for the three glass bead mesh sizes considering mercury as the nonwetting phase. The curves are simulated based on the CT scan images.
Table 6. Computed Properties of Glass Beads with Different Particle Sizes
non-Mil grade mesh size CT
porosity % PNM average pore radius
(μm) PNM throat radius
(μm) air absolute permeability
(Darcy) aspect ratio (pore to throat radius)
extra coarse 20/30 35 144 79 367.2 1.8
coarse 40/50 117.63 50.73 147.1 2.3
medium 70/100 39.3 106 43.91 108.44 2.4
medium-fine 100/170 41.5 133.17 65.38 468.22 2.0
fine 170/325 43.2 74.31 30 85.37 2.5
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imbibition took place, as shown in
Figure 18. An imbibitionfront with a concave shape was observed, where the fastest imbibition front was toward the container’s inner part.
Therefore, less imbibition occurred close to the wall, which is attributed to the hydrophobic wettability of the wall. The height of the imbibed water phase with time was calculated and compared with the classical Lucas−Washburn (LW) model, as shown in
Figure 19. The LW equation, relating the imbibitionheight h to time, is given by
=
h t r t
( ) cos
2 (4)
where r is the tube radius in m,
σis the interfacial tension in N/
m,
θis the contact angle in degrees, and
μis the viscosity of the invading fluid in Pa s.
As shown in
Figure 19, the results obtained by the LWequation show good agreement with the experiment. However, there are some variations during the transit period, which could be related to the limitation of the LW model in capturing the inertia. The parameters used in the LW model are provided in
Table 7.3.6. Simulation Model.
We performed several simulations to replicate the experimental saturation profiles versus times. We represented the two layers of different permeabilities and
saturations and a modified permeability at the layer 1
−layer 2 interface, which is expected to occur due to the mixing zone between the two layers, where the small beads fill the big pores in the coarse glass beads. The plot’s distance represents the layer’s distance from top to bottom. Several ROIs from the experimental data were selected at different times and compared to the simulation results.
Figure 20plots the change in the simulated average water saturations versus distance from top to bottom at different times and compared to the experimental data in layer 2 (Figure 20 left), which are in good agreement.
Figure 20(right) shows water saturation maps in the domain cross- section at different times, which demonstrates fluid exchange and counter-current flow between the two layers. We can observe a noticeable deviation in the initial stages between the simulation and experimental results, which can be attributed to the prominent influence of the bottle wall effect on the flow dynamics during the early time period.
Figure 10.Extracted ROI used for the contact angle measurement showing the oil phase in green and the water phase in blue (a). Representation of ROI while showing the contact line between the oil, water, and the solid surface (b). The extracted contact lines used for contact angle measurements (c).
Figure 11.Computed contact angle distribution showing a Gaussian distribution with an average of 78°, indicating a water-wet system.
Figure 12.Photographs from the experiment showing the time lapse of fluid redistribution, where the red-colored phase is water initially saturating layer 1, placed on the bottom of layer 2, which is initially saturated in oil (transparent color). The final condition shows how the wetting phases imbibed into the upper layer, and the nonwetting phase drained into the bottom layer.
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4. CONCLUSIONS
We introduced a new approach to investigate spontaneous imbibition within the porous media across layers. This approach is more representative than traditional methods that measure imbibition of the oil-saturated porous medium surrounded by water. The proposed experiments were successful in demon- strating spontaneous imbibition and crossflow between layers of various properties. Numerical simulations are then used to reproduce the experimental results.
The main findings are summarized as follows:
•
CT scan is an effective technology for evaluating static and dynamic properties of porous media.
•
The measured in situ contact angle from CT images provided a good match with the expected wettability of the fluid−solid systems, which was used to calculate the capillary pressure curves.
•
PNM was used to estimate the oil−water capillary pressure and relative permeability curves of the porous media.
•
Capillary forces between the two layers of glass beads exhibited spontaneous imbibition and redistribution of saturations, which could be observed and quantified.
•
Spontaneous imbibition leads to the redistribution of fluids between layers of different capillarity until it reaches equilibrium. With this mechanism, oil flow occurred in the
Figure 13.Segmentation of layer 2 shown in grayscale (left) and colored (right) where the green color represents decane, blue for water, and yellow for the solid glass beads and the holder.Figure 14.Time lapse showing fluid redistribution at different time intervals due to spontaneous imbibition across the two-layer glass bead system. The brightest phase is the nonwetting phase, glass is less bright, and the wetting phase is the darkest phase.
Figure 15.Oil phase is drained more near the glass wall. (a) ROI shows the glass wall (dark gray), glass beads (light gray), and oil (green). (b) ROI shows the oil (green) drained more toward the glass wall (dark gray) at the initial time. (c) Top view of the ROI emphasizing the drainage near the glass wall.
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large pathways, while water flow occurred through the narrow pathways, reflecting counter-current flow.
•
Simulations were conducted to replicate the experimental results, which showed good agreement between the experiment and the simulation model.
Figure 16.Evolution of oil phase distribution with time in the bottom layer during the imbibition process, where the wall effect is observed at the early time.
Figure 17.Average water saturation versus time in layer 2 (left) and water saturation distribution versus distance in layer 2 at different times, starting from layer 1−layer 2 interface (right).
Figure 18.Initial and final water (blue label) distribution obtained by the CT scan time-lapse experiment, showing the change in the waterfront height.
Other labels are green for oil, yellow for glass beads, and black for the plastic wall.
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•
The proposed approach could be extended to study imbibition across rock samples under reservoir pressure and temperature conditions. However, certain exper- imental challenges need to be considered. One such challenge is the possibility of introducing air when assembling the two pieces of core plugs together. Another challenge is related to the roughness of the ends of the rocks, which plays a crucial role in ensuring maximum contact between the two rocks. It is important to note that the presence of a gap between the two rocks minimizes the crossflow process between the two rocks.
•
While one of this study’s primary objective is to investigate the role of spontaneous imbibition as a driving
mechanism of crossflow in layered formations, the effect of negative part of capillary pressure in oil−wet systems is also important. The results from coreflooding may be different than spontaneous imbibition, as highlighted in a study by Tang and Firoozabadi.
53■
AUTHOR INFORMATION Corresponding AuthorHussein Hoteit−
Physical Science and Engineering Division, Energy Resources and Petroleum Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia;
orcid.org/0000-0002-3900-7272;Email:
[email protected] AuthorsJamal Alaamri−
Physical Science and Engineering Division, Energy Resources and Petroleum Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
Viswasanthi Chandra−
Physical Science and Engineering Division, Energy Resources and Petroleum Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
Mouadh Addassi−
Physical Science and Engineering Division, Energy Resources and Petroleum Engineering, King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.energyfuels.3c01411
Notes
The authors declare no competing financial interest.
Data will be made available on request.
Figure 19.Comparison of the observed and calculated heights of the wetting phase front with time using the Lucas−Washburn (LW) model shows good agreement between the experiment and the model.
Table 7. Input Parameters for the Lucas−Washburn Model
parameter σ(N/m) θ(degrees) μ(Pa s) r(μm)
value 0.040 63 0.01 30
Figure 20.Average water saturation versus time showing comparisons of simulations and experimental data in layer 2 (left) and simulated water saturation distribution in the domain at different times (right).
https://doi.org/10.1021/acs.energyfuels.3c01411 Energy FuelsXXXX, XXX, XXX−XXX K
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