sustainability Article
Direct Measurement of Static and Dynamic Contact Angles Using a Random Micromodel Considering Geological CO2 Sequestration Mohammad Jafari 1 1 2
*
ID
and Jongwon Jung 2, *
ID
Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, LA 70808, USA;
[email protected] School of Civil Engineering, Chungbuk National University, Chungdae-ro 1, Seowon-Gu, Cheongju, Chungbuk 28644, Korea Correspondence:
[email protected]; Tel.: +82-43-261-2405
Received: 10 October 2017; Accepted: 9 December 2017; Published: 16 December 2017
Abstract: The pore-level two-phase fluids flow mechanism needs to be understood for geological CO2 sequestration as a solution to mitigate anthropogenic emission of carbon dioxide. Capillary pressure at the interface of water–CO2 influences CO2 injectability, capacity, and safety of the storage system. Wettability usually measured by contact angle is always a major uncertainty source among important parameters affecting capillary pressure. The contact angle is mostly determined on a flat surface as a representative of the rock surface. However, a simple and precise method for determining in situ contact angle at pore-scale is needed to simulate fluids flow in porous media. Recent progresses in X-ray tomography technique has provided a robust way to measure in situ contact angle of rocks. However, slow imaging and complicated image processing make it impossible to measure dynamic contact angle. In the present paper, a series of static and dynamic contact angles as well as contact angles on flat surface were measured inside a micromodel with random pattern of channels under high pressure condition. Our results showed a wide range of pore-scale contact angles, implying complexity of the pore-scale contact angle even in a highly smooth and chemically homogenous glass micromodel. Receding contact angle (RCA) showed more reproducibility compared to advancing contact angle (ACA) and static contact angle (SCA) for repeating tests and during both drainage and imbibition. With decreasing pore size, RCA was increased. The hysteresis of the dynamic contact angle (ACA–RCA) was higher at pressure of one megapascal in comparison with that at eight megapascals. The CO2 bubble had higher mobility at higher depths due to lower hysteresis which is unfavorable. CO2 bubbles resting on the flat surface of the micromodel channel showed a wide range of contact angles. They were much higher than reported contact angle values observed with sessile drop or captive bubble tests on a flat plate of glass in previous reports. This implies that more precaution is required when estimating capillary pressure and leakage risk. Keywords: advance contact angle; receding contact angle; static contact angle; dynamic contact angle; CO2 sequestration
1. Introduction Despite all the efforts towards developing renewable energy, fossil fuels are still the main source of energy. CO2 emission is an inevitable consequence of fossil fuel combustion. Geological CO2 sequestration has been recently developed as a promising method to decrease anthropogenic CO2 emission. The main idea of this method is to separate CO2 (i.e., CO2 from other gases in main emitters such as fossil fuel-based power plants and other industrial units), transfer it by pipelines or tanks, and finally inject it into underground layers such as depleted oil and gas reservoirs, deep saline aquifers, Sustainability 2017, 9, 2352; doi:10.3390/su9122352
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deep unmineable coal beds, and methane hydrate bearing sediments. This injected CO2 is trapped underground by two short-term mechanisms: structural trapping and capillary (or residual) trapping. In the long-term, two safer mechanisms, solubility trapping and mineral trapping, are activated to trap CO2 underground [1–5]. The two short-term mechanisms are highly important. They are the focus of this work because they guarantee prompt safety of storage. In addition, they can trigger the safer long-term mechanisms. Capillary force is the main factor governing the multiphase flow in porous media along with viscos and inertial forces. Connected CO2 plume is trapped under a sealing caprock by capillary pressure during structural trapping. Disconnected CO2 bubbles are immobilized among rock pores by water/brine for residual trapping as a result of hysteresis and local capillary trapping [6]. Capillary or residual trapping is the more favorable between the abovementioned two short-term storage trappings. In structural trapping, a pileup and thick layer of connected CO2 causes an enormous uplift pressure under a sealing caprock. Any phenomenon affecting the integrity of the sealing caprock layer can dramatically increase the risk of an abrupt leakage. However, in capillary (or residual) trapping, disconnected bubbles of CO2 are immobilized in a distributed form in rock pores by local capillary pressure difference. Thus, capillary (or residual) trapping is much safer than structural trapping. Also, capillary trapping provides more chance for disconnected CO2 bubbles to be dissolved into water/brine, consequently increasing the rate of mineral trapping [7]. The Inter-governmental Panel on Climate Change (IPCC) has also emphasized the importance of capillary (or residual) trapping for safe and economical geological CO2 storage [8]. Wettability is the most crucial factor among various parameters affecting capillary pressure because of its complexity and uncertainty. Wettability is often quantified by measurement of contact angle which is the angle between the water–CO2 interface and rock surface measured through the denser phase (water here). The contact angle can be categorized into different types. If the water–CO2 interface has no motion, the contact angle is called a static contact angle. A dynamic contact angle is measured when the interface has a motion on the solid (i.e., rock or soil) surface and is categorized as receding and advancing based on the direction of the fluids interface. Any value of the abovementioned contact angle should be considered in a CO2 storage process. For example, when CO2 pushes water during initial injection, a receding contact angle should be considered. When some portion of CO2 with density lower than water migrates upward and reaches under caprock and tends to penetrate into the sealing caprock, a receding contact angle should be considered. After completing CO2 injection, water imbibes into the CO2 storage by pressure rearrangement which traps some portion of CO2 as the form of disconnected bubbles. Each side of the CO2 bubble is under advancing or receding condition depending on the direction of bubble motion. Contact angle is under static condition when the motion of the CO2 bubble stops. The pore-scale numerical model of fluids flow provides considerable information, such as fluid configuration during and after injection, capillary breakthrough pressure, and relative permeability. These can be applied to estimate the capacity and safety of a storage. A robust pore-scale numerical model requires knowledge of in situ contact angle in different modes. However, previous models suffer uncertainty originating from the lack of a direct contact angle measurement inside pores [9]. Technical drawbacks have inhibited researchers from measuring the contact angle inside a rock pore directly. For many years, contact angles have been measured indirectly using methods such as capillary rise or pressure measurements using a capillary tube or thin plate filled with powder or bids of a certain material based on Lucas–Washburn and Young–Laplace equations, capillary pressure curves, USBM (United States Bureau of Mines), or Amott methods [10–17]. These indirect methods only yielded a statistical sense of microscopic behavior of rock or soil samples. Values of in-situ contact angles and local capillary pressure are not distinguishable [9]. In a different approach, static and dynamic contact angles have been vastly measured on a flat surface representing a specific mineral surface (i.e., silica, mica, or natural rock) using various methods such as sessile drop, captive bubble, Wilhelmy plate, and dual-drop dual-crystal (DDDC) methods [18–29].
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High discrepancies in contact angles measured in literature have been observed. This is caused by the use of different measurement methods, rock or mineral surface imperfections, and surface cleaning methods [19]. Whether the contact angle on a flat surface can properly represent wettability inside of a porous medium pore has been a great concern. Microscopic roughness and chemical heterogeneity of pore walls originate from different in-situ minerals and curvature of pore walls, making the contact angle measured on a smooth flat surface an unreliable one for pores inside porous media [30]. Lin et al. [31] had shown a good agreement between receding contact angles both on a flat surface and inside a capillary tube for very smooth polymers. However, Li et al. [32] have recently reported that water contact angle on a flat glass sheet can be different from a contact angle inside of a capillary tube with the same material (the inner diameter of the tube ranged from 100 to 1000 µm). The importance of more realistic wettability in predicting multi-phase flow behavior requires the development of new techniques for measuring contact angle at pore-scale level. The recent X-ray computed tomography (micro-CT) method has provided a powerful tool to study pore and micro-scale characterization of rocks and multiphase fluid flow mechanisms, including pore structure morphology and local capillary pressure measurement [33–37]. Using the micro-CT technique, it is really difficult to measure dynamic contact angles due to the slow imaging process [30]. Thus, static contact angles have been measured with rocks, sand packs, and glass bids, showing a wide range of contact angles at pore level. The wide range of static contact angles are due to the following: (1) pore topology, hysteresis, surface chemical and physical heterogeneity, and injection patterns (i.e., drainage and imbibition) [9,30,33,38–40]; (2) relaxation of contact angle [30]; and (3) low resolution of images. Thus, Scanziani et al. [9] have proposed an “effective contact angle” measurement using fluid–fluid interface curvature instead of “true contact angle” at the contact line of fluids and rock surface. When CO2 injection is stopped, the movement of the CO2 interface front stops and a static contact angle can be measured. At this moment, the interface is approaching an equilibrium condition called the relaxation of contact angle [30]. In present study, considering in-situ CO2 flow in porous media, contact angles are directly measured inside pores using a high-pressure micromodel with random pore network pattern. The transparent micromodel provides high resolution observation of fluids interface, and imaging is fast enough to capture dynamic contact angle. To the best of the authors’ knowledge, it is the first pore-scale dynamic contact angle measurement when the interface of the fluids is moving inside the channels of a randomly pattern micromodel. Moreover, the preferential behavior of wetting and non-wetting fluids in occupying different pores and throat size is also observed by the used micromodel which is not achievable with capillary tube measurement. This study is an effort to determine the effect of pore size on wettability in a micromodel with relatively homogenous material and simple geometry in comparison with a real rock core. The results of this study can provide valuable information regarding pore-scale wettability behavior of porous media that can be applied in simulation of two-phase immiscible fluid flow for geological CO2 sequestration or other projects involved with injection of CO2 underground. 2. Materials and Methods 2.1. Micromodel High-pressure microchips (Micronit Microfluidics, Enschede, The Netherlands) with a random network as a micromodel is used. These microchips are made of a borosilicate glass with a network dimension of 20 × 10 mm encompassed in a polymer (PP) cartridge with dimension of 75 × 25 mm. The micromodel consists of two layers of glass with thickness of 1100 and 700 µm. One of these layers is etched with a random pattern of square channels. These channels exist at different widths (47, 67, 87, 107, and 127 µm) with the same depth of 20 µm.
Scientific, NE-1010, Kats Enterprises, Denton, TX, USA) controlling a high-pressure steel syringe (KD Scientific, 2.5 mL) is used to drain and inject water into the micromodel. The stainless-steel syringe is connected to one side of micromodel with a transparent tubing. The high-pressure transparent tubing is used to observe the interface between CO2 and water. On the other side, the micromodel is connected 2017, to a9,precise-high-pressure ISCO pump (500 HP, Teledyne ISCO, NE, USA) by another Sustainability 2352 4 of 17 transparent tubing. A digital camera records a video during fluid injection into the micromodel. Pressure and temperature data are collected by an OMEGA PX309-3kGV pressure transducer (having 2.2. Experimental 20 MPa capacitySet-Up and accuracy of 0.25%) and a T-type (Copper/Constantan, OMEGA, Norwalk, CT, USA)The thermocouple Norwalk, CT,onUSA), respectively. The sensor information is recorded micromodel(OMEGA, is horizontally placed adjustable jack stages. A precise syringe pump (Kats using a data logger. Scientific, NE-1010, Kats Enterprises, Denton, TX, USA) controlling a high-pressure steel syringe (KD Scientific, 2.5 mL) is used to drain and inject water into the micromodel. The stainless-steel syringe 2.3. Experimental Procedure is connected to one side of micromodel with a transparent tubing. The high-pressure transparent tubing is used to observe interface between CO2by and water. 5On other side, the (Mallinckodt micromodel Before starting tests, the micromodel is cleaned injecting mLthe absolute ethanol is connected to a precise-high-pressure pump (500 HP, Teledyne ISCO, NE, USA)inby Baker, ACS reagent grade,) and then 30 ISCO mL deionized water. The micromodel is dried ananother oven at transparent A digitalmicromodel camera records a video in during fluid injection micromodel. 120 °C for 48tubing. h. The cleaned is assembled the system (Figure 1).into COthe 2 is used to flush Pressure and temperature dataair areincollected by an OMEGA PX309-3kGV pressure transducer (having the whole system to remove the micromodel, tubing, and syringe. The syringe is filled with 20 MPa capacity of 0.25%) a T-type (Copper/Constantan, OMEGA, Norwalk, CT, deionized water and andaccuracy connected to the and micromodel. Using the syringe pump, the micromodel is USA) thermocouple (OMEGA, Norwalk, CT, USA), respectively. The sensor information is recorded saturated with deionized water (DI). The ISCO pump is then used to pressurize the system to target using a data pressures (1 logger. or 8 MPa) gradually. The water–CO2 interface is placed in the tubing at the ISCO pump side. The system is left under constant pressure for 24 h to reach thermodynamic equilibrium. 2.3. Experimental Procedure Water is withdrawn with a syringe pump at a constant flow rate of 0.1 μL/min while the pressure remains constant thethe ISCO pump. Water flow-out continued CO2ethanol percolates into the Before startingby tests, micromodel is cleaned by injecting 5 mL until absolute (Mallinckodt micromodel. After CO 2 percolation, water withdrawal continues for ~100 pore volumes. The amount Baker, ACS reagent grade,) and then 30 mL deionized water. The micromodel is dried in an oven ◦ of 120 CO2 C infor the48micromodel represents the drainage CO2 saturation. Water is then at h. The cleaned micromodel is assembled in the system (Figure 1).injected CO2 is into usedthe to micromodel with a constant flow rate ofthe 0.1 micromodel, μL/min which simulates imbibition process.is Water flush the whole system to remove air in tubing, and the syringe. The syringe filled passes throughwater the micromodel and to then the tubing atthe thesyringe ISCO pump side. amount of with deionized and connected thereaches micromodel. Using pump, the The micromodel is remainingwith CO2deionized in the micromodel trapped CO2 used saturation. An inverted microscope is saturated water (DI).represented The ISCO pump is then to pressurize the system to target used to obtain both photo and video from these micromodel channels during the test. Table 1 shows pressures (1 or 8 MPa) gradually. The water–CO2 interface is placed in the tubing at the ISCO pump the different test is conditions in this study. side. The system left underconducted constant pressure for 24 h to reach thermodynamic equilibrium.
Figure 1. 1. Schematic Schematic design design for for contact contact angle angle measurement measurement using using aa micromodel. micromodel. Figure
Water is withdrawn with a syringe pump at a constant flow rate of 0.1 µL/min while the pressure remains constant by the ISCO pump. Water flow-out continued until CO2 percolates into the micromodel. After CO2 percolation, water withdrawal continues for ~100 pore volumes. The amount of CO2 in the micromodel represents the drainage CO2 saturation. Water is then injected into the micromodel with a constant flow rate of 0.1 µL/min which simulates the imbibition process. Water passes through the micromodel and then reaches the tubing at the ISCO pump side. The amount of remaining CO2 in the micromodel represented trapped CO2 saturation. An inverted microscope is used to obtain both photo and video from these micromodel channels during the test. Table 1 shows the different test conditions conducted in this study.
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Table 1. Test condition. Pressure (MPa)
Test
Type Sustainability 1 1 9, 2352 2017, Type 2 8
Temperature (◦ C)
Water Withdrawal Flow Rate (µL/min) During Drainage
Water Injection Flow Rate (µL/min) During Imbibition
CA Measurement Type
21 21
0.1 0.1
0.1 0.1
Static & dynamic 5 of 17 Static & dynamic
Table 1. Test condition.
2.4. Contact Angle Measurement Pressure Temperature Test
(MPa)
Water Withdrawal Water Injection Flow Flow Rate (μL/min) Rate (μL/min) During CA Measurement Type During Drainage (SCAs) are measured from photos or Imbibition videos when the interface has no motion. 21 0.1 0.1 Static & dynamic are measured using paused video when Receding 21 0.1 0.1 the interface Staticis & moving. dynamic (°C)
Static contact angles Type 1 1 Dynamic contact Type 2 angles 8 contact angles (RCA) and advancing contact angles (ACA) are observed when CO2 displaces water 2.4. Contact Angle Measurement and when water displaces CO2 , respectively. The contact angle measured from the prepared pictures Static contact angles measured from photos accuracy or videos when the interfacewas has no using AutoCAD software. The (SCAs) contactareangle measurement by AutoCAD verified by motion. Dynamic contact angles are measured using paused video when the interface is moving. comparingReceding values with results from an image processing software (ImageJ with a plugin function contact angles (RCA) and advancing contact angles (ACA) are observed when CO2 (Contact Angle)). The accuracy and repeatability of contact angle measurement with ImageJ have been displaces water and when water displaces CO2, respectively. The contact angle measured from the prepared pictures using AutoCAD software. The contact angle measurement accuracy by AutoCAD verified in [41,42]. was verified by comparing values with results from an image processing software (ImageJ with a plugin function (Contact Angle)). The accuracy and repeatability of contact angle measurement with 3. Results and Discussion ImageJ have been verified in [41,42].
Figure 2 shows how the RCA and ACA in the micromodel are measured in same channel. When 3. Results and Discussion CO2 displaces water in the micromodel, receding contact angles are observed (Figure 2a). When water 2 shows contact how the RCA and ACA in the micromodel are measured in same channel. Whenwhile the displaces CO2 ,Figure advancing angles are measured (Figure 2b). Images are captured CO2 displaces water in the micromodel, receding contact angles are observed (Figure 2a). When water interface had motion. Pore throat size is 127 µm in Figure 2a. Results show that the advancing contact displaces CO2, advancing contact angles are measured (Figure 2b). Images are captured while the angle is considerably higherPore thanthroat the size receding contact angle in theshow same throat, consistent with interface had motion. is 127 μm in Figure 2a. Results thatpore the advancing contact previous studies The difference between ACA RCA is throat, attributed to the angle is [18,22,43–45]. considerably higher than the receding contact angle in and the same pore consistent withblemishes previous studies [18,22,43–45]. differencethe between ACA and is attributed to the blemishes on non-ideal surfaces which results The in pinning interfaces toRCA the solid surface [46]. Various RCAs on non-ideal surfaces which results in pinning the interfaces to the solid surface [46]. Various RCAs and ACAs at throat size of 47 µm in the micromodel are also shown in Figure 2c,d, respectively. and ACAs at throat size of 47 μm in the micromodel are also shown in Figure 2c,d, respectively.
(a)
(b)
(c)
(d)
Figure 2. Contact angle measurement in the micromodel at pressure of eight megapascals. (a)
Figure 2. Contact angle measurement in the micromodel at pressure of eight megapascals. (a) Receding Receding contact angle at pore throat size of 127 μm; (b) Advancing contact angle at pore throat size contact angle at pore throat size of 127 µm; (b) Advancing contact angle at pore throat size of 127 µm; (c) Receding contact angles at pore throat size of 47 µm; (d) Advancing contact angles at pore throat size of 47 µm.
3.1. Dynamic Contact Angle Pinning effect of a triple line. Figure 3 shows receding and advancing contact angles changing with various pore throat sizes (ranged from 47 μm to 127 μm) at pressure of eight megapascals for Sustainability 2017,tests. 9, 2352 Results show that for the repeated tests, receding contact angles are 6more of 17 two different reproducible compared with advancing contact angles (Figure 3). For example, when the pore throat size is 87 μm, standard deviations of RCA and ACA are ±4° and ±16°, respectively. This could be due 3.1. Dynamic Contact Angle to the pinning effect of a triple line during the imbibition process. Triple line, which is also called Pinning line, effect of triple line. Figure shows receding advancing contactand angles changing three-phase is athe line that the 3three phases of and the liquid, gaseous, solid surfacewith are various pore throat sizes (ranged from 47 µm to 127 µm) at pressure of eight megapascals for two intersected. During movement of the triple line on the solid surface, triple line has the chance to different tests.some Results show thathigher for thesurface repeated tests,and receding angles more reproducible contacts with spots with energy stickscontact to them. This are stoppage of the triple compared with advancing contact 3). For example, when themovement pore throatof size is 87lines µm, line is called pinning effect whichangles affects(Figure the interface shape [20] Faster triple ◦ and ±16◦ , respectively. This could be due to the pinning standard deviations of RCA and ACA are ± 4 observed during the drainage process decreases the chance of pinned triple line compared with effect a triple line the observed imbibitionduring process. Triple line, whichsimilar is also receding called three-phase line, slowerofmovement ofduring triple line imbibition, causing contact angles is the line that the three phases ofslower the liquid, gaseous, and solid surface areduring intersected. During during repeated tests. However, movement of triple line observed the imbibition movement of the triple line on the of solid line has the chance to contacts with some spots process causes stick-slip behavior thesurface, interfacetriple and wider range of the contact angle. Khishvand et with higher energyaand sticks to of them. Thisangles stoppage of the line is process called pinning effect al. [30] havesurface also reported wide range contact during thetriple imbibition using microwhich affects the and interface shapethat [20]roughness Faster movement of triple lines observed during are the the drainage CT tomography indicated and different minerals on the surface main process decreases the variations chance of in pinned triple line compared with slower movement of triple line reasons for such wide contact angles. observed imbibition, causing similar receding contact angles during tests. However, Pore during throat size. Receding contact angles increase with decreasing porerepeated throat size (Figure 3a), slower movement of triple line observed during the imbibition process causes stick-slip behavior of in agreement with previous studies [32,47]. Li et al. [32] have reported that the contact angle increases the interface widertubes rangeare of the contact al. [30] have also reported a wide when smallerand capillary used. Usingangle. X-ray Khishvand CT images, et Tudek et al. [47] have observed that range of contact anglesinduring imbibition process using micro-CT tomography andto indicated that CO2 bubbles trapped smallerthe pores of a sandstone have higher contact angles due local higher roughness on the are thenumerical main reasons for such variations in pressure ofand CO2different in small minerals pores. Results ofsurface pore-network models have wide also shown higher contact angles. advancing contact angle with smaller pore size for a flooded carbonated rock sample [48].
(a)
(b)
Figure 3. 3. Dynamic Dynamic contact contact angles angles during during drainage drainage and and imbibition imbibition processes. processes. (a) Receding contact contact Figure (a) Receding angle, (b) Advancing contact angle. angle, (b) Advancing contact angle.
Receding contact angle (RCA) and advancing contact angle (ACA). Figure 4 shows the average Pore throat size. Receding contact angles increase with decreasing pore throat size (Figure 3a), and standard deviation of RCA and ACA varying with throat size. In this work, both dynamic contact in agreement with previous studies [32,47]. Li et al. [32] have reported that the contact angle increases angles are observed during both drainage and imbibition processes based on the interface direction. when smaller capillary tubes are used. Using X-ray CT images, Tudek et al. [47] have observed that For example, when a trapped CO2 bubble moves from the right side to the left side in the pore throat, CO2 bubbles trapped in smaller pores of a sandstone have higher contact angles due to local higher right and left sides of CO2 bubbles could be at advancing and receding contact angle, respectively pressure of CO2 in small pores. Results of pore-network numerical models have also shown higher (Figure 2). Our results show that RCA is highly reproducible regardless of pore throat size advancing contact angle with smaller pore size for a flooded carbonated rock sample [48]. (Figure 4a). However, ACA shows high discrepancies (Figure 4b). This could be explained by the Receding contact angle (RCA) and advancing contact angle (ACA). Figure 4 shows the average and pinning effect of a triple line [20]. These results imply that the status of interface direction is more standard deviation of RCA and ACA varying with throat size. In this work, both dynamic contact angles are observed during both drainage and imbibition processes based on the interface direction. For example, when a trapped CO2 bubble moves from the right side to the left side in the pore throat, right and left sides of CO2 bubbles could be at advancing and receding contact angle, respectively (Figure 2). Our results show that RCA is highly reproducible regardless of pore throat size (Figure 4a). However, ACA shows high discrepancies (Figure 4b). This could be explained by the pinning effect of a triple line [20]. These results imply that the status of interface direction is more critical for defining
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critical for defining RCA and ACA and it is not true that every contact angle in drainage and imbibition 2017, phase are RCA and ACA, respectively. Sustainability 9, 2352 7 of 17 Moreover, while RCA is almost independent of injection pattern (Figure 4a), ACA shows higher values during the imbibition process than that those measured during the drainage process RCA and ACA it is notearlier, true that contact angle in drainage and imbibition are RCA (Figure 4b). As and mentioned theevery observed slow movement of triple line duringphase the imbibition and ACA, respectively. process results in the pining effect which causes the increase in advancing contact angle.
(a)
(b)
Figure 4. Dynamic contact angles during drainage and imbibition processes. (a) Receding contact Figure 4. Dynamic contact angles during drainage and imbibition processes. (a) Receding contact angle, (b) Advancing contact angle. angle, (b) Advancing contact angle.
3.2. Static Contact Angle Moreover, while RCA is almost independent of injection pattern (Figure 4a), ACA shows higher Static andthe equilibrium Thermodynamically, the equilibrium (ECA) values during imbibitioncontact processangles. than that those measured during the drainagecontact processangle (Figure 4b). can only be measured at a global minimum free energy configuration, while the static contact angle As mentioned earlier, the observed slow movement of triple line during the imbibition process results (SCA) can be measured at anythekinetically condition between in the pining effect which causes increase instable advancing contact angle. advancing and receding configuration, which can be considered as a meta-stable equilibrium configuration [49]. In our 3.2. Static Contact Anglemovement is stopped in two situations. First, before percolation of the fluids micromodel, interface (CO2 or water) into the micromodel (percolation occurs when the front of injected fluids reaches to Static and equilibrium contact angles. Thermodynamically, the equilibrium contact angle (ECA) can the other side of the micromodel), some interfaces stop at smaller pore throats due to higher capillary only be measured at a global minimum free energy configuration, while the static contact angle (SCA) pressure. Second, after percolation, because almost all the injected fluid passes through the can be measured at any kinetically stable condition between advancing and receding configuration, percolation path, other interfaces remain motionless. In any of these situations, static contact angles which can be considered as a meta-stable equilibrium configuration [49]. In our micromodel, interface (SCA) could be measured with the motionless interfaces. However, the system of the micromodel is movement is stopped in two situations. First, before percolation of the fluids (CO2 or water) into under fluid (water or CO2) injection continuously. Thus, the motionless interfaces are not allowed to the micromodel (percolation occurs when the front of injected fluids reaches to the other side of the rest and completely approach ECA. This is the reason for low reproducibility of SCA presented in micromodel), some interfaces stop at smaller pore throats due to higher capillary pressure. Second, Figure 5. Because of different level of relaxation of the interfaces, various mode of interfaces before after percolation, because almost all the injected fluid passes through the percolation path, other stoppage (i.e., receding or advancing), and pinning effect originated from solid surface imperfection, interfaces remain motionless. In any of these situations, static contact angles (SCA) could be measured SCA shows wide range of values for the two different tests and also for each test in any throat sizes. with the motionless interfaces. However, the system of the micromodel is under fluid (water or CO2 ) The range of SCA at each pore throat size is higher than that of equilibrium contact angle (ECA) injection continuously. Thus, the motionless interfaces are not allowed to rest and completely approach measured with CO2 or water droplet on flat surface (i.e., 8° to 45° on silica or glass surface) ECA. This is the reason for low reproducibility of SCA presented in Figure 5. Because of different level [18,22,43,50–52]. of relaxation of the interfaces, various mode of interfaces before stoppage (i.e., receding or advancing), and pinning effect originated from solid surface imperfection, SCA shows wide range of values for the two different tests and also for each test in any throat sizes. The range of SCA at each pore throat size is higher than that of equilibrium contact angle (ECA) measured with CO2 or water droplet on flat surface (i.e., 8◦ to 45◦ on silica or glass surface) [18,22,43,50–52].
Figure 5. Because of different level of relaxation of the interfaces, various mode of interfaces before stoppage (i.e., receding or advancing), and pinning effect originated from solid surface imperfection, SCA shows wide range of values for the two different tests and also for each test in any throat sizes. The range of SCA at each pore throat size is higher than that of equilibrium contact angle (ECA) measured 2017, with9, 2352 CO2 or water droplet on flat surface (i.e., 8° to 45° on silica or glass surface) Sustainability 8 of 17 Sustainability 2017, 9, 2352 8 of 17 [18,22,43,50–52]. Figure 5. Static contact angle for two repeated tests at pressure of eight megapascals.
Static contact angle during drainage and imbibition processes. Figure 6 shows the effect of injection condition (i.e., drainage and imbibition) on average and standard deviation of static contact angle (SCA) measured at pressure of one or eight megapascals. The motionless interfaces before stoppage can be in any dynamic mode of advancing or receding. After stoppage, the shape of motionless interface is close to its dynamic mode before stoppage. Since the majority of interfaces are in receding mode during drainage, most of SCA measured in drainage behave similar to RCA. The results show SCA measured during drainage is increased with reducing pore throat size, similar to the trend observed for RCA. However, because a minority of the interfaces are in advancing mode before stoppage, the trend is not as clear as the RCA trend and reproducibility is lower. In the same way, because majority of interfaces are in advancing mode during imbibition, the value of SCA measured during imbibition is close to ACA. As shown in Figure 6, there are no Figure 5. Static contact angle for two repeated tests at pressure of eight megapascals. distinguishable relations between SCA measured during imbibition process and pore throat size, consistent with ACA results of the present study. Moreover, SCA measured during imbibition are Figure of 6 shows effect of injection Static during drainage and imbibition processes. higher thancontact thoseangle measured during drainage process at pressure one orthe eight megapascals. condition (i.e., drainage and imbibition) on average and standard deviation of static contact angle Khishvand et al. [30] have also observed that contact angle is increased when injection phase is (SCA) measured at pressure of one or eight megapascals. The motionless interfaces before stoppage can switched from drainage to imbibition. be inAccording any dynamic mode of receding. shape of motionless to Figure 6, advancing when pore or throat size isAfter smallstoppage, (i.e., lessthe than 90 μm), the valuesinterface of SCA is close drainage to its dynamic modemeasured before stoppage. the majority interfaces areother. in receding during and those during Since imbibition becomeofclose to each Whenmode CO2 during drainage, most of SCA measured in drainage behave similar to RCA. The results show SCA injection stops, water tends to move back into smaller pore throats due to wetting characteristic [6], measured duringpore drainage is increased reducing size, similar to the trend observed causing smaller throats to mostlywith become underpore thethroat advancing condition. Therefore, SCAs for RCA. However, because a minority of the interfaces advancing mode before stoppage, the measured during both imbibition and drainage processesare areinsimilar to each other when pore throat trend is not as clear as the RCA trend and reproducibility is lower. sizes are small.
(a)
(b)
Figure 6. Average Averageand and standard deviation of static contact angle during & imbibition Figure 6. standard deviation of static contact angle during drainagedrainage & imbibition processes. processes. (a) At pressure of one megapascal, (b) At pressure of eight megapascals. (a) At pressure of one megapascal; (b) At pressure of eight megapascals.
4. Analysis In the same way, because majority of interfaces are in advancing mode during imbibition, the value of SCA measured duringTypes imbibition is close to ACA. As shown in Figure 6, there are no distinguishable 4.1. Comparing Different of Contact Angle relations between SCA measured during imbibition process and pore throat size, consistent with shows the average standardSCA deviation of all contact angles (RCA, ACA, than and SCA) ACAFigure results7 of the present study.and Moreover, measured during imbibition are higher those measured in this study. These results show that SCA, RCA, and ACA have high discrepancies measured during drainage process at pressure of one or eight megapascals. Khishvand et at al.each [30] pore throat size, consistent with previous studies [38,40,47]. Contact angles measured using microhave also observed that contact angle is increased when injection phase is switched from drainage CT with rock cores and beads packs also have a wide range of values due to hysteresis of contact to imbibition. angle,According exposure to time, complex geometry, andsize physical and chemical heterogeneity the surface Figure 6, when pore throat is small (i.e., less than 90 µm), the of values of SCA [38,40,47]. during drainage and those measured during imbibition become close to each other. When CO2 It is stops, important choose a proper among pore various types of to contact angles in order [6], to injection watertotends to move backvalue into smaller throats due wetting characteristic estimate wettability behavior of rock formation and sealing caprock.condition. RCA is the Therefore, lower boundary causing the smaller pore throats to mostly become under the advancing SCAs of contact angle. It can be used to determine injectability and capillary pressure for CO2 injection into
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measured during both Sustainability 2017, 9, 2352
imbibition and drainage processes are similar to each other when pore throat 9 of 17 sizes are small. CO2 storage. RCA should also be considered to determine CO2 resistivity of the caprock (or capillary 4. Analysis pressure at the caprock) using Young–Laplace equation (Equations (3) or (4)). breakthrough Limitations in measuring dynamic contact angle, especially in situ measurement at pore-scale, 4.1. Comparing Different Types of Contact Angle have forced researchers to focus on SCA. However, static contact angle is of minor importance in Figure 7with shows the average andangle standard all contact angles ACA, for andstable SCA) comparison dynamic contact for deviation geologicalofsequestration. SCA(RCA, is suitable measured in this study. These results show that SCA, RCA, and ACA have high discrepancies at each conditions when there is no motion in the interface of fluids. The danger of leakage increases when pore throatto size, consistent with flow previous studies Contact which angles determine measured using micro-CT CO2 starts move. Moreover, regime and [38,40,47]. sweep efficiency, the capacity of with rock cores and beads packs also have a wide range of values due to viscosity hysteresis(or ofmobility) contact angle, storage, depend on dynamic parameters, including capillary number and ratio exposure time,contact complex geometry, physical and [53]. Dynamic angle has anand important role inchemical capillaryheterogeneity number value.of the surface [38,40,47].
(a)
(b)
Figure Figure 7. 7. Average Average and and standard standard deviation deviation of of advancing advancing contact contact angles angles (ACA), (ACA), receding receding contact contact angles angles (RCA), and and static static contact contact angles angles (SCA) (SCA) during during drainage drainage and and imbibition imbibition processes. (RCA), processes. (a) (a) At At pressure pressure of of one megapascal, (b) At pressure of eight megapascals. one megapascal; (b) At pressure of eight megapascals.
4.2. Pressure Effect on Contact Angle It is important to choose a proper value among various types of contact angles in order to estimate Jung and behavior Wan [51]ofhave contact angle increases with theofdepth of the wettability rockreported formationthat andequilibrium sealing caprock. RCA is the lower boundary contact storage. This could result in possible CO 2 leakage. However, RCA is more critical for evaluation angle. It can be used to determine injectability and capillary pressure for CO2 injection into COof2 CO 2 resistivity the caprock mentionedto in determine Section 4.1.CO Figure 8 shows of that RCA at one(or megapascal storage. RCA of should also beasconsidered the caprock capillary 2 resistivity is similar to that at eight megapascals where CO 2 exists as gas or liquid. This implies that the effect breakthrough pressure at the caprock) using Young–Laplace equation (Equations (3) or (4)). of wettability with increased depth of CO 2 storage on the risk of CO 2 leakage can be disregarded. Limitations in measuring dynamic contact angle, especially in situ measurement at pore-scale, However, pore sizes reduce withon theSCA. increase of depth and effective stress in rise of the have forced researchers to focus However, static contact angle is ofresulting minor importance in breakthrough capillary pressure based on Young–Laplace’s equation (Equation (3) or Equation (4)). comparison with dynamic contact angle for geological sequestration. SCA is suitable for stable It is noteworthy effect of temperature is not For comprehensive conditions when that therethe is no motion in the interface of considered fluids. The here. danger ofaleakage increasesstudy, when temperature changingflow the regime CO2 state supercritical should bethe taken into CO2 starts toeffect move.and Moreover, andinto sweep efficiency,condition which determine capacity account. of storage, depend on dynamic parameters, including capillary number and viscosity (or mobility) ratio [53]. Dynamic contact angle has an important role in capillary number value. 4.2. Pressure Effect on Contact Angle Jung and Wan [51] have reported that equilibrium contact angle increases with the depth of storage. This could result in possible CO2 leakage. However, RCA is more critical for evaluation of CO2 resistivity of the caprock as mentioned in Section 4.1. Figure 8 shows that RCA at one megapascal is similar to that at eight megapascals where CO2 exists as gas or liquid. This implies that the effect of wettability with increased depth of CO2 storage on the risk of CO2 leakage can be disregarded. However, pore sizes reduce with the increase of depth and effective stress resulting in rise of the breakthrough capillary pressure based on Young–Laplace’s equation (Equation (3) or Equation (4)).
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2017, 9,that 2352 the effect of temperature is not considered here. For a comprehensive study, 10 of 17 ItSustainability is noteworthy Sustainability 2017, 9, 2352 10 of 17 temperature effect and changing the CO2 state into supercritical condition should be taken into account.
Figure 8. Receding contact angle at pressure of eight megapascals vs. that at pressure of one megapascal. Figure Recedingcontact contact angle at pressure of megapascals eight megapascals vs.pressure that atofpressure of one Figure 8.8.Receding angle at pressure of eight vs. that at one megapascal. megapascal.
4.3. Contact Contact Angle Angle Hysteresis Hysteresis 4.3. 4.3. Contact Angle Hysteresis Potentialmobility mobility 2 bubble. Figure 9 shows a disconnected bubble of CO2 trapped by water Potential of of COCO 2 bubble. Figure 9 shows a disconnected bubble of CO2 trapped by water Potential mobility of CO 2 bubble. Figure 9 shows aside disconnected bubble of CO2 trapped water inside a pore throat. When the pressure the rightside water1) increases gradually and by becomes inside a pore throat. When the pressure atatthe right (P(P water1 ) increases gradually and becomes inside a pore throat. When the pressure at the right side (P water1 ) increases gradually and becomes higher than a threshold value, the CO 2 starts to move toward the left side. At this point, both ACA higher than a threshold value, the CO2 starts to move toward the left side. At this point, both ACA higher than a threshold value, the COand 2 starts to move the left side. At this point, both ACA andRAC RAC could bemeasured measured on right and leftsides sides ofaatoward CO2bubble. bubble. and could be on right left of CO 2 and RAC could be measured on right and left sides of a CO2 bubble.
Figure 9. A disconnected bubble of CO2 trapped by brine capillary or residual trapping. Figure 9. A disconnected bubble of CO2 trapped by brine capillary or residual trapping. Figure 9. A disconnected bubble of CO2 trapped by brine capillary or residual trapping.
The capillary pressure in the right and left interface can be defined as below (Equations (1) and (2), The pressurein inthe theright rightand andleft leftinterface interface can defined below (Equations (1) and The capillary capillary pressure can bebe defined as as below (Equations (1) and (2), respectively). (2), respectively). respectively). P P P (1) Pcapillary (1) 1 = PCO2 − Pwater 1 P P P (1) Pcapillary (2) P Pwater 2 CO2 − P 2 = PP (2) P P P (2) where is the capillary pressure wherePPcapillary1 capillary1 is pressure in in the theright rightwater–CO water–CO interface,Pcapillary2 Pcapillary2 is the the capillary capillary 2 2interface, pressure in leftthe water–CO interface, PCO2 isright the pressure inside bubble, is the pressure in the the is water–CO 22interface, is pressure inside thethe COCO 2 bubble, Pwater1 is the water where Pcapillary1 capillary pressure Pin the water–CO 2 interface, P2capillary2 is Pthe capillary CO water1 2 the water pressure the right(where side (where P isCO the2 pressure in the inside pressure in left water–CO 2 interface, PCO2 isadvances), the pressure inside bubble, water1 isleft the(where water pressure in the thein right side waterwater advances), and Pand water2 iswater2 thethe pressure in the P left inside (where water recedes). pressure in the right side (where water advances), and Pwater2 is the pressure in the left inside (where water recedes). By subtracting water recedes). By subtractingEquation Equation(2) (2)from fromEquation Equation(1), (1),Equation Equation(3) (3)isisresulted. resulted. By subtracting Equation (2) from Equation (1), Equation (3) is resulted. P P P P (3) P P P P (3) From Young–Laplace’s equation: From Young–Laplace’s equation:
P
r 2γ cos ACA r
(5)
By subtracting Equations (4) and (5) from Equation (3): Sustainability 2017, 9, 2352
P
P
2γ cos RCA r
cos ACA
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(6)
According to Equation (6), by an increase of the dynamic contact angle hysteresis (defined as the difference between RCA and ACA), higher water pressure difference is required before CO Pwater (3)2 1 − Pwater 2 = Pcapillary 2 − Pcapillary 1 migration. In other words, mobility of the CO2 decreases as the hysteresis increases. FromFigure Young–Laplace’s 10 presents equation: contact angle hysteresis for dynamic and static contact angles. The hysteresis of the contact angle generally increases with increasing pore throat size. The hysteresis of a dynamic 2γ cos(ACA) (4) Pcapillary contact angle at eight megapascals is lower than that at one megapascal. This implies that the mobility 1 = r potential of a CO2 bubble increases with increasing CO2 storage depth when the pore throat size is constant. However, as the depth of CO2 storage increases, pores throat size decreases due to higher 2γ cos(RCA) Pcapillary (5) effective stress [50]. According to Equation (6), when deeper aquifer site is selected for CO2 storage, 2 = r higher capillary pressure is expected due to smaller pore throat size. However, the negative effect of By subtracting Equations (4) and (5) from Equation (3): lower hysteresis on the contact angle should be considered for the mobility of trapped CO2 bubble. Relative permeability. Relative permeability 2γ is defined as a dimensionless measurement of − Pin = ) −system. cos(ACAThus, (6) [cos(RCA )] water2 effective permeability of Pawater1 phase a multi-phase flow hysteresis of relative r permeability can be observed during the injection of alternate fluids (water and CO2) into porous According Equation (6), by an increase of the dynamic contact angle hysteresis (defined as the media [54]. Theto relative permeability of non-wetting phase (CO 2) during imbibition is known to be difference between RCA and ACA), higher water pressure difference is before 2 migration. lower than that during drainage [55]. This is due to the followingrequired two facts: (1)CO contact angle In other words, mobility of the COACA as the hysteresis increases. 2 decreases hysteresis (the difference between and RCA) influences the relative permeability, implying that Figure 10 presents angle hysteresis dynamic and static contact hysteresis factors affecting contactcontact angle hysteresis such asfor pressure, and pore throat sizeangles. should The be considered of contact angle generally increases with increasing pore throat size. hysteresis of a dynamic to the select the relative permeability in numerical simulation; and (2) theThe presence of trapped noncontact angle at eight megapascals is lower than that at one megapascal. This implies that the mobility wetting phase (CO2) influences the flow path of wetting fluid (water). When trapped non-wetting potential CO2 bubble increasing COwetting depth when poreits throat is 2 storage phase (COof2) aoccupies largerincreases pores, it with causes the injected fluid (water) tothe change flow size paths, constant. as the depth of CO2 storage[56]. increases, duenumerical to higher resulting However, in decreased relative permeability Spiteripores et al.throat [57] size havedecreases performed effective stress [50]. According to Equation (6), when deeper aquifer site is selected for CO storage, 2 modelling of a Water Alternating Gas (WAG) system for CO2 sequestration and shown favorable higher capillary pressure is expected due to smaller pore throat size. However, the negative effect of results for residual trapping due to relative permeability hysteresis by decreasing leakage risk lower hysteresis theaccumulation contact angleofshould be considered for the mobility of trapped CO2 bubble. through loweringonthe CO2 plum under caprock.
Figure 10. Contact angle hysteresis (dynamic contact angle hysteresis = ACA − RCA, static contact Figure 10. Contact angle hysteresis (dynamic contact angle hysteresis = ACA − RCA, static contact angle hysteresis = SCA in imbibition − SCA in drainage). angle hysteresis = SCA in imbibition − SCA in drainage).
Relative permeability. Relative permeability is defined as a dimensionless measurement of effective permeability of a phase in a multi-phase flow system. Thus, hysteresis of relative permeability can be observed during the injection of alternate fluids (water and CO2 ) into porous media [54]. The relative permeability of non-wetting phase (CO2 ) during imbibition is known to be lower than that during drainage [55]. This is due to the following two facts: (1) contact angle hysteresis (the difference between ACA and RCA) influences the relative permeability, implying that factors affecting contact angle hysteresis such as pressure, and pore throat size should be considered to select the relative permeability in numerical simulation; and (2) the presence of trapped non-wetting phase (CO2 ) influences the flow path of wetting fluid (water). When trapped non-wetting phase (CO2 ) occupies
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larger pores, it causes the injected wetting fluid (water) to change its flow paths, resulting in decreased relative permeability [56]. Spiteri et al. [57] have performed numerical modelling of a Water Alternating Gas (WAG) system for CO2 sequestration and shown favorable results for residual trapping due to relative permeability hysteresis by decreasing leakage risk through lowering the accumulation of CO2 Sustainability 2017, 9, 2352 12 of 17 plum under caprock. Sustainability 2017, 9, 2352
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4.4. Comparing Contact Angle of Bubbles on Flat Surface with Contact Angle of the Interfaces Covering Pore Pore Throat Inside 4.4. Comparing Contact Angle of Bubbles on Flat Surface with Contact Angle of the Interfaces Covering Pore Throat Inside Pores Pores Throat Pores InInside the (or water) water) droplet droplet on on aa In the literature, literature, mostly mostly contact contact angles angles have have been been measured measured with with aa CO CO22 (or flat surface. In the same way and with the similar fluid system configuration, static contact angle In the literature, mostly contact have been with a CO2 (or water) droplet flat surface. In the same way and withangles the similar fluid measured system configuration, static contact angleonona surface inside micromodel can be measured (Figure 11). surface. In thethe same way and with the similar fluid system configuration, static contact angle on aflat flat surface inside the micromodel can be measured (Figure 11). a flat surface inside the micromodel can be measured (Figure 11).
Figure 11. Contact angle measurement inside the micromodel on a flat surface of a channel (one Figure 11. Contact angle measurement inside the micromodel on a flat surface of a channel (one Figure 11. Contact angle measurement inside the micromodel on a flat surface of a channel (one megapascal pressure). megapascal pressure). megapascal pressure).
Contact angle of bubbles on the flat surface inside micromodel. Figure 12 shows all type of Contact angle of of bubbles the flat inside micromodel. Figure 12Figure shows type all of angle contact Contact angle bubbles on thesurface flat surface inside covering micromodel. 12all type of contact angles measured inon this study with the interface throat as well asshows contact angles measured in this thewith interface covering throat reveal as wellthat contact angle of small contact angles on measured in thiswith study the interface throat asaswell as contact angle of small bubbles the flat study surface inside micromodels. Ourcovering results a contact angle on the bubbles on the flat surface inside micromodels. Our results reveal that a contact angle on the flat small bubbles on the flat surface inside micromodels. Our results reveal that a contact angle on the flat surface is not directly affected by pore throat size. However, in the Figure 12, the contact angles surface is not directly affected by pore throat However, in the Figure 12, the contact angles of flatthe surface is not affected by pore throat size. However, in the Figure the contact angles of bubbles are directly shown with red dots (this is size. shown against throat size only to12, show the location of the bubbles areare shown with red dots (this of the bubbles shown with red dots (thisisisshown shownagainst againstthroat throatsize sizeonly onlyto toshow showthe the location location of measurement). measurement). measurement).
(a) (a)
(b) (b)
Figure 12. Range of contact angle values according to various pore throat sizes. (a) At pressure of one Figure 12. Range of contact angle values according to various pore throat sizes. (a) At pressure of one megapascal; (b) At of eight megapascals. Figure 12. Range ofpressure contact angle values according to various pore throat sizes. (a) At pressure of one megapascal; (b) At pressure of eight megapascals. megapascal; (b) At pressure of eight megapascals.
Average contact angles on flat surface inside micromodel at pressure of one and eight Averageare contact angles on ±flat insideinmicromodel at pressure one and eight megapascals 62° ± 7° and 49° 21°, surface respectively, agreement with Kim et al.of[58] observations megapascals arerange 62° ± of 7° contact and 49°angles ± 21°, from respectively, agreement with micromodel. Kim et al. [58] observations showing a wide 40° to 80°ininside a uniform Contact angles showing a wide in range contact 40° to shown 80° inside a uniform micromodel. Contactbubble angles on a flat surface this of study are angles higher from than those in previous sessile drop or captive on a flat surface in this study are higher than those shown in previous sessile drop or captive bubble tests with large droplet of water or bubble of CO2 (i.e., 8° to 45° on silica or glass surface) [18,22,43,50– testsThis withcould largebe droplet water or bubble CO of CO 2 (i.e., 8° to on 45°aon silica or glass surface) [18,22,43,50– 52]. due toofthe micro-scaled 2 bubble size flat surface inside the micromodel of 52].present This could bein due to the micro-scaled CO2 studies bubble size a flatdimension surface inside the micromodel of the study comparison with the other withon larger of bubble ranging from
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Average contact angles on flat surface inside micromodel at pressure of one and eight megapascals are 62◦ ± 7◦ and 49◦ ± 21◦ , respectively, in agreement with Kim et al. [58] observations showing a wide range of contact angles from 40◦ to 80◦ inside a uniform micromodel. Contact angles on a flat surface in this study are higher than those shown in previous sessile drop or captive bubble tests with large droplet of water or bubble of CO2 (i.e., 8◦ to 45◦ on silica or glass surface) [18,22,43,50–52]. This could be due to the micro-scaled CO2 bubble size on a flat surface inside the micromodel of the present study in comparison with the other studies with larger dimension of bubble ranging from a few to tens of millimeter. Shojai Kaveh et al. [59] have reported that smaller bubbles have higher contact angles in comparison with larger ones as a result of buoyancy force. Previous studies have also shown that contact angles on a flat surface of rocks are smaller than those measured inside rock pores using X-ray tomography method due to gravity and buoyancy [40,47]. These results indicate the important conclusion that glass (or rock) in pore-scale are as water-wet as already recognized by conventional macro-scale measurement. Capillary or residual trapping. In capillary or residual trapping, CO2 bubbles are entrapped inside rock pores by three mechanisms: (1) snap-off, (2) dead-end, and (3) by-passing. In snap-off, when water is invaded into a water-wet media, the water in the corner of a throat will swell gradually until it disconnects the non-wetting phase in the throat and forcibly pushes non-wetting into pore bodies [60,61]. The snap-off trapping mechanism is dominant for water-wet rocks with a high aspect ratio of pore-body diameter to pore-throat diameter [62]. The snap-off mechanism starts when the non-wetting phase (CO2 ) fills the pore throat first. The water layer in the corner then swells by water injection until it completely separates the non-wetting phase (CO2 ) from the rock surface, similar to a bubble resting on a flat surface inside the micromodel as shown in Figure 11. In the dead-end, the non-wetting phase (CO2 ) is trapped in dead-end pores that it carries no flow. By-passing can be defined by a pore-doublet model. When two tubes with different sizes are branched and rejoined, non-wetting fluid is trapped in the larger tube. Thus, wetting phase by-passes the larger tube and passes through the smaller tube. For both dead-end and by-passing trapping mechanisms, the water-CO2 interface covers whole the pore throat. Thus, contact angles measured inside the micromodel can give more realistic values for numerical simulations compared with a contact angle of a bubble/droplet measured on a flat surface. 5. Conclusions Capacity and safety prediction of geological CO2 sequestration require a realistic wettability behavior to model multiphase immiscible fluid flow. In this paper, a new method of pore-scale contact angle measurement was presented. A series of dynamic and static contact angles were determined inside a high-pressure glass micromodel with randomly patterned channels. In addition, contact angles of CO2 bubbles on flat surfaces of micromodel channel were measured for comparison. Results observed in this study are summarized below: (1)
(2)
(3)
Although contact angles are measured inside a highly smooth and chemically homogenous glass micromodel, a wide range of pore-scale contact angles are observed in our results, implying the complexity of the pore-scale contact angle. Thus, higher discrepancy in the contact angle is plausibly expected in real rocks containing various minerals with high roughness, irregular shape pores, and various pore throat sizes. Receding contact angle (RCA) shows more reproducibility than advancing contact angle (ACA) or static contact angle (SCA). This higher reproducibility is observed for each throat size and in repeated tests. The lower reproducibility for ACA and SCA could be due to the pinning effect of the triple line. Both RCA and ACA can occur during both drainage and imbibition processes. RCA shows more reproducibility even during different patterns of injections (i.e., drainage and imbibition).
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(4)
(5) (6)
(7) (8)
(9)
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By decreasing pore size from 127 µm to 47 µm, RCA increases from 11◦ to 26◦ at pressure of eight megapascals and from 9◦ to 30◦ at pressure of one megapascal. Local constrictions increase the pressure inside CO2 bubbles in the small pores resulting in an increase of the interfaces curvature. Generally, SCA during imbibition is higher than SCA during drainage. SCA is close to the dynamic contact angle (receding or advancing) before interface stops. Although SCA is not as reproducible as RCA, it shows an increasing trend with decreasing pore throat sizes from 25◦ to 48◦ at pressure of eight megapascals and from 52◦ to 62◦ at pressure of one megapascal pressure during drainage. RCA and ACA are lower boundaries of contact angles while SCA rests between them. The upper boundary is not as distinct as the lower one due to the pinning effect. Hysteresis of dynamic contact angle (ACA—RCA) is higher at pressure of one megapascal than that at pressure of eight megapascals. A CO2 bubble has higher mobility in larger depths due to lower hysteresis which is unfavorable. However, higher density of CO2 requires its injection in deep depths (800~2000 m). Contact angle of CO2 bubbles resting on the flat surface of the micromodel channel show a wide range from 40◦ to 80◦ . Its average values at pressure of one and eight megapascals are 62◦ and 49◦ , respectively. These contact angles are much higher than those observed with sessile drop or captive bubble test on a flat plate of glass in the literature. Our results are not affected by gravity or buoyancy due to the micro-scale dimensions of the CO2 bubble.
Our measurement method can also be applied in pore-scale models for a wide range of problems involving multiphase fluid flow in porous media, such as enhanced oil/gas recovery and methane extraction from methane-hydrate-bearing sediments. Acknowledgments: This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2017R1D1A3B03031369). Author Contributions: Mohammad Jafari and Jongwon Jung conceived, designed, and performed the experiments. Mohammad Jafari and Jongwon Jung analyzed the data and wrote the paper. All authors read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.
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