Magnetic Resonance Imaging 32 (2014) 574–584

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Study of the fluid flow characteristics in a porous medium for CO2 geological storage using MRI Yongchen Song a, Lanlan Jiang a,⁎, Yu Liu a, Mingjun Yang a, Xinhuan Zhou a, Yuechao Zhao a, Binlin Dou a, Abuliti Abudula b, Ziqiu Xue c a b c

Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian, Liaoning 116024, China North Japan New Energy Research Center, Hirosaki University, Aomori City 0300813, Japan Research Institute of Innovative Technology for the Earth, Kizugawa City, Kyoto 6190292, Japan

a r t i c l e

i n f o

Article history: Received 5 September 2013 Revised 22 January 2014 Accepted 24 January 2014 Keywords: CO2 immiscible displacement Velocity Relative permeability CO2 storage MRI

a b s t r a c t The objective of this study was to understand fluid flow in porous media. Understanding of fluid flow process in porous media is important for the geological storage of CO2. The high-resolution magnetic resonance imaging (MRI) technique was used to measure fluid flow in a porous medium (glass beads BZ02). First, the permeability was obtained from velocity images. Next, CO2–water immiscible displacement experiments using different flow rates were investigated. Three stages were obtained from the MR intensity plot. With increasing CO2 flow rate, a relatively uniform CO2 distribution and a uniform CO2 front were observed. Subsequently, the final water saturation decreased. Using core analysis methods, the CO2 velocities were obtained during the CO2–water immiscible displacement process, which were applied to evaluate the capillary dispersion rate, viscous dominated fractional flow, and gravity flow function. The capillary dispersion rate dominated the effects of capillary, which was largest at water saturations of 0.5 and 0.6. The viscous-dominant fractional flow function varied with the saturation of water. The gravity fractional flow reached peak values at the saturation of 0.6. The gravity forces played a positive role in the downward displacements because they thus tended to stabilize the displacement process, thereby producing increased breakthrough times and correspondingly high recoveries. Finally, the relative permeability was also reconstructed. The study provides useful data regarding the transport processes in the geological storage of CO2. Crown Copyright © 2014 Published by Elsevier Inc. All rights reserved.

1. Introduction CO2 capture and storage (CCS) is based on capturing CO2 from large point sources and storing the CO2 instead of freely releasing it into the atmosphere. The process is implemented by either stripping the CO2 from the smokestacks of conventional power stations or by burning the fuel in special ways to produce exhausts of pure CO2. CO2 then is stored under the ground, usually in exhausted oil and gas reservoirs [1] (geological sequestration of CO2). A potential problem with geological sequestration is the leakage of CO2 from such reservoirs. To assess and safely perform such a proposed technique, it is necessary to understand the mechanisms of the interactions of injected CO2 with the original geo-fluids and geo-formation. In addition, understanding the fluid flow process in porous media is important for the geological sequestration of CO2. Recently, high-resolution magnetic resonance imaging (MRI), which is a topographic imaging technique, has been extensively used ⁎ Corresponding author. E-mail address: [email protected] (L. Jiang).

to characterize the properties of porous media [2–6]. For example, MRI was used in analyzing the pore types, producible porosity, pore structure, and spatial disposition of pore-fractures in coals by Kulkarni and Watson [7]. Some studies of fluid flow were performed using the MRI technique. Usually, the porosity was measured using the MRI T2 decay curves of water in a porous medium [8]. However, it is well known that T2 decay curves are not single exponential, due to the distribution of relaxation times related to the pore size distribution. T2 values are strongly dependent on the details of the experiment, i.e., magnetic field strength and the echo time. The measurement of T2 is affected by the susceptibility inhomogeneities [9,10]. Swider et al. [11] used the MRI intensity method to perform a porosity measurement. By choosing a threshold of intensities, the intensity images were changed into binary gated images. Next, the locally varying parameters of porosity and liquid saturation can be calculated. With the intensity method, two-dimensional and threedimensional image data were evaluated to quantify the porosity profiles and the gas/liquid distributions in packed beds. The concept of the relative permeability for two-phase flow is not new [12–18].

0730-725X/$ – see front matter. Crown Copyright © 2014 Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.mri.2014.01.021

Y. Song et al. / Magnetic Resonance Imaging 32 (2014) 574–584

These quantities arise from a generalization of Darcy's law, originally defined for single-phase flow. The relative permeability is used as an input for simulation studies used to predict the performance of the potential strategies for hydrocarbon-reservoir exploitation. The relative permeability is usually determined from flow experiments performed on core samples. The most direct way to measure the relative permeability is by using the steady-state method. In the steady-state method, each experimental run provides only one point on the relative permeability curve (relative permeability vs. saturation). Three-phase flow experiments for determining the relative permeability relationships are very difficult to perform. Measuring fluid saturations in a rock during three-phase steady-state flow experiments was previously virtually impossible until the recent advent of techniques to monitor in situ fluid saturations directly during flow experiments. Sezalinski et al. [19] investigated the stable liquid gas flow of water and SF6 within a packing bed. The velocity images of the gas phase were influenced by the magnetic susceptibility variation between the gas phase and the solid phase of a porous medium. In addition, it was necessary to change the coil without interrupting the flow. The inaccuracies became larger between the changed procedures. Gladden and Gnadon [20] investigated two different two-phase flows involving air/water and air/silicone oil under the same flow conditions and in a vertical pipe. A steady-state core flooding experiment for CO2 and brine was conducted to measure the relative permeability and to obtain a high-resolution data set to study the factors controlling the CO2 saturation distribution. The relative permeability can be calculated from a displacement experiment. Typically, the core is initially saturated with a single-phase fluid. This phase is then displaced by injecting the other phases into the core. Goodfield et al. [21] used the dynamic relative permeability – capillary pressure technique (dyrectSCAL technique) to calculate the ratio of the relative permeability from a displacement experiment. In previous papers [22–25], we presented the application of high-resolution MRI to obtain the pore distribution and the fluid flow in a porous medium. In this study, CO2–water displacement processes were investigated for relative permeability, where the permeability was obtained from velocity images. The study provided useful data regarding the transport processes that occur in CO2 storage. 2. Experimental 2.1. Experimental equipment The experimental setup includes three parts, as shown in Fig. 1. The first part is the MRI system for image acquisition. The MRI experiments were performed using a Varian 400 MHz NMR system (Varian, Inc., Palo Alto, CA, US), comprising a 9.4-Telsa magnet equipped with shielded gradient coils that provides a maximum gradient strength of 50 Gauss/cm and a proton (1H) millipede vertical imaging probe. The acquired MRI raw data were first processed using a Fourier transform and then transferred to local computers. The mean MR signal intensity of image was detected using the data acquisition and image processing software vnmrJ (the Varian software platform for MR-based research, supporting the entire data acquisition and analysis pipeline) embedded in the console of the local computers. The vessel was made of polytef, which was polyimide for the displacement experiments. The vessel was placed in the center of the magnet. The material of the vessel was nonmagnetic, so it did not affect the magnetic signals during the measurements. The porous medium was packed in the inner tube of 15-mm inner diameter and 200-mm length. The maximum working pressure and working temperature are 15 MPa and 343 K, respectively. The images obtained from the bottom of the vessel were used for the calibration of distribution of water, where it is ensured to be accurate. The second part is the water injection system. The water maintained

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at a constant flow rate was injected into the porous medium via a syringe pump (model 260D, Teledyne Isco. Inc.). The back pressure was controlled by the back pressure regulator (model BP-2080-M, JASCO). The temperature was controlled by fluorocarbon oil, which was used because it did not contain hydrogen atoms, circulating in the water jacket of the vessel. Temperatures at the inlet and outlet of the packed beds were measured using thermocouples. The data of the temperature and pressure were transferred into the local computers via the monitoring systems. The last part is the recycling system. The experimental setup was connected via tubes. The material of the tube was paramagnetic, which had negligible effects on the magnetic field. Deionized water was injected into the packed medium from a water reservoir through a copper tube. 2.2. Experimental procedures To ensure that the surfaces of the glass beads are free of air bubbles, the vessel was evacuated and kept for 1 hour, and then was placed in the center of magnet. The porous medium was saturated with water. After being saturated with water, the packed bed was left for 1 hour before the images were acquired. The Cartesian coordinate axes were defined such that positive z corresponded to the water flow direction. First, the porosity is measured by using a standard spin echo sequence. Then, 2D velocity images are obtained for permeability measurement by using a modified spin echo sequence in addition to the velocity gradients in the flow direction [22]. The flow rates used were 0.1 ml/min, 0.3 ml/min, 1 ml/min and 5 ml/min. For a displacement experiment, after being saturated with water, the porous medium was left for some hours. Next, CO2 was injected downward into the porous medium for the displacement process experiments. In this study, a temperature of 298 K and pressure of 6 MPa were selected to ensure gaseous properties for the immiscible displacement process. The immiscible displacement experiments were performed in BZ-02 at 0.01 ml/min, 0.03 ml/min, 0.08 ml/min, 0.1 ml/min, 0.3 ml/min, 0.5 ml/min and 0.8 ml/min. 2.3. Experimental porous medium One quart of glass beads (AS-ONE, Co., Ltd., Japan), BZ-02 (0.177–0.250 mm, average 0.20 mm), was used to simulate the porous medium. The porous medium exhibited a porosity of approximately 0.368, as measured by a traditional method. The traditional method determines the porosity by using the total volume of water and the sample, the density of the glass beads and the dry weight of the sample. The absolute permeability measured using the traditional method is 13.3 Da. Additionally, the BZ-02 sample was a wet porous medium. 3. Results and discussion 3.1. Porosity measurement The characteristics of the glass beads BZ-02 were first investigated. Using MRI technology, the intensity images were transformed into binary images via Images J soft (a public domain Java image processing program inspired by NIH Image for the Macintosh). Next, the porosity φ is defined as: ϕ ¼ V pores =V tot

ð1Þ

ϕ ¼ Npores =Ntot

ð2Þ

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Y. Song et al. / Magnetic Resonance Imaging 32 (2014) 574–584

a

b

Fig. 1. Illustration of (a) experimental setup and (b) the cross-section diagram of the vessel. (1) Thermocouple interface, (2) outlet of circulating fluid, (3) end pieces, (4) sealing O-ring, (5) core plugs, (6) inner tube, (7) high-pressure polyimide tube, (8) porous media, (9) filter screen, (10) pressure pad, and (11) inlet of circulating fluid.

where Vpores is the volume of the pores, and Vtotal is the volume of the total sample. Npores is the number of pixels in the pores, and Ntotal is the number of pixels in the total sample.

The porosity, φ, is simply the fractional volume of all the void spaces inside a porous medium, regardless of whether the voids are interconnected and form a continuous channel throughout the sample.

Fig. 2. (a) 2D images of glass beads BZ-02 in a container filled with water (black/solid, gray/water). (b) MR-segmented image (black/solid, white/water), obtained by the threshold x = 0.00065. (c) Corresponding histogram.

Y. Song et al. / Magnetic Resonance Imaging 32 (2014) 574–584

When considering fluid flow, a more useful quantity is the effective porosity: the volume fraction of the pore spaces that are fully interconnected and contribute to fluid flow through the material, excluding dead-end or isolated pores that are not part of a flow path. Here, the effective porosity also equals to the porosity. Fig. 2a shows the image of a slice of the sample. The intensity distribution shown in Fig. 2b is the segmented image obtained using the threshold x = 0.00065. Fig. 2c is the histogram of the signal intensities. The porosity is 0.38. The range of porosity distribution along the sample Z direction is small, and the mean porosity is 0.375. The bulk porosity measured using the traditional method is 0.368. The traditional method for porosity is determined by the total volume of water and sample, the density of glass bead and the dry weight of the sample. The value of the bulk porosity agrees well with that measured using MRI. In fact, the local porosity measured using MRI may be influenced by the slice selected. Usually, due to wall effects, the porosity on the wall is larger than elsewhere. The wall effects are more obvious for larger diameter glass beads. From the porosity images, the heterogeneous water distribution is clearly observed. This distribution may directly reveal information of the geometric, internal pore structure. These measurements show that MRI has the advantage of providing not only bulk properties but also the local distribution of their properties. Based on the data on pore distribution, it is possible to investigate pore size distribution and the correlation among pore structure parameters in the future. 3.2. Absolute permeability measurement

kA ΔP lμ

ð3Þ

where k is the permeability (m 2), and A is the total cross-sectional area of the porous medium. ΔP is the pressure gradient. μ is the viscosity of fluid, where Q (m 3/s) is the flow rate, and l is the length of the porous medium.

k¼−

ϕvlμ ΔP

and 5 ml/min were used for the permeability measurement. These decreased rates allowed one to track fluid particles all along the sample without loss of information. Fig. 3 shows the velocity field images with 0.1 ml/min, 0.5 ml/min, 1 ml/min and 5 ml/min. Fig. 4 shows histograms of the flow velocity distribution and velocity profile on diameter, which illustrates the heterogeneity of the fluid velocity in a section of the sample. For each flow rate, the axial velocity varied from negative values to rather large ones [22]. The heterogeneous flow distribution also indicates that the pore distribution is heterogeneous. There are some paths for water to flow through the sample. In particular, the phenomenon is obvious in the case of a porous matrix with significant irregular variations, for example sandstone and natural porous media. By differential pressure transducer, the pressure differences are obtained during the flowing process. The permeability calculated according to Eq. (4) is presented in Table 1. Here, l is 200 mm. The pressure difference is measured from the inlet to the outlet of the porous medium. With flow rates of 0.1 ml/min and 0.5 ml/min, the permeability is 28.6 μm 2 and 28.3 μm2, respectively. The measurement for the permeability is in agreement with that of traditional methods. With flow rates of 1 ml/min and 5 ml/min, the permeability is 42.9 μm 2 and 49.6 μm2, respectively. So the accuracy decreases with increasing flow rate. The flow pattern changes with increasing flow rate. The velocity measurements become more difficult to perform with increasing flow rate. The error of the velocity measurement results in the error of the permeability. 3.3. Relative permeability measurement

Absolute permeability is a measure of the ability of a porous material to transmit fluid and is defined by Darcy's law as the proportionality constant relating the flow rate to pressure gradient, Q ¼−

577

Relative permeability is an important characteristic of multiphase flow in porous media. The relative permeability is reconstructed from the results of the analysis of the saturation and velocity. This section describes these stages in detail for saturation data and velocity data in space and time. 3.3.1. Saturation measurement CO2 does not emit a 1H MR signal. Thus, the MR signal intensity reflects the local water saturation. Previous works have confirmed that the MR signal intensity from any local position was proportional to the water content [22]. From the MR intensity images, the saturation of water can be calculated by [22,23]:

ð4Þ

where v is the mean velocity. With the MRI technique, knowing that porosity and fluid flow distribution were measured with good accuracy, permeability was found to be at the Darcy level. The velocity measurements were presented in Song et al. [22]. To obtain a significant pressure gradient, four constant flow rates with 0.1 ml/min, 0.5 ml/min, 1 ml/min

Sw ¼

Ii S Io 0

ð5Þ

where S0 is the initial water saturation before the injection of CO2, and its value is 1. Ii denotes the MR signal intensity at the time i, and I0 denotes the initial MR signal intensity.

Fig. 3. The velocity images measured with MRI with different flow rates: (a) 0.1 ml/min; (b) 0.5 ml/min; (c) 1 ml/min; and (d) 5 ml/min.

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Fig. 4. Velocity distribution and velocity profile on diameter: (a) 0.1 ml/min; (b) 0.5 ml/min; (c) 1 ml/min; and (d) 5 ml/min.

Y. Song et al. / Magnetic Resonance Imaging 32 (2014) 574–584 Table 1 The mean velocity and permeability with BZ-02.

Table 2 Final residual saturation and displacement coefficient.

BZ-02

P (kPa)

V (cm/s)

K (μm2)

0.1 ml/min 0.5 ml/min 1 ml/min 5 ml/min

0.6 2.7 3.6 17.2

0.0226 0.0102 0.0207 0.114

28.6 28.3 42.9 49.6

0.01 0.03 0.08 0.1 0.3 0.5 0.8

The saturation of CO2 is defined as follows: Sg ¼ 1−Sw

  S 1− wr  100% S0

Breakthrough time (min)

Average velocity of water (cm/s)

Residual saturation

Displacement efficiency

36 29 27 26 12 12 10

0.00248 0.00238 0.00254 0.00254 0.00365 0.00373 0.003753

0.165 0.149 0.141 0.113 0.111 0.107 0.105

83.5% 85.1% 85.9% 88.7% 88.9% 89.3% 89.5%

ð6Þ

The water and CO2 saturation distribution along the porous medium is shown in Fig. 5. The displacement efficiency of gaseous CO2 and supercritical CO2 was also estimated using the following equation: E¼

579

ð7Þ

where E is the displacement efficiency, and Swr is the final residual water saturation at the end of the displacement. The final residual saturation and displacement efficiency of different displacement procedures are listed in Table 2. Fig. 5 shows a series of MRI images at flow rates 0.01 ml/min, 0.03 ml/min, 0.08 ml/min, 0.1 ml/min, 0.3 ml/min,0.5 ml/min and 0.8 ml/min. From the changes of the MR signal intensity (Fig. 6), the displacement process is divided into three stages. The first stage is from the beginning of injection to when the CO2 front moved into the FOV (stage OA). During this stage, the water MR signal intensity increases gradually as the water from the region outside FOV is displaced into the FOV. Meanwhile, as the CO2 front moves, CO2 dissolves into the water. With increasing flow rates, the phenomenon of increasing intensity becomes less obvious. The second stage is from when the CO2 front moved into the FOV to CO2 breakthrough

(stage AB). During this stage, the CO2 moves because of fluid viscosity and gravity forces. It is found from this stage that CO2 channeling or fingering fronts are formed. The packed porous medium is not perfectly homogeneous, so the CO2 fills the high-permeability regions when they are accessible to the flow. The low connectivity between the high-permeability regions and the inlet face of the core results in the low CO2 saturation in the high-permeability regions, which is contrary to common expectations. Therefore, some thin channels become established, and the CO2 can run through the channels vertically in a short period. The time of CO2 breakthrough is different for different flow rates. The water MR signal intensity decreases at this stage. Subsequently, the displacement moves into the third stage (stage BC). With the continual injection of CO2, the water MR signal intensity decreases gradually. The MR signal intensity of water becomes stable. For stage AB, the water MR signal intensity decreases linearly. As a result, the average velocity of water can be evaluated. The average velocity of water U w can be expressed as follows: Uw ¼

ΔV w tAφ

ð8Þ

where ΔVw is the variation of water volume, A is the cross-sectional area, φ is the porosity of the porous medium, t is the time during the second stage.

Fig. 5. MRI images of CO2 displacement in BZ-02 at 6 MPa/298 K: (a) 0.01 ml/min; (b) 0.03 ml/min; (c) 0.08 ml/min; (d) 0.1 ml/min; (e) 0.3 ml/min; (f) 0.5 ml/min and (g) 0.8 ml/min.

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So the Eq. (8) can be described as: Uw ¼

Fig. 6. The changes of MR signal intensity in the FOV along the porous media at 6 MPa/298 K.

ΔV w ¼ ΔSw V p

ΔV p ¼ ALφ

ð9Þ

ð10Þ

where ΔSw is the variation of water saturation, Vp is the pore volume, L is the length of the porous medium in FOV, which in this case is 30 mm.

ΔSw L t

ð11Þ

From Fig. 6, we can obtain the values of ΔSw/t for the saturation with the linear portion in relation to the MR signal intensity. The average velocity of water is listed in Table 2. The CO2 saturation distribution at the flow rates of 0.03 ml/min, 0.1 ml/min, 0.3 ml/min and 0.8 ml/min along the FOV is shown in Fig. 7. With the injection of CO2, the CO2 saturation increases gradually from the inlet of the FOV. The saturation distribution directly reflects the displacement process. The processes coincide with the stage OA of Fig. 6. During stage AB, the average CO2 saturation increases sharply and linearly. Subsequently, the CO2 saturation becomes stable during stage BC, indicating that the remaining part remains inaccessible. The final residual water saturation Swr and the displacement efficiency E is presented in Table 2. For a flow rate of 0.01 ml/min, 0.03 ml/min, 0.08 ml/min, 0.1 ml/min, 0.3 ml/min,0.5 ml/min and 0.8 ml/min, the final residual water saturation Swr is 0.165, 0.149, 0.141, 0.113, 0.111, 0.107 and 0.105, respectively, and the displacement efficiency E is 83.5%, 85.1%, 85.9%, 88.7%, 88.9%, 89.3% and 89.5% for a flow rate of 0.01 ml/min, 0.03 ml/min, 0.08 ml/min, 0.1 ml/min, 0.3 ml/ min,0.5 ml/min and 0.8 ml/min, respectively. Finally, we obtained the graph of the water saturation vs. CO2 saturation (Fig. 8). The relationship of water saturation to CO2 saturation is linear (Table 3), with a slope that is nearly 1. It is clear that the water displacement efficiency or the average CO2 saturation depends on the flow rate. At a small flow rate, the breakthrough time is long. The immiscible CO2 flooding increases

Fig. 7. CO2 saturation distribution during displacement process with the following flow rates: (a) 0.03 ml/min; (b) 0.1 ml/min; (c) 0.3 ml/min and (d) 0.8 ml/min.

Y. Song et al. / Magnetic Resonance Imaging 32 (2014) 574–584

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where Ug(z, t) and Uw(z, t) are the local phase velocity of CO2 and water at the position z, respectively, U(t) is the total Darcy velocity, and Uw(z, t) is the fractional flow of CO2 at time t. Fig. 9 clearly shows the distribution of the CO2 velocity. The velocities vary with time along the porous medium. In the injection of CO2, the temperature and pressure were kept constant. However, the temperature of CO2 in the vessel from the inlet and the outlet fluctuated within a range. The temperature fluctuation results in a change of the CO2 volume, thereby causing a change of the CO2velocity. We also obtained the graph of water velocity vs. CO2 velocity (Fig. 10). A linear relationship exists between the water velocity and the CO2 velocity (Table 2); the slope increases as the CO2 flow increases, but when the flow rate is 0.8 ml/min, the slope is small. 3.3.3. Model of the relative permeability The Darcy law in the interpretation methods for the phase velocities is expressed as follows: Fig. 8. Water saturation vs. CO2 saturation during displacement process with flow rates.

the displacement efficiency by raising the capillary number due to the relatively low interfacial tension values between the water and the injected gaseous CO2. Additionally, the CO2 water interface usually becomes unstable, and fingering or channeling occurs when a low viscous fluid (CO2) displaces a high-viscosity fluid (water). This phenomenon causes premature breakthrough of the CO2 to occur, thereby reducing the displacement efficiency of the water. The channeling or fingering phenomenon is of considerable importance in efficiency of displacement operations, especially at high-viscosity ratios. For the immiscible displacement process, the density difference between CO2 and water is small, which causes the problems of poor sweep efficiencies and gravity override. Gravity determines the gravity segregation of water and hence controls the displacement efficiency of the displacement process. So the small density difference results in a low-displacement efficiency. 3.3.2. Velocity measurement In one of our pervious papers [23], we introduced the velocity and saturation of a two-phase fluid during CO2 displacement experiments. Here, we extend the method to investigate the relative permeability. The phase volume per unit cross-sectional area is determined as follows: z

V g ðz; t Þ ¼ ∫0 φðlÞSg ðl; t Þdl

ð12Þ

where φ(l) is the porosity at position l, and Sg(l, t) is the CO2 saturation at position l and time t. According to the relationship between volume and velocity, the following equations can be obtained: inj

U g ðz; t Þ ¼ U ðt ÞF g ðt Þ− U w ðz; t Þ ¼ −

∂V g ðz; t Þ

U α ¼ −κλα

pcw ¼ pg ðSw Þ−pw ðSw Þ

ð14Þ

  1 0 κg ρw −pg λw λg λ λ @1 þ A−κ g w dpcw ∂Sw U g ¼ U ðt Þ λg þ λw Ut λg þ λw dSw ∂z

The viscous-dominant fraction flow function fg, the gravity countercurrent flow function Gg, and the capillary dispersion rate dcpw are defined as Eqs. (18)–(20), respectively: f g ðSw Þ ¼

λg λg þ λw

Y Y Y Y

= = = =

1.00014 − 1.00014X 1−X 1−X 0.995 − 0.9999X

Water velocity (X) vs. CO2 saturation (Y) Y Y Y Y

= = = =

2.356 0.0008 0.0004 0.0056

ð18Þ

  λ λ g w Gg ðSw Þ ¼ g ρw −ρg λg þ λw

dcpw ðSw Þ ¼ −

ð19Þ

λg λw dpcw λg þ λw dSw

ð20Þ

We define the following equation: f g ðSw Þ ¼ f g ðSw Þ þ

g

0.03 ml/min 0. 1 ml/min 0.3 ml/min 0.8 ml/min

ð17Þ

κ G ðS Þ U g w

ð21Þ

so that Ug can be expressed as follows:

Table 3 The saturation and velocity relationship during the displacement. Water saturation (X) vs. CO2 saturation (Y)

ð16Þ

From Eqs. (15) and (16), the local Darcy velocity of CO2 can be expressed as follows:

g

∂V w ðz; t Þ ∂t

ð15Þ

where κ denotes each phase of CO2 and water, U is the local Darcy velocity, λα = κγα/μα is the mobility, κ is the absolute permeability, p is pressure, ρ is the density, g is the gravitational acceleration, κγ is the relative permeability and μ is the viscosity. The capillary pressure is defined in the standard convention by

ð13Þ

∂t

  ∂pα þ ρα g ∂z

− − − −

0.436X 0.908X 0.999X 0.0337X

U g ðz; t Þ ¼ U ðt Þf g ðSw ; U Þ þ κdcpw ðSw Þ

∂Sw ∂z

ð22Þ

For any saturation Sw⁎, the corresponding position in the sand pace can be expressed as a function of time:     Sw z ðt Þ; t ¼ Sw ð23Þ

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Fig. 9. CO2 velocity distribution during displacement process with the following flow rates: (a) 0.03 ml/min; (b) 0.1 ml/min; (c) 0.3 ml/min and (d)0.8 ml/min.

So Eq. (22) can be expressed as follows:        ∂Sw  g   U g z ; t ¼ U ðt Þf g Sw ; U þ κdcpw Sw ∂z z ;t

ð24Þ

 κdcpw ðSw Þ ∂Sw  U g ðz ; t Þ g   ¼ f g Sw ; U þ U ðt Þ U ðt Þ ∂z z ;t

ð25Þ

data. The gradient



∂Sw   are calculated from the MRI saturation ∂z z ;t κdcpw ðSw Þ and intercept f gg(Sw⁎, U) are obtained. Next, U ðt Þ

where Ug(z*, t) and

we separate out information about dcpw(Sw⁎). Eq. (16) can be expressed as follows:

   κ   g  f g Sw ; U i ¼ f g Sw þ Gg Sw ð26Þ Ui The gradient Gg(Sw⁎) and intercept fg(Sw⁎) can also be calculated. The capillary dispersion rate can be estimated from only the in situ phase distribution data and the injection flow rate without the need for additional measurements, such as the pressure drop across the porous medium. Briefly, the dispersion rate dominates the effects of capillarity. The calculated results of the parameter for the displacements in BZ-02 are shown in Fig. 11. Although the profiles are different, their actual profiles are identical. The capillary dispersion rate increases with increasing water saturation. The capillary dispersion rate dominates the effects of capillarity, which was largest at water saturations of 0.5 and 0.6 before finally decreasing. The difference may be caused by the experimental conditions; for example, it was difficult to control the CO2 displacement speed during the test because of the dissolution of CO2 into the water. The results of viscosity-dominated fractional flow and gravity flow function are shown in Fig. 12. The viscosity-dominated fractional flow function varies with the saturation of the water.

The gravity fractional flow reaches peak values at the saturation of 0.6. The fluid distribution is therefore controlled by the combination of viscous, gravity and capillary forces. Gravity override is strongly flow rate dependent and segregates more CO2 and water when the flow rate is low. With a smaller flow rate, the displacement process is affected by the gravity force. The gravity forces play a positive role in downward displacements because they then tend to stabilize the displacement process (i.e., reduce fingering), thereby producing increased breakthrough times and correspondingly high recoveries of the displaced phase. The relative permeability curves (Fig. 13), are determined by solving Eqs. (18), (19) and (26). Laboratory measurements of relative permeability can still have errors if capillary end-effects are not taken into account. The end-effects are known to cause pressure gradients and by extension saturation gradients, resulting in a non-uniform distribution of fluids in the core, particularly at low flow rates. Ignoring this effect may result in the underestimation of the relative permeability of the wetting phase, leading to the attribution of a permeability value for the non-wetting phase to an incorrect saturation value. Although this type of error can be avoided for twophase two-component flows under isothermal conditions, all of the experiments meant to determine the steam and water relative permeability relations reported in the past have not been able to eliminate these errors for two main reasons: 1) measurements of fluid saturations are not easy to perform because the phase change with pressure drop along the core implies that the material balance methods used in isothermal cases are inapplicable and 2) the changing pressure gradients along the core due to the combined effect of the end-effects and changing fractions with phase change generally imply that any average pressure gradient measurement across the core would be different from the actual gradients at the points along the core.

Y. Song et al. / Magnetic Resonance Imaging 32 (2014) 574–584

Fig. 10. Water velocity vs. CO2 velocity during displacement process with the following flow rate: (a) 0.03 ml/min; (b) 0.1 ml/min; (c) 0.3 ml/min and (d)0.8 ml/min.

4. Conclusions In this paper, high-resolution MRI was used to investigate the properties of a porous medium and two-phase fluids flow of CO2 and water in the porous medium. 1) Using the MRI technique, the bulk porosity obtained was homogeneous in the z direction. The porosity measured using the traditional method was 0.368. The mean porosity measured using MRI was 0.375. The mean porosity obtained using MRI agrees well with that obtained using the traditional method. 2) Using the MRI technique, the velocity distribution of water flow in BZ-02 was obtained. The heterogeneous flow distribution also means that the pore distribution is also heterogeneous. The high velocities indicated large pore spaces of high porosity. The high intensity indicated a larger porosity and more fluid. The higher velocity flows were also induced in some regions that were not large pore spaces of the slices. The permeability was calculated from the velocity images. With flow rates of 0.1 ml/min and 0.5 ml/min, the permeability was 28.6 μm 2 and 28.3 μm 2 , respectively. The measurement for permeability was in agreement with the measurements using traditional methods. With flow rates of 1 ml/min and 5 ml/min, the permeability was 42.9 μm 2 and 49.6 μm2, respectively. So the accuracy reduced with increasing flow rate.

Fig. 11. The results of capillary dispersion rate during displacement process in BZ-02.

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Fig. 12. The results of gravity flow function and viscous dominated fractional flow during displacement process in BZ-02.

3) Using the MRI core flood analysis method, the capillary dispersion rate, viscosity-dominated fraction flow and gravity flow function were obtained using the core analysis methods. The capillary dispersion rate dominated the effects of capillarity, which was largest at water saturations of 0.5 and 0.6. The viscosity-dominated fractional flow function varied with water saturation. The gravity fractional flow reached peak values at the saturation of 0.6. The gravity forces played a positive role in downward displacements because they then tended to stabilize the displacement process, thereby producing increased breakthrough times and correspondingly high recoveries of the displaced phase. Next, relative permeability curves of CO2 and water were obtained.

Acknowledgments This study has been supported by the National Natural Science Foundation of China (Grant Nos. 51106019, 51006017, and 50736001), the National Basic Research Program of China (973) Program (Grant No. 2011CB707300), and the National High Technology Research and Development of China (863) Program (Grant No. 2009AA63400). This study has also been supported by the Fundamental Research Funds for the Central Universities.

Fig. 13. The relative permeability curve during displacement process in BZ-02.

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Study of the fluid flow characteristics in a porous medium for CO2 geological storage using MRI.

The objective of this study was to understand fluid flow in porous media. Understanding of fluid flow process in porous media is important for the geo...
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