Experimental Investigation of Spontaneous Imbibition in a Tight

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Experimental Investigation of Spontaneous Imbibition in Tight Reservoir with Nuclear Magnetic Resonance Testing Fengpeng Lai, Zhiping Li, Qing Wei, Tiantian Zhang, and Qianhui Zhao Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b01324 • Publication Date (Web): 10 Oct 2016 Downloaded from http://pubs.acs.org on October 10, 2016

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Figure 1 Typical imbibition curves measured by the gas/water/rock imbibition experiments figure 1 209x296mm (300 x 300 DPI)

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Figure 2 Measured T2 distributions of 4 samples: (a) Measured NMR responses before imbibition and after imbibition for core sample 002-3; (b) Measured NMR responses before imbibition and after imbibition for core sample 005-4; (c) Measured NMR responses before imbibition and after imbibition for core sample CQ22; (d) Measured NMR responses before imbibition and after imbibition for core sample 929-30. figure 2 254x142mm (120 x 120 DPI)


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Figure 3 Typical imbibition curves measured by the oil/water/rock imbibition experiments figure 3 146x116mm (300 x 300 DPI)


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Figure 4 Measured T2 distributions of 4 types: (a) Measured NMR responses at different imbibition time for core sample T10B; (b) Measured NMR responses at different imbibition time for core sample T20B; (c) Measured NMR responses at different imbibition time for core sample T23B; (d) Measured NMR responses at different imbibition time for core sample W09B. figure 4 261x148mm (120 x 120 DPI)


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Figure 5 Imbibition recovery of oil/water/rock system under different boundary conditions figure 5 209x296mm (300 x 300 DPI)


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Figure 6 The influence of wettability on gas/water/rock imbibition experiment: (a) The variation of imbibition recovery factor as a function of imbibition time for three core samples with different wettability; (b) Measured NMR responses before imbibition and after imbibition for core sample 430-200g-3; (c) Measured NMR responses before imbibition and after imbibition for core sample 929-39; (d) Measured NMR responses before imbibition and after imbibition for core sample CQ-22. figure 6 262x191mm (120 x 120 DPI)


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Figure 7.a Influence of temperature on the imbibition recovery factor for core samples 006-2 and 006-3. Kerosene is used in all these tests. figure 7.a 144x116mm (300 x 300 DPI)


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Figure 7.b Influence of viscosity on the imbibition recovery factor for core samples 006-1 and 006-4. The test temperature is kept as 20℃. figure 7.b 145x116mm (300 x 300 DPI)


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Experimental Investigation of Spontaneous Imbibition in Tight Reservoir with Nuclear Magnetic Resonance Testing

Fengpeng Lai, Zhiping Li, Qing Wei, Tiantian Zhang, Qianhui Zhao

School of Energy Resources, China University of Geosciences, Beijing 100083, China.

*Corresponding Author: Dr. Fengpeng Lai Assistant Professor, Petroleum Engineering China University of Geosciences, Beijing Phone: 86-10-13401154289 Fax: 86-10-82326850 Email: [email protected]


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Abstract: Hydraulic fracturing is the significant technology for exploiting tight resources. Spontaneous water imbibition is an important mechanism governing the process of hydraulic fracturing, and the water imbibition from the fracture into the matrix is an essential factor that affects the reservoir production performance. In this study, imbibition experiments and nuclear magnetic resonance (NMR) testing were combined to analyze fluid flow tight core samples in a pore-scale level. The imbibition experiments were categorized into two systems, gas/water/rock system and oil/water/rock system. The NMR measurements were performed at different times for these two systems. The relationship between T2 relaxation time, pore radius and pore types were established. Theoretical models describing water imbibition into porous media were used to facilitate the interpretation of the experimental results. The results demonstrate that the volume of imbibed water is large during the early imbibition period, and the imbibition recovery increases rapidly as time proceeds. The volume of imbibed water reaches a constant level at the end of the experiment. The volume of imbibed water in the oil/water/rock experiment is less than that in the gas/water/rock experiment, however, the experiment shows an inverse relation for the duration of the imbibition. For the gas/water/rock system, the water is originally imbibed into micro-pores and small meso-pores present in the natural core samples. There are four types of T2 distributions related to the oil/water/rock imbibition process. Finally, the experimental results indicate the effect of boundary conditions, wettability, temperature and oil viscosity on water imbibition. The oil recovery due to water imbibition for the oil/water/rock is mainly controlled by the capillary force, gravity force and characteristic length of the core sample. Water-wet conditions are more preferable for spontaneous imbibition. Through a detailed study of


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imbibition experiment and NMR testing, significant insight is provided into the fluid flow in the tight porous media. Keywords: Tight Reservoir; Spontaneous Imbibition; Nuclear Magnetic Resonance; Theoretical Modeling; Influencing Factor


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1. Introduction Tight oil and gas reservoirs have emerged as significant sources of energy supply in the world. Multistage hydraulic fracturing is a key technology for stimulating tight oil and gas reservoirs to enable an economic production (Novlesky et al., 2011). However, the fracturing process uses large volumes of water that can become trapped in the pore spaces of the rock. Recent studies show that the tight reservoirs retain a significant fraction of injected fluid and that the flowback recovery is generally lower than 30% (Makhanov et al., 2014). Spontaneous imbibition is partly responsible for the high volumes of water loss during long shut-in times of wells, and it results in that water saturation near the fracture face is generally higher than that in the formation. Imbibition experiments can be conducted to explore imbibition characteristics, which are meaningful for understanding fracturing fluid retention (Odusina et al., 2011; Roychaudhuri et al., 2011). Spontaneous imbibition of water and brine into the tight resources has also been considered as an enhanced oil recovery technique (Wang et al., 2011, 2012; Alamdari et al., 2012; Kathel and Mohanty, 2013; Roychaudhuri et al., 2014). Imbibition can occur in co-current and counter-current flow modes. Brownscombe and Dyes (1952) performed a series of counter-current spontaneous imbibition experiments and concluded that large fracture system would provide a conductive system enhancing the imbibition process. Bourbiaux and Kalaydjian (1990) examined the co-current and counter-current imbibition process on a laterally coated core. Much experimental work on countercurrent imbibition has been reported in the literature. In these experiments, the oil-saturated cores are either immersed in water, or sealed such that water in-flow and oil out-flow occur through the same faces (Pooladi-Darvish and Firoozabadi, 2000).


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Published research studies have contributed to understanding of the imbibition mechanisms. The imbibition phenomenon involves a complex interaction between capillary, gravity and viscous forces. Schechter et al. (1994) studied low-interfacial tension (IFT) capillary imbibition and observed that gravity may dominate the matrix recovery at low values of IFT. This observation entails an inclusion of the gravity factor into scaling formulation. Al-Lawati and Saleh (1996) proposed an approach to incorporate both the gravity and capillary forces, but they observed a poor correlation with the experimental data. Imbibition due to capillary forces is known as spontaneous capillary imbibition or natural imbibition (Rose, 2001). Capillary pressure controls spontaneous imbibition in both conventional (Zhang et al., 1996; Cai et al., 2010, 2012) and low-permeability reservoirs (Zhou et al., 2002; Takahashi and Kovscek, 2010). Dehghanpour et al. (2013) mentioned the water adsorption on the clay surface as a mechanism for water imbibition. Makhanov et al. (2014) demonstrated that the spontaneous imbibition rate in tight rocks would depend on factors including clay content, properties of secondary fractures, shut-in duration, and matrix mineralogy. Yildiz et al. (2006) examined the effects of shape factor, characteristic length, and boundary conditions on the spontaneous imbibition phenomenon. Imbibition experiments have been performed in welded tuff, dolomite, chalks, sandstone and, to a lesser extent, shale (Takahashi and Kovscek, 2010). The pore throats in a porous medium control permeability, drainage, and straining through their pore scale geometry and through the way they are connected via pore bodies on the macroscale. Likewise, imbibition is controlled through the geometry of the pore bodies (pore scale) and through the way the pore bodies are connected via pore


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throats on the macroscale (Glantz and Hilpert, 2008). Nuclear magnetic resonance (NMR) is a fast and nondestructive method for characterize the pore structure of porous media. NMR has been long applied for petrophysical analysis and well logging in oil and gas fields (Tinni et al., 2015; Meng et al., 2016). NMR T2 distribution was measured to characterize the pore structures of tight reservoir. Comparing other techniques which measure pore size distribution, NMR T2 distribution can be used to estimate absolute pore size distribution (Wang et al., 2016). Zhao et al (2015) compared the applicability of NMR and mercury injection capillary pressure (MICP) in characterizing pore structure of tight sandstones. NMR can also provide insights into wettability, saturation, and oil viscosity values in rocks that are partially saturated with oil and brine (Freedman et al., 2003). Previous imbibition experimental researches mainly focused on one system, i.e., gas/water/rock system or oil/water/rock system. They did not compare the differences between two systems in terms of imbibition mechanism. NMR results can effectively describe the pore characteristics, however, there is no much study available on the study of spontaneous imbibition in tight reservoirs with experiment and NMR testing. In this study, we collected 42 rock samples among which 33 natural cores were extracted from the Ordos Basin in China. Imbibition experiments and NMR technology are combined to describe the saturations of gas and oil as a function of imbibition degree. This paper can be divided into three parts. We first describe the preparation and experimental procedures, then we review the theoretical models applied to spontaneous imbibition and examine the typical governing equations for the gas/water/rock and oil/water/rock systems. Finally, we discuss the results of our experiments and explain how these influencing factors affect


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the imbibition process.

2. Experiments The imbibition experiments are categorized into two systems; gas/water/rock and oil/water/rock. Gas/water/rock system is mainly gas-saturated rock, and the rock is used to describe the process of spontaneous water imbibition. Oil/water/rock system is used to characterize the process of spontaneous water imbibition into oil-saturated rock. Imbibition experiments and NMR testing are included in this study. The procedures for conducting imbibition experiment for different systems are similar. There is obvious mobility difference between oil and gas in porous media, which results in different procedures in NMR measurement for two systems. For a gas/water/rock system, the NMR tests were conducted before and at the end of the imbibition experiment. For the oil/water/rock system, the NMR were used to measure the T2 spectra at different times during the imbibition experiments.

2.1 Materials Materials used in the experiments include rock samples, oil and water used for imbibition testing. Forty-two tight rock samples were used in the imbibition experiments. Thirtythree samples representing tight formations were obtained from Yanchang formation of the tight sandstone of the Triassic, Ordos Basin, China. The tight rock samples were cut using NaCl brine and dried in an oven at 90℃ for 24 hours. After drying, the samples were baked in a furnace at 550℃ for 24 hours in order to reduce the reactivity of the clay minerals in the tight rock samples. The cores were then slowly cooled down to the room temperature over a period of 24 hours. Table 1 shows the petrophysical properties of all samples.


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The formation water was prepared in the lab, with a salinity of 62000 mg/L. In order to produce anionic surface solution, 0.05% of sodium dodecyl benzene sulfonate and sodium oleate were added into the simulated reservoir water. Oil collected from the field was degassed, and then the simulated oil was prepared by mixing kerosene and oil sample in a 1:4 volume ratio. Table 1 Petrophysical properties of core samples Categories

Natural core for gas/water imbibition experiment

Berea sandstone for gas/water imbibition experiment

Natural core for oil/water imbibition experiment

Sample No.

Length (cm)

Diameter (cm)

Pore Volume (cm3)

Porosity (%)

Permeability (10-3µm2)

002-3

5.087

2.521

2.889

11.378

0.046

005-4

5.19

2.532

3.183

12.179

0.034

006-2

5.164

2.529

4.110

15.843

6.251

006-3

5.075

2.532

4.009

15.687

6.185

006-4

4.984

2.536

4.082

16.216

6.375

009-1

5.186

2.533

3.229

12.356

0.056

009-2

3.983

2.534

2.407

11.985

0.049

009-3

5.023

2.535

3.063

12.082

0.052

009-4

5.065

2.535

3.125

12.226

0.053

CQ-22

9.086

2.521

8.919

19.666

0.657

CQ-23

9.176

2.513

9.135

20.071

0.851

CQ-24

8.943

2.496

8.498

19.420

0.210

929-30

9.748

2.497

10.350

21.682

5.068

929-37

9.076

2.502

9.621

21.561

4.929

929-39

9.163

2.497

9.704

21.627

4.91

430-200g-1

7.101

2.494

7.801

22.488

11.872

430-200g-3

7.608

2.502

8.962

23.959

70.239

430-200g-4

7.483

2.497

7.894

21.543

2.709

002-1

5.134

2.513

2.492

9.787

0.026

002-2

5.053

2.521

2.597

10.286

0.031

002-3

5.087

2.521

2.889

11.378

0.046

005-1

5.356

2.534

3.292

12.187

0.033

005-2

5.100

2.556

3.204

12.243

0.035

005-3

5.016

2.535

3.001

11.851

0.028

005-4

5.190

2.532

3.183

12.179

0.034


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006-1

4.942

2.535

4.137

16.586

6.485

006-2

5.164

2.529

4.110

15.843

6.251

006-3

5.075

2.532

4.009

15.687

6.185

006-4

4.984

2.536

4.082

16.216

6.375

009-1

2.593

2.533

1.615

12.356

0.056

009-2

3.983

2.534

2.407

11.985

0.049

009-3

5.023

2.535

3.063

12.082

0.052

009-4

5.065

2.535

3.125

12.226

0.053

W01B

4.984

2.533

2.221

9.600

0.495

W09B

5.023

2.534

2.228

9.710

0.026

W11B

5.065

2.535

2.073

9.294

0.105

T10B

5.016

2.535

1.311

5.983

0.014

T19B

5.190

2.536

2.512

8.781

0.078

T20B

4.906

2.533

1.752

14.630

0.097

T23B

4.875

2.534

2.070

9.389

0.020

T29B

4.616

2.535

1.640

7.353

0.071

T30B

5.190

2.533

0.983

4.230

0.014

2.2 Experimental setup The major experimental setups include imbibition cell and NMR spectrometer. Some literatures described the imbibition cell with schematic diagrams, like Babadagli (2005) and Wang et al (2015). NMR spectrometer is produced by Beijing SPEC S&T Development Company Ltd. The magnetic field strength is 0.28 Tesla, and the resonance frequency of hydrogen proton is 12 megahertz. The other devices include ultra-low permeability core saturation device, thermostat, electronic balance, vernier caliper and glassware etc.

2.3 Experimental procedure The imbibition rate of tight rocks is relatively low, and experimental results can be easily influenced by ambient conditions and the precision of the analytical equipment used. Measures were used to control potential errors and improve the experimental accuracy.


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An analytical balance is used to determine the mass change of a small sample. It could reduce the error resulting from a lowering of fluid levels. A chamber maintained at a constant temperature and humidity can reduce the effects of variations in the environment temperature on the experimental results. 2.3.1 Gas/water/rock imbibition experiment The test includes the following steps: 1) We insert the dried core sample into the vacuum saturation device, saturate the sample with water, and then measure the T2 spectrum with the NMR spectroscopy method. 2) The saturated core is inserted in an oven at 88℃ for 8 hours. 3) We place the sample in the imbibition cell and measure the volume change of the liquid at selected time intervals. 4) Finally, we acquire the T2 spectra of the core sample after the imbibition experiment. 2.3.2 Oil/water/rock imbibition experiment We described the experimental procedure as follows: 1) Evacuate the core in the sealed container, and saturate the sample by formation water. 2) Flood the core with simulated oil, and record the volume of water absorbed by the core. 3) Take out the core from the core holder, and immerse it into simulated oil for 48 hours. 4) Get the sample out of the simulated oil, dry it, and place the sample in the imbibition cell to measure the oil production at selected time intervals. NMR measures the T2 spectra at different time intervals during the imbibition process, like one day, two days, three days, and so on.

3. Theoretical models The amount and the rate of water imbibition by spontaneous imbibition are essential to the understanding of reservoir production performance. The process of spontaneous water


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imbibition is controlled by the properties of the porous medium and the fluids, and their interactions. Many scaling methods have been developed to characterize the experimental results. The dimensionless time groups are developed and modified by Mattax and Kyte (1962), Ma et al. (1997), Zhou et al. (2002), and Li and Horne (2006). Olafuyi et al. (2007) upscaled experimental data using curves (the imbibed volume normalized by pore volume vs. the square root of time). Hu et al. (2012) considered that in the curve [log (cumulative imbibition) vs. log (imbibition time)], the imbibition slope can represent pore connectivity. Lan and Dehghanpour (2014) characterized experimental results to present the imbibition rate well, which is the slope of curves (cumulative imbibed volume per unit cross-sectional area vs. square root of time). Sun et al. (2015) analyzed the imbibition characteristics depending on the curves (the mass gain in the shale sample vs. time) and divided imbibition curves into two stages. Mirzaei-Paiaman (2015) reviewed the basic governing equation and an approximate analytical solution to the countercurrent spontaneous imbibition process in the presence of resisting gravity effects, followed by a brief introduction into the recently published universal scaling equations for the infinite acting period of the counter-current spontaneous imbibition in small-size systems. Li and Horne (2001, 2004) derived and developed the equation to correlate the imbibition rate and the recovery.

A linear relationship between the water imbibition rate and

reciprocal recovery by spontaneous imbibition was found. The effects of relative permeability, capillary pressure, wettability, and the gravity on the spontaneous water imbibition were considered in the model.


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dN wt 1 =a −b dt R b R  b  a − td 1 − R  e = e  a  Ak w ( S wf − S wi ) a= Pc µw L Ak b = w ∆ρg sin β µw 2 b k P S −S td = 2 w c wf 2 wi t a φ µw La Qw =

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(1) (2)

(3) (4)

(5)

where Qw is the volumetric rate of water imbibition in L3/t, Nwt is the accumulative volume of water imbibed into rocks in L3, R is the recovery in terms of pore volume at time t, A is the cross-sectional of the core in L2, L is the core length in L, La is the characteristic length in L, µw is the viscosity of water in m/Lt, Swi is the initial water saturation, Swf is the water saturation behind the imbibition front, kw is the effective permeability of water in L2, Pc is the capillary pressure in m/Lt2, ∆ρ is the density difference between water and gas in m/L3, g is the gravity constant in L/t2, β is the angle between the axis of the core sample and the horizontal direction, td is the dimensionless time with gravity and capillary force included, φ is the core porosity, t is the imbibition time in t, a is the coefficient representing capillary forces in m/t, b is the coefficient representing gravity in m/t. Viksund et al (1998) proposed another empirical equation for oil recovery from strongly water-wet porous media with zero initial water saturation. They showed that equation 6 represented all their experimental data for oil-water system with zero initial water saturation in sandstone and chalk core samples.


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R 1 = 1− 1.5 R∞ (1 + 0.04td )

(6)

where R∞ is the ultimate recovery.

4. Results and Discussion We present the imbibition and NMR experimental results, and then discuss the influencing factors of imbibition.

4.1 Results of gas/water/rock imbibition experiments 4.1.1 Imbibition experiment results Spontaneous imbibition of water into gas-saturated porous rocks is akin to piston-like displacement. Table 2 and Figure 1 display the experimental results. The quantity of water imbibed versus imbibition time for natural core and Berea sandstone, respectively. The volume of imbibed water is larger during early imbibition, and the imbibition recovery increases rapidly. The volume of imbibed water reaches a fixed value at the end of the experiment. For example, natural core sample 005-4 contains 0.80 ml of imbibed water during the first 90 minutes, then the volume diminishes to 1.05 ml from 90 to 2100 min of imbibition time, and reaches a constant value of 0.19 ml for the last 10500 minutes. Berea sandstone sample CQ-22 contains 4.05 ml of imbibed water during the first 90 minutes, then the volume diminishes to 0.695 ml from 90 to 2100 min of imbibition time, and reaches a constant value of 0.585 ml for the last 9900 minutes.

Table 2 Imbibition test results for gas/water/rock system Sample 002-3 005-4 006-2 006-3 006-4 009-1 009-2 009-3

Imbibition time, min 12600 12600 12600 12600 12600 12600 12000 12600

Imbibed water, ml 2.040 2.040 2.810 3.000 2.890 3.030 1.755 2.570

Recovery % 78.46 68.00 90.65 75.00 70.83 94.81 73.13 83.99

Sample CQ-22 CQ-23 CQ-24 929-30 929-37 929-39 430-200g-1 430-200g-3

Imbibition time, min 12000 12000 12000 12000 12000 12000 12600 12600


Imbibed water, ml 5.330 7.520 5.500 5.914 6.700 5.370 3.665 4.025

Recovery % 93.51 94.00 91.67 57.14 69.79 55.34 46.99 44.91

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009-4

12600

2.750

88.14

430-200g-4

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12600

3.436

43.49

The early imbibition time represents a period dominated by capillary force whereas the later period toward the end of the experiment is controlled by diffusion. The transition period between two regions shows the effect of gravity forces slowing down the imbibition front.

Figure 1 Typical imbibition curves measured by the gas/water/rock imbibition experiments 4.1.2 NMR testing results The petrophysical properties of the core samples are diverse, leading to variations in the T2 distributions obtained for the 18 core samples. Figure 2 presents the T2 distributions of 4 core samples. The relation between T2 relaxation time and pore radius are reproduced in Table 3 following the procedures of Zou et al. (2011, 2012) and Gao et al. (2016). Variations in the T2 spectrum for the natural core mainly occur when the T2 relaxation time is > 10 ms. The water is first imbibed into micro-pores and small meso-pores, while some remaining gases are left in the meso-pores and macro-pores.


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Table 3 The relationship between T2 relaxation time, pore radius and pore type T2 relaxation time, ms ≤1 1﹤T2 relaxation time≤10 10﹤T2 relaxation time≤100 100﹤T2 relaxation time≤1000

Pore radius, µm ≤2 2﹤Pore radius≤10 10﹤Pore radius≤20 20﹤Pore radius≤200

Pore type Micro-pore Small meso-pore Meso-pore Macro-pore

Some differences appear between natural cores and the Berea sandstone samples. The Berea samples contain abundant meso-pores and macro-pores. Water is first imbibed into small meso-pores and meso-pores, while some remaining gases are left in the macropores (Sample CQ-22). Third, the sandstone has high-permeable channels that has significant effect on the imbibition process. Sample 929-30 is from a Berea core, with a larger permeability to that of sample CQ-22. The water is first imbibed into fractures, and a large amount of remaining gases are left in the meso-pores and macro-pores. The wettability of sample CQ-22 and 929-30 are labeled as water wet, but the moisture of core CQ-22 is higher relative to that of sample 929-30. The imbibition recovery of sample CQ-22 and 929-30 is 93.51% and 57.14%, respectively.


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Figure 2 Measured T2 distributions of 4 samples: (a) Measured NMR responses before imbibition and after imbibition for core sample 002-3; (b) Measured NMR responses before imbibition and after imbibition for core sample 005-4; (c) Measured NMR responses before imbibition and after imbibition for core sample CQ-22; (d) Measured NMR responses before imbibition and after imbibition for core sample 929-30.

4.2 Results of oil/water/rock imbibition experiments 4.2.1 Imbibition experiment results Table 4 and Figure 3 present the experimental results for natural cores in which an imbibed water versus imbibition time binary plot is shown. The volume of imbibed water is higher during the early period of imbibition, and the recovery increases. The volume of imbibed water reaches a constant value at the end of the experiment. For example, for the first 65 hours, sample 006-1 has an imbibed water volume of 0.438 ml. It is 0.132 ml from 65 to 292 hours, and reaches a plateau of 0.02 ml for the last 228 hours.

Table 4 Imbibition test results for oil/water/rock system Sample

Imbibition time, hr

Imbibed water, ml

Recovery %

Sample

Imbibition time, hr


Imbibed water, ml

Recovery %

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005-1 005-2 005-3 005-4 006-1 006-2

490 470 470 467 520 473

0.269 0.374 0.260 0.266 0.590 0.722

8.80 11.96 8.59 8.78 14.40 17.74

006-3 006-4 009-1 009-2 009-3 009-4

500 471 420 450 420 450

0.461 0.635 0.177 0.260 0.240 0.240

11.69 15.80 10.97 10.76 7.82 7.69

Figure 3 Typical imbibition curves measured by the oil/water/rock imbibition experiments The volume of imbibed water in oil/water/rock experiment is less than the imbibed water volume in the gas/water/rock experiment, whereas it shows the reverse relation for the imbibition time.

4.2.2 NMR testing results The NMR measurement of gas/water/rock imbibition is distinct. It is performed at different time intervals throughout the imbibition process. For this test we used the following cores samples: W01B, W09B, W11B, T10B, T19B, T20B, T23B, T29B and T30B. The NMR results describe the dynamic change of fluid flow in the pores. Figure 4 shows four types of T2 distributions throughout the oil/water/rock imbibition process. The first type is represented by the T2 distribution of T10B core sample in which micro-


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pores and small meso-pores are abundant. The wettability of core T10B is qualified as oil-wet. Gravity plays a major role in the imbibition experiment. The second category is represented by core T20B in which small meso-pores and mesopores are abundant. The wettability is labeled water-wet. The water is originally imbibed into micro-pores and small meso-pores. Some remaining oil is left in meso-pores and macro-pores. The third type of T2 distribution is given by core T23B. The core is labeled water-wet. The crude oil is principally stored in the micro-pores and meso-pores showing good connectivity. At the beginning of imbibition experiment, the water is imbibed into the micro-pores. Twenty days later, some oil is still left in the meso-pores. The last type is represented by core sample W09B in which the meso-pores and small meso-pores are abundant. The wettability of the core is qualified as neutral. The water is first imbibed into micro-pores and small meso-pores, and some oil is left in partial mesopores and macro-pores. Because of the wettability, gravity plays a major role at the beginning of the imbibition experiment, followed by capillary imbibition toward the end.


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Figure 4 Measured T2 distributions of 4 types: (a) Measured NMR responses at different imbibition time for core sample T10B; (b) Measured NMR responses at different imbibition time for core sample T20B; (c) Measured NMR responses at different imbibition time for core sample T23B; (d) Measured NMR responses at different imbibition time for core sample W09B. Moreover, the core wettability and the pore structure exhibit great influence on the imbibition process throughout the entire NMR oil/water/rock testing.

4.3 Influencing factors of imbibition The imbibition rate is primarily related to the rock permeability, pore structure, wetting affinity characteristic and fracturing fluid (or treatment fluid) viscosity, density, and IFT between the resident and imbibing phases. Here, we investigate the effect of boundary conditions, wettability, temperature and viscosity of the oil on the water imbibition.


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4.3.1 Boundary condition We applied the following boundary conditions to simulate the behavior of tight reservoir: 1) All Face Open (AFO), 2) Two Ends Closed (TEC), and 3) Two Ends Open (TEO). We use core samples 009-1, 009-3 and 009-4 to achieve our comparative gas/water/rock imbibition experiment since they present similar petrophysical properties. In the same manner, core samples 002-1, 002-2 and 002-3 are used to carry out our comparative oil/water/rock imbibition experiments. The cores are sealed with polytetrafluoroethylene (PTFE) tape. The side of core 009-1 is sealed, to form the TEO boundary condition. Two extremities of core 009-4 are sealed corresponding to the TEC boundary condition. Core 009-3 fulfills the AFO boundary condition. In the cocurrent spontaneous water imbibition case in this study, La equals the core length. Different core cross-sectional areas are expressed by different boundary conditions. Equations 2 and 5 indicate there is no correlation between the imbibition recovery and the core cross-sectional area. Our experimental results reveal that the boundary conditions have no significant effect on the gas/water/rock imbibition recovery. However, the results show they exert an obvious influence on the imbibition rate. Equations 1, 3 and 4 highlight the relation between the core cross-sectional area and the imbibition rate. In the oil/water/rock imbibition experiment, the side of core 002-1 is sealed and represents the TEO boundary condition. Two extremities of core 002-2 are sealed and satisfy the TEC boundary condition. Core 002-3 fulfills the AFO boundary condition. Figure 5 shows the imbibition recovery under different boundary conditions. When the imbibition reaches 14 hours, the recovery ratio at time t and ultimate recovery under AFO,


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TEC, and TEO boundary condition are 0.58, 0.44, 0.32, respectively. Lan (2014) compared characteristic length for a cylindrical core under different boundary conditions. We calculated the core characteristic lengths for different boundary conditions. We obtained values of 1.68, 0.89, 2.57 under AFO, TEC, TEO boundary conditions, respectively. Equations 3 to 6 show that the imbibition recovery is determined by multiple factors, such as capillary force, gravity and core characteristic length.

Figure 5 Imbibition recovery of oil/water/rock system under different boundary conditions 4.3.2 Wettability The wettability, defined as the affinity of a reservoir rock to a particular fluid, depends on rock mineralogy, properties of the materials coating the rock surface (Anderson, 1986; Rao and Girard, 1994; Hamon, 2000; Alotaibi et al., 2010; Mohammadlou and Mork, 2012) and the temperature (Hjelmeland and Larrondo, 1986). It is the tendency of a fluid to spread on and preferentially adhere to or “wet” a solid surface in the presence of other immiscible fluids. We used three core samples having different wettability properties in our gas/water/rock imbibition experiment to describe its influence on imbibition. Three


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other core samples are used for the same purpose in our oil/water/rock imbibition experiment. Figure 6 shows the imbibition recovery and NMR T2 distribution of cores having different wettability properties during the gas/water/rock imbibition experiments. A strong water-wet property results in a better recovery. For three cores of Berea sandstone, the meso-pores and macro-pores are abundant. The water is originally imbibed into small meso-pores and meso-pores. Capillary pressure drives the imbibition for strong water-wet cores. The same rule applies for the results obtained in the oil/water/rock imbibition experiment.

(a)


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Figure 6 The influence of wettability on gas/water/rock imbibition experiment: (a) The variation of imbibition recovery factor as a function of imbibition time for three core samples with different wettability; (b) Measured NMR responses before imbibition and after imbibition for core sample 430-200g-3; (c) Measured NMR responses before imbibition and after imbibition for core sample 929-39; (d) Measured NMR responses before imbibition and after imbibition for core sample CQ-22. 4.3.3 Temperature and viscosity The scaling of capillary imbibition under thermal effect has been examined in a few studies. Babadagli (1997, 2002) proposed an approach for scaling the capillary imbibition under temperature effect. In this study, temperature and viscosity are integrated in our oil/water/rock imbibition experiment. Core 006-2 and 006-3 were saturated in kerosene, and the experimental temperatures are set at 30℃ and 50℃, respectively. The imbibition phenomenon involves a complex interaction between capillary, gravity and viscous forces. When the temperature increases, the fluid viscosity decreases. With the viscous force being lowered, the imbibition rate increases. Core 006-1 and 006-4 were saturated in kerosene and simulated reservoir oil, respectively. The viscosity of kerosene is 1.80 cp, and the viscosity of simulated reservoir oil is 2.23 cp. Figure 7.a and Figure 7.b shows the influence of these two factors on imbibition recovery.


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Figure 7.a Influence of temperature on the imbibition recovery factor for core samples 006-2 and 006-3. Kerosene is used in all these tests.

Figure 7.b Influence of viscosity on the imbibition recovery factor for core samples 0061 and 006-4. The test temperature is kept as 20℃.

Conclusions Spontaneous imbibition experiments and NMR measurement were performed in gas/water/rock system and oil/water/rock system. The following conclusions are made;


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(1) For the gas/water/rock system, the volume of imbibed water increases rapidly at the beginning of the imbibition experiment, and reaches a constant value at the end. For a natural core, the water is first imbibed into micro-pores and small meso-pores, and variations in the T2 spectrum is principally reflected in the T2 stage when the relaxation time is ≥ 10 ms. (2) The relation between imbibed water and imbibition time is similar in the two systems of imbibition experiments, but the volume of imbibed water in the oil/water/rock experiment is less relative to that in the gas/water/rock experiment. There are four types of T2 distributions related to the oil/water/rock imbibition process. Wettability and pore structure significantly affect the T2 distributions. (3) Boundary conditions have no significant effect on the gas/water/rock imbibition recovery. The imbibition recovery is affected by the capillary, gravity and characteristic core length for the oil/water/rock system under different boundary conditions. A water-wet core is beneficial to the imbibition. (4) High temperatures and lower oil viscosities are helpful for enhancing the imbibition recovery.

Acknowledgments F. Lai greatly acknowledges the financial supports of the Fundamental Research Funds of the Central Universities (2-9-2015-144) for conducting this research, as well as the China Scholarship Council for providing funding for F. Lai`s stay at the University of Alberta. The authors gratefully thank valuable manuscript modification suggestions from Huazhou Li who is an assistant professor of University of Alberta in Canada.


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Experimental Investigation of Spontaneous Imbibition in a Tight

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