Experimental Investigation of Spontaneous Imbibition in a TightReservoir with Nuclear Magnetic Resonance TestingFengpeng Lai,* Zhiping Li, Qing Wei, Tiantian Zhang, and Qianhui Zhao

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

ABSTRACT: Hydraulic fracturing is the significant technology for exploiting tight resources. Spontaneous water imbibition is animportant mechanism governing the process of hydraulic fracturing, and the water imbibition from the fracture into the matrix isan essential factor that affects the reservoir production performance. In this study, imbibition experiments and nuclear magneticresonance (NMR) testing were combined to analyze fluid flow tight core samples in a pore-scale level. The imbibitionexperiments were categorized into two systems, the gas/water/rock system and the oil/water/rock system. The NMRmeasurements were performed at different times for these two systems. The relationship between T2 relaxation time, pore radius,and pore types was established. Theoretical models describing water imbibition into porous media were used to facilitate theinterpretation of the experimental results. The results demonstrate that the volume of imbibed water is large during the earlyimbibition period and that the imbibition recovery increases rapidly as time proceeds. The volume of imbibed water reaches aconstant level at the end of the experiment. The volume of imbibed water in the oil/water/rock experiment is less than that inthe gas/water/rock experiment; however, the experiment shows an inverse relation for the duration of the imbibition. For thegas/water/rock system, the water is originally imbibed into micropores and small mesopores 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 indicatethe effect of boundary conditions, wettability, temperature, and oil viscosity on water imbibition. The oil recovery due to waterimbibition for the oil/water/rock is mainly controlled by the capillary force, gravity force, and characteristic length of the coresample. Water-wet conditions are more preferable for spontaneous imbibition. Through a detailed study of imbibitionexperiment and NMR testing, significant insight is provided into the fluid flow in the tight porous media.

1. INTRODUCTIONTight oil and gas reservoirs have emerged as significant sourcesof energy supply in the world. Multistage hydraulic fracturing isa key technology for stimulating tight oil and gas reservoirs toenable economic production.1 However, the fracturing processuses large volumes of water that can become trapped in thepore spaces of the rock. Recent studies show that the tightreservoirs retain a significant fraction of injected fluid and thatthe flowback recovery is generally lower than 30%.2

Spontaneous imbibition is partly responsible for the highvolumes of water loss during long shut-in times of wells, and itresults in water saturation near the fracture face being generallyhigher than that in the formation. Imbibition experiments canbe conducted to explore imbibition characteristics, which aremeaningful for understanding fracturing fluid retention.3,4

Spontaneous imbibition of water and brine into the tightresources has also been considered as an enhanced oil recoverytechnique.5−9

Imbibition can occur in cocurrent and counter-current flowmodes. Brownscombe and Dyes10 performed a series ofcounter-current spontaneous imbibition experiments andconcluded that a large fracture system would provide aconductive system enhancing the imbibition process. Bourbiauxand Kalaydjian11 examined the cocurrent and counter-currentimbibition process on a laterally coated core. Muchexperimental work on countercurrent imbibition has beenreported in the literature. In these experiments, the oil-saturated cores are either immersed in water or sealed such thatwater in-flow and oil out-flow occur through the same faces.12

Published research studies have contributed to understanding

of the imbibition mechanisms. The imbibition phenomenoninvolves a complex interaction between capillary, gravity, andviscous forces. Schechter et al.13 studied low-interfacial tension(IFT) capillary imbibition and observed that gravity maydominate the matrix recovery at low values of IFT. Thisobservation entails an inclusion of the gravity factor into scalingformulation. Al-Lawati and Saleh14 proposed an approach toincorporate both the gravity and the capillary forces, but theyobserved a poor correlation with the experimental data.Imbibition due to capillary forces is known as spontaneouscapillary imbibition or natural imbibition.15 Capillary pressurecontrols spontaneous imbibition in both conventional and low-permeability reservoirs.16−20 Dehghanpour et al.21 mentionedthe water adsorption on the clay surface as a mechanism forwater imbibition. Makhanov et al.2 demonstrated that thespontaneous imbibition rate in tight rocks would depend onfactors including clay content, properties of secondary fractures,shut-in duration, and matrix mineralogy. Yildiz et al.22 examinedthe effects of shape factor, characteristic length, and boundaryconditions on the spontaneous imbibition phenomenon.Imbibition experiments have been performed in welded tuff,dolomite, chalks, sandstone, and, to a lesser extent, shale.20

The pore throats in a porous medium control permeability,drainage, and straining through their pore scale geometry andthrough the way they are connected via pore bodies on the

Received: June 1, 2016Revised: August 19, 2016Published: October 10, 2016

Article

pubs.acs.org/EF

© 2016 American Chemical Society 8932 DOI: 10.1021/acs.energyfuels.6b01324Energy Fuels 2016, 30, 8932−8940

macroscale. Likewise, imbibition is controlled through thegeometry of the pore bodies (pore scale) and through the waythe pore bodies are connected via pore throats on themacroscale.23 Nuclear magnetic resonance (NMR) is a fastand nondestructive method to characterize the pore structureof porous media. NMR has been long applied for petrophysicalanalysis and well logging in oil and gas fields.24,25 NMR T2

distribution was measured to characterize the pore structures ofa tight reservoir. Comparing other techniques which measurepore size distribution, NMR T2 distribution can be used toestimate absolute pore size distribution.26 Zhao et al.27

compared the applicability of NMR and mercury injectioncapillary pressure (MICP) in characterizing pore structure oftight sandstones. NMR can also provide insights intowettability, saturation, and oil viscosity values in rocks thatare partially saturated with oil and brine.28

Previous imbibition experimental research mainly focused onone system, i.e., the gas/water/rock system or the oil/water/rock system. It did not compare the differences between twosystems in terms of imbibition mechanism. NMR results caneffectively describe the pore characteristics; however, there isnot much study available of spontaneous imbibition in tightreservoirs with experiment and NMR testing. In this study, wecollected 42 rock samples. 33 natural cores were extracted fromthe Ordos Basin in China, and other 9 rock samples were Bereasandstones. Imbibition experiments and NMR technology arecombined to describe the saturations of gas and oil as afunction of imbibition degree. This paper can be divided intothree parts. We first describe the preparation and experimentalprocedures, and then we review the theoretical models appliedto spontaneous imbibition and examine the typical governingequations for the gas/water/rock and oil/water/rock systems.

Table 1. Petrophysical Properties of Core Samples

category sample no. length, cm diameter, cm pore volume, cm3 porosity, % permeability, 10−3 μm2

natural core for gas/water imbibition experiment 002-3 5.087 2.521 2.889 11.378 0.046005-4 5.19 2.532 3.183 12.179 0.034006-2 5.164 2.529 4.110 15.843 6.251006-3 5.075 2.532 4.009 15.687 6.185006-4 4.984 2.536 4.082 16.216 6.375009-1 5.186 2.533 3.229 12.356 0.056009-2 3.983 2.534 2.407 11.985 0.049009-3 5.023 2.535 3.063 12.082 0.052009-4 5.065 2.535 3.125 12.226 0.053

Berea sandstone for gas/water imbibition experiment CQ-22 9.086 2.521 8.919 19.666 0.657CQ-23 9.176 2.513 9.135 20.071 0.851CQ-24 8.943 2.496 8.498 19.420 0.210929-30 9.748 2.497 10.350 21.682 5.068929-37 9.076 2.502 9.621 21.561 4.929929-39 9.163 2.497 9.704 21.627 4.91430-200g-1 7.101 2.494 7.801 22.488 11.872430-200g-3 7.608 2.502 8.962 23.959 70.239430-200g-4 7.483 2.497 7.894 21.543 2.709

natural core for oil/water imbibition experiment 002-1 5.134 2.513 2.492 9.787 0.026002-2 5.053 2.521 2.597 10.286 0.031002-3 5.087 2.521 2.889 11.378 0.046005-1 5.356 2.534 3.292 12.187 0.033005-2 5.100 2.556 3.204 12.243 0.035005-3 5.016 2.535 3.001 11.851 0.028005-4 5.190 2.532 3.183 12.179 0.034006-1 4.942 2.535 4.137 16.586 6.485006-2 5.164 2.529 4.110 15.843 6.251006-3 5.075 2.532 4.009 15.687 6.185006-4 4.984 2.536 4.082 16.216 6.375009-1 2.593 2.533 1.615 12.356 0.056009-2 3.983 2.534 2.407 11.985 0.049009-3 5.023 2.535 3.063 12.082 0.052009-4 5.065 2.535 3.125 12.226 0.053W01B 4.984 2.533 2.221 9.600 0.495W09B 5.023 2.534 2.228 9.710 0.026W11B 5.065 2.535 2.073 9.294 0.105T10B 5.016 2.535 1.311 5.983 0.014T19B 5.190 2.536 2.512 8.781 0.078T20B 4.906 2.533 1.752 14.630 0.097T23B 4.875 2.534 2.070 9.389 0.020T29B 4.616 2.535 1.640 7.353 0.071T30B 5.190 2.533 0.983 4.230 0.014

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Finally, we discuss the results of our experiments and explainhow these influencing factors affect the imbibition process.

2. EXPERIMENTSThe imbibition experiments are categorized into two systems: gas/water/rock and oil/water/rock. The gas/water/rock system is mainlygas-saturated rock, and the rock is used to describe the process ofspontaneous water imbibition. The oil/water/rock system is used tocharacterize the process of spontaneous water imbibition into oil-saturated rock. Imbibition experiments and NMR testing are includedin this study. The procedures for conducting imbibition experimentsfor different systems are similar. There is obvious mobility differencebetween oil and gas in porous media, which results in differentprocedures in NMR measurement for two systems. For a gas/water/rock system, the NMR tests were conducted before and at the end ofthe imbibition experiment. For the oil/water/rock system, the NMRtests were used to measure the T2 spectra at different times during theimbibition experiments.2.1. Materials. Materials used in the experiments include rock

samples, oil, and water used for imbibition testing. Forty-two tight rocksamples were used in the imbibition experiments. Thirty-three samplesrepresenting tight formations were obtained from Yanchang formationof the tight sandstone of the Triassic, Ordos Basin, China. The tightrock samples were cut using NaCl brine and dried in an oven at 90 °Cfor 24 h. After drying, the samples were baked in a furnace at 550 °Cfor 24 h in order to reduce the reactivity of the clay minerals in thetight rock samples. The cores were then slowly cooled down to roomtemperature over a period of 24 h. Table 1 shows the petrophysicalproperties of all samples.The formation water was prepared in the lab, with a salinity of

62 000 mg/L. To produce the anionic surface solution, 0.05% sodiumdodecyl benzenesulfonate and sodium oleate were added into thesimulated reservoir water. Oil collected from the field was degassed,and then the simulated oil was prepared by mixing kerosene and theoil sample in a 1:4 volume ratio.2.2. Experimental Setup. The major experimental setups include

imbibition cell and NMR spectrometer. Some literature described theimbibition cell with schematic diagrams, like Babadagli29 and Wang etal.30 The NMR spectrometer is produced by Beijing SPEC S&TDevelopment Company, Ltd. The magnetic field strength is 0.28 T,and the resonance frequency of the hydrogen proton is 12 MHz. Theother devices include an ultralow permeability core saturation device,thermostat, electronic balance, vernier caliper, glassware, etc.2.3. Experimental Procedure. The imbibition rate of tight rocks

is relatively low, and experimental results can be easily influenced byambient conditions and the precision of the analytical equipment used.Measurements were used to control potential errors and improve theexperimental accuracy. An analytical balance is used to determine themass change of a small sample. It could reduce the error resulting froma lowering of fluid levels. A chamber maintained at a constanttemperature and humidity can reduce the effects of variations in theenvironment 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 thevacuum saturation device, saturate the sample with water, and thenmeasure the T2 spectrum with the NMR spectroscopy method. (2)The saturated core is inserted in an oven at 88 °C for 8 h. (3) Weplace the sample in the imbibition cell and measure the volume changeof the liquid at selected time intervals. (4) Finally, we acquire the T2spectra of the core sample after the imbibition experiment.2.3.2. Oil/Water/Rock Imbibition Experiment. We describe the

experimental procedure as follows: (1) Evacuate the core in the sealedcontainer and saturate the sample by formation water. (2) Flood thecore with simulated oil and record the volume of water absorbed bythe core. (3) Take out the core from the core holder and immerse itinto simulated oil for 48 h. (4) Get the sample out of the simulated oil,dry it, and place the sample in the imbibition cell to measure the oilproduction at selected time intervals.

NMR measures the T2 spectra at different time intervals during theimbibition process, such as 1 day, 2 days, 3 days, and so on.

3. THEORETICAL MODELSThe amount and the rate of water imbibition by spontaneousimbibition are essential to the understanding of reservoirproduction performance. The process of spontaneous waterimbibition is controlled by the properties of the porousmedium, the fluids, and their interactions. Many scalingmethods have been developed to characterize the experimentalresults. The dimensionless time groups are developed andmodified by some researchers.31−34 Olafuyi et al.35 upscaledexperimental data using curves (the imbibed volumenormalized by pore volume vs the square root of time). Huet al.36 considered that in the curve [log(cumulative imbibition)vs log(imbibition time)] the imbibition slope can representpore connectivity. Lan and Dehghanpour37 characterizedexperimental results to present the imbibition rate well, whichis the slope of curves (cumulative imbibed volume per unitcross-sectional area vs square root of time). Sun et al.38

analyzed the imbibition characteristics depending on the curves(the mass gain in the shale sample vs time) and dividedimbibition curves into two stages. Mirzaei-Paiaman39 reviewedthe basic governing equation and an approximate analyticalsolution to the counter-current spontaneous imbibition processin the presence of resisting gravity effects, followed by a briefintroduction into the recently published universal scalingequations for the infinite acting period of the counter-currentspontaneous imbibition in small-size systems.Li and Horne40,41 derived and developed the equation to

correlate the imbibition rate and the recovery. A linearrelationship between the water imbibition rate and reciprocalrecovery by spontaneous imbibition was found. The effects ofrelative permeability, capillary pressure, wettability, and gravityon the spontaneous water imbibition were considered in themodel.

= = −QN

ta

Rb

dd

1w

wt(1)

− = −⎜ ⎟⎛⎝

⎞⎠

ba

R1 e eb a R t( / ) d

(2)

μ=

−a

Ak S SL

P( )w wf wi

wc

(3)

μρ β= Δb

Akg sinw

w (4)

φ μ=

−t

ba

k P S SL

td

2

2w c

w

wf wi

a2

(5)

where Qw is the volumetric rate of water imbibition in L3/t, Nwtis the accumulative volume of water imbibed into rocks in L3, Ris 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 thecharacteristic length in L, μw is the viscosity of water in m/(L t),Swi is the initial water saturation, Swf is the water saturationbehind the imbibition front, kw is the effective permeability ofwater in L2, Pc is the capillary pressure in m/(L t2), Δρ is thedensity difference between water and gas in m/L3, g is thegravity constant in L/t2, β is the angle between the axis of thecore sample and the horizontal direction, td is the dimensionless

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time with gravity and capillary force included, φ is the coreporosity, t is the imbibition time in t, a is the coefficientrepresenting capillary forces in m/t, b is the coefficientrepresenting gravity in m/t.Viksund et al.42 proposed another empirical equation for oil

recovery from strongly water-wet porous media with zero initialwater saturation. They showed that eq 6 represented all theirexperimental data for the oil−water system with zero initialwater saturation in sandstone and chalk core samples.

= −+∞

RR t

11

(1 0.04 )d1.5

(6)

where R∞ is the ultimate recovery.

4. RESULTS AND DISCUSSIONWe present the imbibition and NMR experimental results andthen discuss the influencing factors of imbibition.4.1. Results of Gas/Water/Rock Imbibition Experi-

ments. 4.1.1. Imbibition Experiment Results. Spontaneousimbibition of water into gas-saturated porous rocks is akin topiston-like displacement. Table 2 and Figure 1 display the

experimental results. The quantity of water imbibed is shownversus imbibition time for natural core and Berea sandstone,respectively. The volume of imbibed water is larger during earlyimbibition, and the imbibition recovery increases rapidly. Thevolume of imbibed water reaches a fixed value at the end of theexperiment. For example, natural core sample 005-4 contains0.80 mL of imbibed water during the first 90 min, and then thevolume diminishes to 1.05 mL from 90 to 2100 min of

imbibition time and reaches a constant value of 0.19 mL for thelast 10 500 min. Berea sandstone sample CQ-22 contains 4.05mL of imbibed water during the first 90 min, and then thevolume diminishes to 0.695 mL from 90 to 2100 min ofimbibition time and reaches a constant value of 0.585 mL forthe last 9900 min.The early imbibition time represents a period dominated by

capillary force, whereas the later period toward the end of theexperiment is controlled by diffusion. The transition periodbetween the two regions shows the effect of gravity forcesslowing down the imbibition front.

4.1.2. NMR Testing Results. The petrophysical properties ofthe core samples are diverse, leading to variations in the T2distributions obtained for the 18 core samples. Figure 2presents the T2 distributions of four core samples. The relationbetween T2 relaxation time and pore radius is reproduced inTable 3 following the procedures of Zou et al.43,44 and Gao etal.45 Variations in the T2 spectrum for the natural core mainlyoccur when the T2 relaxation time is >10 ms. The water is firstimbibed into micropores and small mesopores, while someremaining gases are left in the mesopores and macropores.Some differences appear between natural cores and the Berea

sandstone samples. The Berea samples contain abundantmesopores and macropores. Water is first imbibed into smallmesopores and mesopores, while some remaining gases are leftin the macropores (Sample CQ-22). Third, the sandstone hashigh-permeable channels that has significant effect on theimbibition process. Sample 929-30 is from a Berea core, with apermeability larger than that of sample CQ-22. The water isfirst imbibed into fractures, and a large amount of remaininggases are left in the mesopores and macropores. Thewettabilities of samples CQ-22 and 929-30 are labeled aswater wet, but the moisture of the core of CQ-22 is higherrelative to that of sample 929-30. The imbibition recoveries ofsamples CQ-22 and 929-30 are 93.51% and 57.14%,respectively.

4.2. Results of Oil/Water/Rock Imbibition Experi-ments. 4.2.1. Imbibition Experiment Results. Table 4 andFigure 3 present the experimental results for natural cores inwhich an imbibed water versus imbibition time binary plot isshown. The volume of imbibed water is higher during the earlyperiod of imbibition, and the recovery increases. The volume ofimbibed water reaches a constant value at the end of theexperiment. For example, for the first 65 h, sample 006-1 has animbibed water volume of 0.438 mL. It is 0.132 mL from 65 to292 h and reaches a plateau of 0.02 mL for the last 228 h.The volume of imbibed water in oil/water/rock experiment

is less than the imbibed water volume in the gas/water/rockexperiment, whereas it shows the reverse relation for theimbibition time.

Table 2. Imbibition Test Results for the Gas/Water/Rock System

sample imbibition time, min imbibed water, mL recovery % sample imbibition time, min imbibed water, mL recovery %

002-3 12600 2.040 78.46 CQ-22 12000 5.330 93.51005-4 12600 2.040 68.00 CQ-23 12000 7.520 94.00006-2 12600 2.810 90.65 CQ-24 12000 5.500 91.67006-3 12600 3.000 75.00 929-30 12000 5.914 57.14006-4 12600 2.890 70.83 929-37 12000 6.700 69.79009-1 12600 3.030 94.81 929-39 12000 5.370 55.34009-2 12000 1.755 73.13 430-200g-1 12600 3.665 46.99009-3 12600 2.570 83.99 430-200g-3 12600 4.025 44.91009-4 12600 2.750 88.14 430-200g-4 12600 3.436 43.49

Figure 1. Typical imbibition curves measured by the gas/water/rockimbibition experiments.

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4.2.2. NMR Testing Results. The NMR measurement of gas/water/rock imbibition is distinct. It is performed at differenttime intervals throughout the imbibition process. For this testwe used the following core samples: W01B, W09B, W11B,T10B, T19B, T20B, T23B, T29B, and T30B. The NMR resultsdescribe the dynamic change of fluid flow in the pores. Figure 4shows four types of T2 distributions throughout the oil/water/rock imbibition process.The first type is represented by the T2 distribution of the

T10B core sample in which micropores and small mesoporesare 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 mesopores and mesopores are abundant. The wettabilityis labeled water-wet. The water is originally imbibed intomicropores and small mesopores. Some remaining oil is left inmesopores and macropores.

The third type of T2 distribution is given by core T23B. Thecore is labeled water-wet. The crude oil is principally stored inthe micropores and mesopores, showing good connectivity. Atthe beginning of the imbibition experiment, the water isimbibed into the micropores. Twenty days later, some oil is stillleft in the mesopores.The last type is represented by the core sample W09B in

which the mesopores and small mesopores are abundant. Thewettability of the core is qualified as neutral. The water is firstimbibed into micropores and small mesopores, and some oil isleft in partial mesopores and macropores. Because of thewettability, gravity plays a major role at the beginning of theimbibition experiment, followed by capillary imbibition towardthe end.Moreover, the core wettability and the pore structure exhibit

great influence on the imbibition process throughout the entireNMR oil/water/rock testing.

Figure 2.Measured T2 distributions of four 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 afterimbibition for core sample CQ-22; (d) and measured NMR responses before imbibition and after imbibition for core sample 929-30.

Table 3. Relationship between T2 Relaxation Time, Pore Radius, and Pore Type

T2 relaxation time, ms pore radius, μm pore type

≤1 ≤2 micropore1 < T2 relaxation time ≤ 10 2 < pore radius ≤ 10 small mesopore10 < T2 relaxation time ≤ 100 10 < pore radius ≤ 20 mesopore100 < T2 relaxation time ≤ 1000 20 < pore radius ≤ 200 macropore

Table 4. Imbibition Test Results for the Oil/Water/Rock System

sample imbibition time, h imbibed water, mL recovery % sample imbibition time, h imbibed water, mL recovery %

005-1 490 0.269 8.80 006-3 500 0.461 11.69005-2 470 0.374 11.96 006-4 471 0.635 15.80005-3 470 0.260 8.59 009-1 420 0.177 10.97005-4 467 0.266 8.78 009-2 450 0.260 10.76006-1 520 0.590 14.40 009-3 420 0.240 7.82006-2 473 0.722 17.74 009-4 450 0.240 7.69

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4.3. Influencing Factors of Imbibition. The imbibitionrate is primarily related to the rock permeability, pore structure,wetting affinity characteristic, and fracturing fluid (or treatmentfluid) viscosity, density, and IFT between the resident andimbibing phases. Here, we investigate the effect of boundaryconditions, wettability, temperature, and viscosity of the oil onthe water imbibition.4.3.1. Boundary Condition. We applied the following

boundary conditions to simulate the behavior of a tightreservoir: (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 similarpetrophysical properties. In the same manner, core samples002-1, 002-2, and 002-3 are used to carry out our comparativeoil/water/rock imbibition experiments.The cores are sealed with polytetrafluoroethylene (PTFE)

tape. The side of core 009-1 is sealed, to form the TEOboundary condition. Two extremities of core 009-4 are sealedcorresponding to the TEC boundary condition. Core 009-3fulfills the AFO boundary condition. In the cocurrentspontaneous water imbibition case in this study, La equals thecore length. Different core cross-sectional areas are expressedby different boundary conditions. Equations 2 and 5 indicatethere is no correlation between the imbibition recovery and thecore cross-sectional area. Our experimental results reveal thatthe boundary conditions have no significant effect on the gas/water/rock imbibition recovery. However, the results show theyexert an obvious influence on the imbibition rate. Equationss 1,3, and 4 highlight the relation between the core cross-sectionalarea 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 TECboundary conditions. Core 002-3 fulfills the AFO boundarycondition. Figure 5 shows the imbibition recovery underdifferent boundary conditions. When the imbibition reaches 14h, the recovery ratio at time t and ultimate recovery under AFO,TEC, and TEO boundary conditions are 0.58, 0.44, and 0.32,respectively. Lan37 compared characteristic length for acylindrical core under different boundary conditions. Wecalculated the core characteristic lengths for different boundary

Figure 3. Typical imbibition curves measured by the oil/water/rockimbibition experiments.

Figure 4. Measured T2 distributions of four types: (a) Measured NMR responses at different imbibition times for core sample T10B; (b) measuredNMR responses at different imbibition times for core sample T20B; (c) measured NMR responses at different imbibition times for core sampleT23B; and (d) measured NMR responses at different imbibition times for core sample W09B.

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conditions. We obtained values of 1.68, 0.89, and 2.57 underAFO, TEC, and TEO boundary conditions, respectively.Equations 3−6 show that the imbibition recovery is determinedby multiple factors, such as capillary force, gravity, and corecharacteristic length.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, andtemperature.46−51 It is the tendency of a fluid to spread on andpreferentially adhere to or “wet” a solid surface in the presenceof other immiscible fluids. We used three core samples having

different wettability properties in our gas/water/rock imbibi-tion experiment to describe its influence on imbibition. Threeother 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 propertiesduring the gas/water/rock imbibition experiments. A strongwater-wet property results in a better recovery. For three coresof Berea sandstone, the mesopores and macropores areabundant. The water is originally imbibed into small mesoporesand mesopores. Capillary pressure drives the imbibition forstrong water-wet cores. The same rule applies for the resultsobtained in the oil/water/rock imbibition experiment.

4.3.3. Temperature and Viscosity. The scaling of capillaryimbibition under a thermal effect has been examined in a fewstudies. Babadagli52,53 proposed an approach for scaling thecapillary imbibition under a temperature effect. In this study,temperature and viscosity are integrated in our oil/water/rockimbibition experiment. Cores 006-2 and 006-3 were saturatedin kerosene, and the experimental temperatures are set at 30and 50 °C, respectively. The imbibition phenomenon involves acomplex interaction between capillary, gravity, and viscousforces. When the temperature increases, the fluid viscositydecreases. With the viscous force being lowered, the imbibitionrate increases. Cores 006-1 and 006-4 were saturated inkerosene and the simulated reservoir oil, respectively. Theviscosity of kerosene is 1.80 cP, and the viscosity of thesimulated reservoir oil is 2.23 cP. Figure 7a,b shows theinfluence of these two factors on imbibition recovery.

Figure 5. Imbibition recovery of the oil/water/rock system underdifferent boundary conditions.

Figure 6. Influence of wettability on the gas/water/rock imbibition experiment: (a) The variation of imbibition recovery factor as a function ofimbibition time for three core samples with different wettabilities; (b) measured NMR responses before imbibition and after imbibition for coresample 430-200g-3; (c) measured NMR responses before imbibition and after imbibition for core sample 929-39; and (d) measured NMR responsesbefore imbibition and after imbibition for core sample CQ-22.

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■ CONCLUSIONSSpontaneous imbibition experiments and NMR measurementwere performed in the gas/water/rock system and oil/water/rock system. The following conclusions are made:

(1) For the gas/water/rock system, the volume of imbibedwater increases rapidly at the beginning of the imbibitionexperiment and reaches a constant value at the end. For anatural core, the water is first imbibed into microporesand small mesopores, and variations in the T2 spectrumare principally reflected in the T2 stage when therelaxation time is ≥10 ms.

(2) The relations between imbibed water and imbibitiontime are similar in the two systems of imbibitionexperiments, but the volume of imbibed water in theoil/water/rock experiment is less relative to that in thegas/water/rock experiment. There are four types of T2distributions related to the oil/water/rock imbibitionprocess. Wettability and pore structure significantly affectthe T2 distributions.

(3) Boundary conditions have no significant effect on thegas/water/rock imbibition recovery. The imbibitionrecovery is affected by the capillary, gravity, andcharacteristic core length for the oil/water/rock system

under different boundary conditions. A water-wet core isbeneficial to the imbibition.

(4) High temperatures and lower oil viscosities are helpfulfor enhancing the imbibition recovery.

■ AUTHOR INFORMATIONCorresponding Author*(F.L.) Phone: 86-10-13401154289. Fax: 86-10-82326850. E-mail: laifengpeng@cugb.edu.cn.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSF. Lai greatly acknowledges the financial support of theFundamental Research Funds of the Central Universities (2-9-2015-144) for conducting this research, as well as the ChinaScholarship Council for providing funding for F. Lai’s stay atthe University of Alberta. The authors are grateful for valuablemanuscript modification suggestions from Huazhou Li, who isan assistant professor at University of Alberta in Canada.

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