Advances in Understanding Wettability of Gas Shales - ACS Publications

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Advances in Understanding Wettability of Gas Shales M. Xu and H. Dehghanpour* Department of Civil and Environmental Engineering, School of Mining and Petroleum Engineering, University of Alberta, Markin/CNRL Natural Resources Engineering Facility, 9105 116th Street, Edmonton, Alberta, Canada T6G 2W2 ABSTRACT: Recent experiments show the strong water uptake of gas shales which are strongly oil-wet based on contact angle measurements.1,2 Clay hydration, microfracture induction, lamination, and osmotic effect are collectively responsible for the excess water uptake. However, the previous measurements are not sufficient to isolate the above factors nor to explain why the bulk of shale samples can hardly imbibe the oil which completely spreads on their surface. To answer the remaining questions, we measure and compare spontaneous imbibition of oil and water into the crushed packs of the similar shales. In contrast to the intact samples, the crushed samples consistently imbibe more oil than water. The comparative study suggests that the connected pore network of the intact samples is water wet while the majority of rock including poorly connected pores is oil-wet. This argument is backed by complete spreading of oil on fresh surfaces of the rock. In contrast to the artificial pores of crushed rock, the existing pores of intact rock are already wetted by a film of water and/or covered by precipitated salt, which gives the pores a preference for water over oil. Furthermore, the presence of salt in the pore space provides an additional force for water uptake through an osmotic effect. This argument is backed by the observed reduction in shale alteration and water imbibition through increasing the salt concentration. permeability curves,18 and the nuclear magnetic resonance (NMR).19 Spontaneous imbibition has been used as a reliable technique to quantify the wettability of reservoir rocks such as sandstones and carbonates.20−23 This technique is specifically attractive for tight rocks such as shales since a forced displacement in such low-permeability rocks requires a significant pressure drop, which may induce artificial cracks. Therefore, measuring and interpreting spontaneous imbibition of oleic and aqueous phases can be an alternative approach to quantify wettability of tight rocks such as shales.24 However, quantification of shales wettability is challenging due to the adsorption of water by clay minerals and oil by organic material, and also due to the complexity of their pore structure.25 Recent imbibition studies2 show that brine and water uptake of several samples from the Horn River Basin26,27 are considerably higher than their oil uptake. However, oil completely spreads on the fresh break of these samples while water does not. Therefore, the samples are oil-wet based on contact angle measurement but they imbibe significantly more water than oil. In the following we list and discuss various reasons which may be hypothesized for the excess water uptake: 1.1. Sample Expansion. The previous imbibition experiments, using unconfined intact core samples,2 show that water uptake induces microfractures in some of the shale samples. The clay hydration leads to sample expansion, which also increases the porosity and permeability of the samples and results in higher water imbibition rate and volume. 1.2. Lamination. It is well-known that shales commonly have a layered structure. Previous measurements28 show that

1. INTRODUCTION Rapid increase of energy demand has shifted the focus of the petroleum industry toward vast unconventional resources worldwide. Organic shales have become an important energy source for the production of hydrocarbon in North America, and they are being explored as a resource in other continents as well. From 2000 to 2012, the contribution of shale gas to the total natural gas production increased from 1% in the United States and Canada, to 39% in the United States and 15% in Canada.3,4 Recent advances in drilling multilateral horizontal wells and multistage hydraulic fracturing have unlocked tight resources such as organic shales. During a hydraulic fracturing operation, fracturing fluids are pumped into the well to create fractures or fissures in the rock formation. The induced fracture network produces a pathway for hydrocarbon flow toward the wellbore.5 However, a significant fraction of injected fracturing fluid leaks off into natural fractures and shale matrix, which can damage the reservoir. The damage mechanisms include reduction in fracture conductivity, fracture effective length, and fracture face permeability.6,7 Furthermore, spontaneous imbibition of fracturing fluid into the shale matrix has been identified as a mechanism for fracturing fluid loss and reservoir damage.8−11 Moreover, spontaneous imbibition of water, brine or surfactants has also been considered as an enhanced oil recovery method in shale reservoirs.12,13 The interaction of fracturing and treatment fluids with shale matrix strongly depends on shale wettability, which is poorly understood. Wettability is in general the affinity of a particular fluid to wet the surface of the target rock.14 The wetting state of a reservoir rock can be identified by measuring the equilibrium contact angle, the Amott wettability index,15 the United States Bureau of Mines (USBM) wettability index,16 the spontaneous imbibition rate/volume,17 the hysteresis of the relative © 2014 American Chemical Society

Received: February 19, 2014 Revised: May 21, 2014 Published: May 21, 2014 4362

dx.doi.org/10.1021/ef500428y | Energy Fuels 2014, 28, 4362−4375

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Table I. Average Mineral Concentration (wt %) of the Shale Sections Determined by X-ray Diffraction label

Calcite

Quartz

Dolomite

Chlorite IIb2

Illite 1Mt

Plagioclase Albite

Pyrite

Matrix Density

FS M OP

0.5 ± 0.4 0 12.9 ± 0.4

29 ± 1.3 36.7 ± 1.2 43.6 ± 1.1

2.7 ± 0.3 5.2 ± 0.4 2.2 ± 0.5

6.5 ± 0.8 4.4 ± 0.4 0

55.4 ± 1.7 48.3 ± 1.5 33.8 ± 1.2

4.1 ± 0.5 3.6 ± 0.5 4.4 ± 0.4

1.7 ± 0.2 1.7 ± 0.2 3.2 ± 0.2

2.747 2.744 2.772

Table II. Average TVD, Matrix Density Determined by XRD Data (ρXRD), Matrix Density after the Adjustment for TOC Content (ρm), TOC, Length, Cross-sectional Area, Pack Density, Porosity, and Permeability of All the Samples Used in the Crushed-Shale Pack Experiments Label FS1 FS2 FS3 FS4 FS5 FS6 FS7 M1 M2 M3 M4 M5 M6 M7 OP1 OP2 OP3 OP4 OP5 OP6 OP7

Layer Fort Simpson Fort Simpson Fort Simpson Fort Simpson Fort Simpson Fort Simpson Fort Simpson Muskwa Muskwa Muskwa Muskwa Muskwa Muskwa Muskwa Otter Park Otter Park Otter Park Otter Park Otter Park Otter Park Otter Park

TVD (m)

ρXRD (g/cm3)

ρm (g/cm3)

TOC (wt %)

Length (cm)

Cross-sectional Area (cm2)

Pack Density (g/cm3)

Porosity (%)

Permeability (mD)

1755

2.747 97

2.737

1.73

25

5.067

1.973

27.36

21

1755

2.747 97

2.737

1.73

25

5.067

1.973

27.36

21

1755

2.747 97

2.737

1.73

25

5.067

1.973

27.36

21

1755

2.747 97

2.737

1.73

25

5.067

1.973

27.36

21

1755

2.747 97

2.737

1.73

5

5.067

1.973

27.36

21

1755

2.747 97

2.737

1.73

5

5.067

1.973

27.36

21

1755

2.747 97

2.737

1.73

5

5.067

1.973

27.36

21

1772 1772 1772 1772 1772 1772 1772 2639 2639 2639 2639 2639 2639 2639

2.744 40 2.744 40 2.744 40 2.744 40 2.744 40 2.744 40 2.744 40 2.772 25 2.772 25 2.772 25 2.772 25 2.772 25 2.772 25 2.772 25

2.711 2.711 2.711 2.711 2.711 2.711 2.711 2.727 2.727 2.727 2.727 2.727 2.727 2.727

2.25 2.25 2.25 2.25 2.25 2.25 2.25 3.01 3.01 3.01 3.01 3.01 3.01 3.01

25 25 25 25 5 5 5 25 25 25 25 5 5 5

5.067 5.067 5.067 5.067 5.067 5.067 5.067 5.067 5.067 5.067 5.067 5.067 5.067 5.067

1.973 1.973 1.973 1.973 1.973 1.973 1.973 1.973 1.973 1.973 1.973 1.973 1.973 1.973

27.01 27.01 27.01 27.01 27.01 27.01 27.01 27.39 27.39 27.39 27.39 27.39 27.39 27.39

35 35 35 35 35 35 35 32 32 32 32 32 32 32

stabilize the water film.35 The affinity of the pore network coated by a brine film to water is stronger than that to oil.36 1.5. Connectivity of Hydrophobic and Hydrophilic Pore Networks. The shale pores can be in either organic or inorganic materials.37 The organic part of the rock is hydrophobic,38 while the inorganic part can be hydrophilic, especially in the presence of clay minerals. Therefore, organic shales are usually a mixture of hydrophilic and hydrophobic materials. Significant water uptake of gas shales may indicate that the hydrophilic pore network is relatively well-connected. Furthermore, this network may be coated by water film and salt, which increase its affinity to water, as discussed above. On the other hand, insignificant oil uptake of gas shales may indicate that the hydrophobic pore space, mainly coated by organic carbon, is poorly connected. 1.6. Water Adsorption. In the previous work,2 the high water uptake of gas shales was related to the adsorption of water molecules by clay minerals. Clay minerals in shale samples can adsorb a considerable amount of water, which is controlled by clay chemistry and water salinity.39,40 The negatively charged clay platelets strongly attract polar water molecules, and this driving force is absent in the case of oil imbibition.41

water imbibition parallel to the bedding plane is faster than that perpendicular to the bedding plane. The data suggests that water permeability parallel to the bedding plane is higher than that perpendicular to the bedding plane.29 Furthermore, clay swelling during water imbibition tests enhances the anisotropy by increasing the distance between the clay platelets, which leads to more water imbibition than oil imbibition along the bedding plane.30 1.3. Chemical Osmosis. The higher chemical potential of fresh water provides some additional force for water imbibition.31−34 It is possible that some salt precipitates are present inside the shales pore network, primarily due to the core dehydration. During water imbibition tests, the salt dissolves into the imbibed water and results in the chemical potential difference between the pore water and the external water. This chemical potential difference acts as an additional driving force for the transport of water molecules into the sample. 1.4. Water Film. It is well-known that petroleum reservoirs were initially saturated with brine before the migration of hydrocarbons.16 Although the samples used in the previous study were dehydrated, parts of the pore space, originally saturated with water, may still be coated by a film of water. In addition, the possible salt precipitates in the pore space can 4363


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The overall water uptake of gas shales is controlled by the above factors, which can not be isolated using the previous experiments conducted on unconfined intact samples. This article extends the previous studies via measuring and comparing spontaneous imbibition of oil and water into the crushed packs of the similar shales. Recent studies42−44 show the application of crushed-shale packs for investigating wettability of shales. A crushed-shale pack has a confined volume which is not allowed to expand during the imbibition process. Furthermore, a crushed-shale pack is relatively isotropic compared with intact samples which are significantly anisotropic. In addition, both hydrophobic and hydrophilic pore networks of crushed shale packs are artificially wellconnected. We also conduct imbibition tests using similar intact rocks and high salinity water to investigate the osmotic effect.

Figure 2. Crushed-shale pack (25-cm-long) used in the horizontal and vertical imbibition experiments. chloride (NaCl) of various concentrations and deionized (DI) water in intact rock samples. 2.1. Shale Samples and Crushed-Shale Packs. A total of 15 crushed-shale packs and 9 intact shale samples were selected for this study. All the shale powders and shale samples are from two wells drilled in the Horn River Basin. The powders and samples are classified into three sections of Fort Simpson (FS), Muskwa (M) and Otter Park (OP). The average mineral concentration of the shale sections is listed in Table I. The samples are mainly composed of Illite (clay mineral) and quartz (nonclay mineral). The FS samples have the highest clay content, and the OP samples have the lowest clay content. It has been shown previously that water imbibition in these shale sections is positively correlated to clay content.1 The average true vertical depth (TVD), total organic carbon (TOC), and matrix density before and after considering TOC content, length, cross-sectional area, porosity, and permeability of the crushed-shale packs are presented in Table II. The mass, depth and geometry of the intact shale samples for brine and water imbibition experiments are listed in Table III. The porosity of crushed-shale packs was calculated by

2. MATERIALS We measured vertical and horizontal spontaneous imbibition of DI water and kerosene using crushed-shale packs from Fort Simpson

Table III. Mass, Depth, Cross-Sectional Area, Diameter, and Thickness of the Intact Shale Samples Used in Imbibition Experiments Using NaCl Brine and DI Water Label

Mass (g)

Cross-sectional Area (cm2)

Thickness (cm)

Diameter (cm)

Depth (m)

FS8 FS9 FS10 M8 M9 M10 OP8 OP9 OP10

149.17 149.40 144.02 179.96 187.91 168.76 217.58 187.50 215.21

78.5 78.5 78.5 78.5 78.5 78.5 78.5 78.5 78.5

1.0 1.1 1.1 1.3 1.2 1.3 1.4 1.3 1.4

10 10 10 10 10 10 10 10 10

1755 1755 1755 1772 1772 1772 2639 2639 2639

V− ϕ=

Density (g/cm3)

Viscosity (cp)

Surface Tension (dyn/cm)

DI water 10 wt % NaCl 20 wt % NaCl Kerosene

1.0 1.06 1.12 0.8

0.9 1.04 1.26 1.32

72 76 79 28

(1)

V

where ϕ is porosity. m(g) and V(mm ) are the mass and volume of the crushed-shale pack, respectively. ρm is the matrix density of the sample after adjustment for the TOC content. ρm was calculated by using the weight fractions of each mineral obtained from XRD analysis and TOC: 3

Table IV. Density, Viscosity, and Surface Tension of Different Fluids at 25°C Used for the Imbibition Experiments47−50 Fluid

m ρm

n

ρm = (1 − ωTOC ) × (∑ ωiρi ) + ωTOC × ρTOC i=1

(2)

Here, we assume the shale samples are only composed of the organic materials and the minerals detected by XRD. ωi and ρi are the mass fraction and density of each mineral, respectively. ωTOC and ρTOC are the weight fraction and density of TOC, respectively. ρTOC is close to water density and ranges between 0.95 and 1.45 g/cm3.45 In this paper, ρTOC is assumed to be 1.25 g/cm3.46 The permeability of each sample can be measured independently using Darcy’s Law. We measured the permeability of one sample from

(FS), Muskwa (M) and Otter Park (OP) formations of the Horn River Basin. We also measured the spontaneous imbibition of sodium

Figure 1. Shale particles from (a) FS, (b) M, and (c) OP sections visualized using a microscope. 4364


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each layer and assumed that all samples from the same layer have almost the same permeability. The procedure and setup schematic of the permeability test of FS5, M5 and OP5 are presented in the Appendix. 2.2. Fluids. Kerosene, DI water and sodium chloride (NaCl) solutions of various concentrations were used for the imbibition tests. The density, viscosity and surface tension of different fluids used for the imbibition experiments are listed in Table IV. 2.3. Preparation of Crushed-Shale Packs. The crushed-shale packs were prepared in the following steps: (1) Break the shale cores by a hammer into pieces less than 1 cm3. (2) Clean the grinding container with ethanol and silicon before grinding the rock samples from different layers. (3) Pour the shale pieces into the dish-shaped grinding container in a shatter box. Set the grinding time to 1 min. (4) Measure the particle size of the powders by using a microscope. Figure 1 shows the shale particles visualized by the microscope. (5) Heat the powder in an oven at 100 °C for 24 h or until no weight loss is recorded. (6) Pack the shale powders into a 1-in. inner diameter (ID) plastic tube. Both ends of the tube are fixed to prevent expansion of the shale powder during the imbibition test. Figure 1 shows that the shale powder diameter is on the order of 1 μm. A crushed-shale pack used for the imbibition experiment is shown in Figure 2. A plastic-plug with a nozzle was mounted on one side (plug side), and a cloth-screen was mounted on the other side (mesh side). During the imbibition experiment, fluid was imbibed from the mesh side toward the plug side.

In horizontal imbibition experiments, the 25 cm-long crushed-shale pack was put into a container filled with DI water or kerosene (Figure 3). During the test, the fluid gradually imbibes from the screen-side to the plug-side (Figure 4). In order to get the cocurrent imbibition volume, a graduated cylinder was placed on the outlet to collect the air bubbles displaced by the fluid. In vertical imbibition experiments, before starting the experiment, we measured the weight of dry crushed-shale packs, M0. The crushed shale pack was placed on a mesh stand inside an imbibition cell. The fluid level in the imbibition cell was slightly above the mesh to ensure continuous fluid exposure during the test. The crushed shale pack is removed from the imbibition cell and the mass of the imbibed sample at time Ti is recorded as Mi. Therefore, the imbibed mass is given by Mi − M0. The imbibition front of oil and water at different Ti values is shown in Figure 5. 3.2. Set 2 (Counter-Current Imbibition Experiments). The counter-current imbibition experiments were set to compare the water uptake of oil-saturated samples with the oil uptake of water-saturated samples. The objective of Set 2 is to know whether the samples still have the same affinity to oil (or water) when their pore space is initially saturated with water (or oil). A total of 6 crushed-shale packs (FS6-FS7, M6-M7, OP6-OP7) were made for the counter-current tests with the following procedure: (1) Immerse a 5 cm-long crushed-shale pack into DI water or kerosene until the weight gain is stabilized. (2) Put the water/oil-saturated crushed-shale pack into oil/water for 72 h. (3) Investigate the occurrence of counter-current imbibition by visualizing the possible water/oil bubbles expelled out of the sample for 72 h. 3.3. Set 3 (Spontaneous Imbibition of Brine). Set 3 compares the imbibition rates of water and brine of 20 and 10 wt % sodium chloride (NaCl). The objective is to investigate the role of osmotic potential on water uptake. It is possible that salt precipitates are present in the pore space. In this case, increasing the salt concentration of imbibing water is expected to decrease the concentration gradient, the osmotic potential, and, in turn, the water imbibition volume. The general test procedure includes the following steps: (1) Heat selected shale samples at 100 °C for 24 h or until no weight change is recorded. (2) Measure the mass and bulk volume of shale samples. (3) Place the shale samples in an imbibition cell and measure the sample weight at selected time intervals. (4) Stop the experiment when the shale samples’ weight does not increase with time.

3. EXPERIMENTS A total of 27 imbibition tests were conducted, which can be categorized into three sets. In Set 1, the cocurrent imbibition of

4. RESULTS This section presents and discusses the results of three sets of imbibition experiments. 4.1. Set 1. Figure 6 shows the cumulative imbibition volume versus time for both vertical and horizontal tests. For each shale section (FS, M, or OP), the binary shale packs, used for the comparative imbibition tests, are produced using the same procedure. It is expected that the crushed shale packs used for water and oil tests are almost identical in terms of the particle average size, pore size distribution, and specific surface volume. Therefore, the difference between oil and water imbibition is primarily due to the difference between the affinity of crushed rock surface to oil and water, not to the amount of surface per volume.51 It is observed that oil imbibes faster than DI water especially for Fort Simpson samples. However, based on the previous experiments,2 water imbibes considerably faster than oil in intact samples. Therefore, based on the imbibition behavior, the crushed packs are preferentially oil-wet, while the intact shale samples are preferentially water-wet. This contradiction will be discussed later.

Figure 3. Schematic illustration of the setup for horizontal experiments. The fluid is imbibed from left to the right and displaces the air in the crushed-shale pack. The air is collected in an inverted cylinder. water and oil in dry packs is measured. The objective is to compare the imbibition rate of oil and water in dry shale packs, where the effects of anisotropy, expansion, and pore connectivity are artificially absent. In Set 2, the counter-current imbibition of water (or oil) into the shale packs saturated with oil (or water) is measured. The objective is to investigate the imbibition in samples initially saturated with a liquid phase. In Set 3, the spontaneous imbibition of brine of different salinities in intact samples is measured. The objective is to investigate the effect of osmotic potential on the imbibition behavior. 3.1. Set 1 (Cocurrent Imbibition of Kerosene and DI Water). The spontaneous imbibition experiments for the crushed-shale packs were conducted to compare the imbibition volume of kerosene and DI water. A total of 12 crushed-shale packs were made from the shale powders from the three formations. Both horizontal and vertical imbibition experiments are designed to measure and compare the imbibition with and without a gravity effect. 4365


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Figure 4. Water (left) and oil (right) imbibition front position at 4.5 h (a, b), 12.5 h (c, d), 30.5 h (e), and 25.5 h (f) for Muskwa crushed sample packs.

5. QUANTITATIVE INTERPRETATION OF IMBIBITION DATA The results of cocurrent imbibition show that the oil imbibition rate is higher than the water imbibition rate. In the previous work,1,2 we measured the equilibrium contact angle values and the rate of water and oil imbibition into intact shale samples. We concluded that capillary pressure calculated by the Young− Laplace equation cannot explain the significant water uptake of intact samples compared with their oil uptake. However, the crushed samples show an opposite behavior, as presented in section 4. In this section, we use (1) Handy’s model to model the imbibition rate, (2) the Lucas and Washburn equation to model the imbibition front position, and (3) dimensionless time to investigate the difference between the wettability of the shale samples to oil and water. 5.1. Modeling Imbibition Rate. In Set 1, the crushedshale packs are relatively homogeneous and isotropic, so the fluid imbibition can be assumed as a piston-like displacement process. When the gravity can be ignored, the correlation between the time and the imbibition volume is52,53

Figure 5. Front position for vertical imbibition of water (left) and kerosene (right) into Muskwa crushed-shale packs (a) after 3.5 h, (b) after 9 h, and (c) after 69 h.

4.2. Set 2. We analyzed the pictures of the imbibition cell before and during the counter-current imbibition tests, and we did not observe any expelled water (or oil) droplets. This observation indicates that oil (or water) does not imbibe into water (or oil) saturated packs, even after 72 h. The results indicate that if the pore space is initially covered by oil (or water), its wetting affinity to water (or oil) will be significantly reduced. 4.3. Set 3. Figure 7 shows the pictures of samples before and after exposure with DI water and brine with the salinity of 10 wt % and 20 wt %. Comparing the pictures of samples, before and 72 hours after imbibition tests, shows that increasing the salt concentration significantly reduces the degree of samples physical alteration. For OP samples, we did not observe induced cracks, which indicates the lack of swelling clays. Figure 8 compares the imbibition profiles of water and brine of different salinities. Water uptake of all samples is significantly higher than their brine uptake. Furthermore, the imbibition rate of the low salinity brine (10 wt % NaCl) is higher than that of the high salinity brine (20 wt % NaCl).

⎛ 2PkϕA2 S ⎞ ⎟t Q2 = ⎜ c μ ⎝ ⎠

(3)

where Q is the volume of imbibed liquid, k is the effective liquid permeability, ϕ is the fractional porosity, and A is the crosssectional area of the sample. S is the liquid saturation behind the imbibition front. μ is the liquid viscosity, and Pc is the capillary pressure at the saturation of S. The capillary pressure of oil and water can be approximated using the Young−Laplace equation. Figure 9 shows the Q2 versus t curves from horizontal and vertical imbibition experiments. We observe that the slopes of the oil curves are consistently higher than those of water curves, especially for the Fort Simpson samples. The ratio between the slopes of the water and oil curves can be defined as 4366


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Figure 6. Comparison between imbibition rate of DI water and kerosene in horizontal (a, c, e) and vertical (b, d, f) crushed-shale packs from FS (a, b), M (c, d), and OP (e, f) sections. Q2 t

( ) R= ( )

based on Handy’s theory and the Young−Laplace equation, the slope of the water imbibition curves should be almost 3 times higher than that of oil imbibition curves for Muskwa and Otter Park sections, and it should be almost 2.4 times higher than that of oil for the Fort Simpson section. In brief, capillarydriven imbibition theory suggests that the water imbibition rate should be much higher than the oil imbibition rate, primarily because the surface tension of water is considerably higher than that of oil. However, both the horizontal and vertical spontaneous imbibition experiments indicate that oil imbibition rates are higher than water imbibition rates, as the values of RH and RV are around 0.8 for the Muskwa and Otter Park sections, and around 0.1 for the Fort Simpson section. 5.2. Modeling Front Position. In section 5.1, we compared the rates of oil and water imbibition using the theoretical and experimental data, and we observed inconsistent results. In this section, we compare the imbibition front position versus time for oil and water using the theoretical and experimental data. From the Lucas and Washburn equation,54,55 the horizontal imbibition front is given by

water

Q2 t

(4)

oil

The R value of horizontal experiments (RH) can be directly obtained from Figure 9. The R value of vertical experiments (RV) can also be obtained from the linear part of the curves. For the vertical experiments, the curves are nearly straight lines at the early times, when the imbibition height is less than 10 cm. In Set 1, ϕ, S, k and A are approximately the same for every crushed-shale pack, as listed in Table II. Therefore, from eq 3, R can also be calculated using

() = () Pc μ

RC

Pc μ

water

oil

( ) = ( ) σ cos θ μ

σ cos θ μ

water

oil

(5)

The experimental (RH and RV) and theoretical (RC) values of R are listed in Table V. We observe that the RC values are higher than the RH and RV values. The RC values indicate that 4367


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Figure 7. Pictures of FS, M, and OP shale samples used in the spontanous imbibition experiments using 20 wt % NaCl brine, 10 wt % NaCl brine, and DI water.

Ls(t ) =

λσ cos θ 1/2 t 4μ

Here we assume that the effective pore diameter (λ) is equal to the average pore diameter (λav), which can be calculated by56

(6)

⎛ Df ⎞1/4 ⎟⎟ λav = λmax⎜⎜ ⎝ 4 − Df ⎠

where Ls is the distance between the inlet and the imbibition front at time t. λ is the effective pore diameter. σ and μ are the surface tension and viscosity of the imbibition fluid listed in Table IV. θ is the equilibrium contact angle of water or oil on the rock surface. If we consider the effect of gravity, the flux equation for vertical imbibition is given by55 ⎛ 4σ cos θ ⎞ dLs λ2 = ×⎜ − ρgLs⎟ ⎠ λ dt 32μLs ⎝

The pore fractal dimension, Df, and the maximum pore diameter, λmax, can be estimated using the theoretical models:57 Df = d −

(7)

(8)

λmax =

where,

Pc =

4σ cos θ λ

ln ϕ ln ξ

(11)

where ξ = (λmin/λmax) and λmin is the minimum pore diameter. d is the Euclidean dimension (a value of 2 is used in this work), and ϕ is porosity. The maximum pore diameter can be calculated based on combining the models of equilateraltriangle arrangement and square arrangement of circular particles:58

By solving the integration, the relationship between imbibition height (front) and time is given by ⎛ Pc ⎞ ρgλ 2 Pc ⎜ ρg − Ls ⎟ ln⎜ P ⎟ t = −Ls − c ⎟ 32μ ρg ⎜ ⎝ ρg ⎠

(10)

Ds ⎡ 2ϕ ⎢ + 4⎣ 1−ϕ

ϕ + 1−ϕ

⎤ π − 1⎥ 4(1 − ϕ) ⎦ (12)

where Ds is characteristic particle diameter and ϕ is porosity.

(9) 4368


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Figure 8. NaCl brine and deionized water normalized imbibed mass versus time in (a) FS, (b) M, and (c) OP samples. The curves stop for M8, M9, FS8, and FS9 samples because of their reaction with water, which leads to sample expansion, and thus the imbibition mass cannot be measured.

To calculate the front position, the fluid parameters in Table IV, the sample parameters in Table II, and the contact angle values in Table V are used in eqs 6 and 8. The mathematical solution and experimental results from horizontal and vertical imbibition experiments are shown in Figures 10 and 11, respectively. The mathematical solution shows that the oil imbibition rate should be lower than the water imbibition rate, which is contradictory to the experimental results. In summary, mathematical models for the rate of imbibition volume and frontal advance suggest that water should imbibe faster than oil, while the corresponding measurements show that oil imbibes faster than water. This contradiction indicates that the Young−Laplace equation cannot sufficiently account for the strong affinity of crushed-shale media to an oleic phase. 5.3. Dimensionless Time. It is well-known that the rate of imbibition primarily depends on rock/fluid properties including porosity and permeability of porous media, fluid viscosity, interfacial tension and wettability, and also geometrical parameters such as boundary conditions and sample shape. The basic model for scaling laboratory imbibition data was investigated by Rapoport.59 For scaling imbibition results for oil/water/rock systems, Mattax and Kyte60 proposed the most frequently used dimensionless time (tD): tD = t

k σ 1 ϕ μgm Lc2

Lc =

L 2

(14)

The normalized water and oil volume imbibed in the horizontal and vertical crushed-shale packs is plotted versus the corresponding dimensionless time in Figure 12. We observe that all the oil curves are much higher than the water curves. The difference between oil and water imbibition rate in dimensionless plots (Figure 12) is more pronounced than that in dimensional plots (Figure 6). The observed difference between water and oil curves can be explained by the wettability difference. The crushed-shale samples are preferentially oil-wet, while based on the previous research,2 the intact shale samples are preferentially water-wet.

6. DISCUSSION OF EXPERIMENTAL RESULTS A total of 24 imbibition tests were conducted to compare the water, oil and brine uptake of intact and crushed samples from three different shale formations. The imbibition rate and front position were measured and compared with theories. The key results are summarized as follows: (1) Crushed shale samples imbibe more oil than water, but the intact samples from the same formations imbibe more water than oil based on the previous study.2 (2) The water (or oil) does not imbibe spontaneously into the crushed samples, which are initially fully saturated with oil (or water). (3) Increasing the concentration of NaCl inhibits the expansion and physical alteration of intact shale samples. (4) Increasing the NaCl concentration decreases the brine uptake of all samples.

(13)

where μgm is the geometric mean of water and oil viscosities.61 Lc is the characteristic length, which depends on the sample’s shape and boundary condition. For the two-ends-open boundary condition:62 4369


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Figure 9. Square of imbibed volume versus time for the imbibition of DI water and kerosene into horizontal (a, c, e) and vertical (b, d, f) crushedshale packs from FS (a, b), M (c, d), and OP (e, f) sections.

Table V. Values of Water and Oil Contact Angles, the R Value Defined by Eq 4 and Obtained from Eq 5 (RC), Horizontal (RH) and Vertical (RV) Imbibition Experiments. Subscripts o and w Represent Kerosene and Water respectively Parameter

Fort Simpson

Muskwa

Otter Park

θw(Degree) θo(Degree) RC RH RV

27 0 3.36 0.12 0.11

38 0 2.96 0.78 0.77

50 0 2.42 0.85 0.87

Result 1 indicates that the hydrophobic pore structure of intact samples may not be well-connected. Our previous studies1,2 show that water uptake of intact samples is significantly higher than their oil uptake. However, the crushed-shale samples imbibe more oil than water. In a crushed sample, both hydrophobic and hydrophilic pores are wellconnected. Therefore, the observed difference between the oil uptake of crushed and intact samples is primarily due to the difference in connectivity of the pore network in crushed and intact samples. In brief the poorly connected hydrophobic pore network of intact samples becomes artificially well-connected by crushing the samples. This interpretation is backed by the complete spreading of oil on fresh breaks of all samples. Furthermore, another possible reason for the observed difference between the imbibition behavior of crushed and intact samples is related to the laminated structure of intact samples. The lamination causes more water imbibition along

(5) Based on capillary-driven imbibition models and the Young−Laplace equation, water is expected to imbibe faster than oil into the crushed samples, while the measurements show that oil imbibes faster than water. 4370


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Figure 10. Mathematical solution of imbibition front position (Ls) versus time (t) from eq 6 for (a) FS, (c) M, and (e) OP samples and experimental imbibition front position versus time for (b) FS, (d) M, and (f) OP samples.

the bedding plane.28 In contrast to the intact samples, the crushed shale packs are relatively isotropic. Result 2 indicates that initial exposure of the rock surface to a particular liquid phase increases its affinity to the same phase. In other words, if the pore surface is initially coated by water (or oil), the samples tend to be water-wet (or oil-wet).63 The counter-current imbibition tests reported here started at zero saturation of imbibing phase. Investigating the occurrence of counter-current water/oil imbibition, when the initial saturation of the imbibing phase is not zero and the pore surface is initially coated by a film of imbibing phase, remains the subject of future studies. Results 3 and 4 indicate that the salt precipitates initially present in the shale pore space influence the water uptake and physical alteration of the shale samples. The difference between salt concentration in the pore water and external water creates a chemical potential (osmotic effect) that acts as an additional

driving force for water uptake. Therefore, increasing the salt concentration of external water reduces the osmotic effect and, in turn, reduces the liquid uptake. Result 5 indicates that the actual driving force imbibing the oleic phase into the crushed samples is stronger than the capillary pressure modeled by the Young−Laplace equation. Since the geometry and average pore diameter of the samples used for the comparative water and oil imbibition tests are very similar, the observed contradiction indicates that the strong affinity of the shale powders to the oleic phase cannot be simply modeled by the contact angle of zero (i.e., complete spreading of oil on fresh break of rock samples). It can be hypothesized that the adsorption of oil on the surface of crushed shale grains, partly coated by organic materials, acts as an additional driving force for oil uptake, and this mechanism is not accounted for in the Young−Laplace equation through the conventional definition of contact angle. However, detailed examination of 4371


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Figure 11. Mathematical solution of imbibition front position (Ls) versus time (t) from eq 8 for (a) FS, (c) M, and (c) OP samples and experimental imbibition front position versus time for (b) FS, (d) M, and (f) OP samples.

this hypothesis needs further experiments, which remain the subject of future studies.

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(3) Calculate the inlet pressure from the gas volume change (ideal gas law), accounting for the gravity effect. The outlet pressure is atmospheric pressure. (4) Calculate the permeability of the crushed sample pack using the measured pressure drop and flow rate and Darcy’s Law.

APPENDIX. PERMEABILITY TEST

Permeability is an important physical property for analyzing and scaling imbibition data. Here we set the permeability test based on Darcy’s Law. The schematic of the permeability test apparatus is shown in Figure 13. The procedure of the permeability test includes the following steps:

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

(1) Set the water pump flow rate as 0.1 mL/min and read the water level in the manometer after reaching the equilibrium. (2) Change the water pump flow rate to 0.2 mL/min, 0.3 mL/min, etc. Read the water level in the manometer under different flow rates.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Doug Bearinger for useful discussions and guidance, Todd Kinnee for his help in designing the experimental setup, and the BC Oil and Gas Commission for providing the shale 4372


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Figure 12. Imbibition volume versus dimensionless time of DI water and kerosene for horizontal (a, c, e) and vertical (b, d, f) crushed-shale packs from FS (a, b), M (c, d), and OP (e, f) sections.

samples. This work was supported by the Natural Sciences and Engineering Council of Canada (NSERC), FMC Technologies, Trican Well Service, and Nexen Energy ULC.

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