Study of the Imbibition Behavior of Hydrophilic Tight Sandstone

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Study of imbibition behavior of hydrophilic tight sandstone reservoirs based on nuclear magnetic resonance Xiaoxia Ren, aifen Li, Guijuan Wang, Bingqing He, and Shuaishi Fu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b00768 • Publication Date (Web): 25 Jun 2018 Downloaded from http://pubs.acs.org on July 1, 2018

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Study of imbibition behavior of hydrophilic tight sandstone reservoirs based on nuclear magnetic resonance Xiaoxia Rena,b, Aifen Li a,b*, Guijuan Wang a,b, Bingqing He a,b, Shuaishi Fu a,b

a School of Petroleum Engineering, China University of Petroleum, Qingdao 266580, China

b Research Centre of Multiphase Flow in Porous Media, China University of Petroleum, Qingdao 266580, China

ABSTRACT: Hydraulic fracturing is one of the key technologies to enhance the oil recovery from tight sandstone reservoirs. The study on the behavior of imbibition for tight sandstone reservoir is of great significance to increase oil production after fracturing. In this paper, nuclear magnetic resonance (NMR) and high-pressure mercury injection were implemented on the samples taken from Yanchang Formation of Ordos Basin. The NMR T2 curves of core at the state of 100% water saturated were converted to pore-throat radius distribution curves. On this basis, the experiments of imbibition and displacement were conducted, the changes of fluid distribution, imbibition quantity and imbibition rate with different scale pores and at different imbibition times were analyzed. Moreover, the results of imbibition and displacement were compared to assess the distribution of the recoverable and the remaining oil under two

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exploitation modes, and the contribution of imbibition made to displacement in pores at different scales. The result shows that imbibition is a relatively slow process. The entire imbibition process is mainly affected by nano-pore which are widely distributed in cores, and the imbibition rate of total pore constantly decreases as the imbibition time increases. Moreover, the relative recovery in pores at different scales shows huge difference under the two exploitation modes of imbibition and displacement. During imbibing, smaller pores produced higher degrees of oil, while during displacing, larger pores have higher relative recovery. The contribution of imbibition made to displacement in nano-pore were the highest and decreased with the increase of pore throat size.

KEYWORDS: Tight sandstone, Hydrophilic, NMR, Imbibition, Water flooding

1 INTRODUCTION Hydraulic fracturing technology is an effective stimulation measure for studying the exploitation of tight sandstone. A reservoir can transform from a single porous medium system into a double media system with fractures and pores after fracturing, resulting a great change in the oil-displacement mechanism1. In early 1950s, while recovering oil from Spraberry sandstone and siltstone fractured reservoirs in Texas(USA), oil recovery by imbibition was explored for the first time as an important mechanism in secondary oil recovery for the fractured reservoirs. The initial oil production of this fractured reservoir was high, while it was featured to have a very short time duration and a low primary recovery rate. Hence, the engineers began to explore effective measures of secondary exploitation that could be applied for the low permeability fractured reservoirs, this is when oil production by imbibition was developed2.


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Imbibition is defined as displacement of non-wetting phase by wetting phase with the dominant effect of capillary forces in porous media

1, 3, 4

. Generally, the fluid outside the

formation matrix is either the water or the water based fracturing fluid5. The fluid inside the rock matrix includes crude oil, gas, and other formation fluids. Imbibition occurs at any time the fracturing fluid meets the formation4. During the imbibition in sandstone and carbonates, capillarity action is usually considered to be the only mechanism causing the fluid displacement3, 6. However, in clay rich shale, osmosis diffusion should also be considered1. According to the reservoir physics and the experimental study of low permeability reservoirs, the capillary differential pressure is generated by the difference in pore sizes. For a reservoir with certain wettability, the capillary pressure in a small pore is larger than that in a larger pore of the porous media. Over the past few years, investigation of oil recovery by imbibition has been a research focus in multiphase flow in porous media7, 8. Morrow and Mason have provided an excellent review of the recent developments in spontaneous imbibition9. The mechanism of capillary imbibition is important in the evaluation of rock wettability10-15. The rate of imbibition is mainly dependent on the properties of rock, the chemistry of the fluids, and the complex interfacial reaction between the rock and the fluids6, 10, 16. Pore geometry (size, shape and structure), permeability, wettability and boundary conditions of the matrix17-31, relative permeabilities32, 33, interfacial tension24, 31, 34

and fluids viscosities 35-39 have a great impact on the volume of imbibition. The model describing the process of imbibition has been developed since 1918, there are

several main models. Lucas40and Washburn41 studied the movement tendencies of the front edge of spontaneous imbibition in vertical throats. Handy6 simplified rocks as capillary bundles and proposed the earliest spontaneous imbibition model, which considered that the cumulative core


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imbibition mass was linear with the square root of imbibition time. Zhang et al 42, Li and Horne 43

, and Schechter et al

44

contributed to the development of a spontaneous imbibition model

driven by capillary force under different conditions. However, those models did not consider the effects of pore tortuosity and intersection on imbibition, and merely simplified pore space as groups of capillary tubes. Shen et al

45

calculated the imbibition process within asymmetric

branch structure by a newly established mathematical model, and the influence of both the pore structure and the fluid characteristics. However, these models describing imbibition were mostly based on idealized assumptions and lacked the support of experimental data. Li et al46 studied the effect of different factors such as water saturation, oil-water interfacial tension, and wettability on the efficiency of oil recovery by imbibition. The authors found that for tight sandstone reservoirs with certain wettability and water saturation, the rock permeability (rock structure) was the key factor in influencing the recovery percentage by imbibition47-49. Other scholars have also performed numerous studies focusing on the influence of porosity, permeability and rock structure on imbibition rate. Dutta et al50 conducted experiments on water imbibition in cores with different permeability (about 5–7 mD and about 100 mD). They observed that the imbibition velocity of the lower-permeability core was lower than that of the higher permeability core. Yang et al51 conducted experiments and simulated the process of retained fracturing fluid imbibition in shale. The results illustrated that the imbibition velocities were lower for the cores with lower porosity and permeability and the experimental velocities were smaller than those predicted theoretically. Therefore, the cumulative imbibed volume increased with the square root of the imbibition time according to the Handy's equation6. Additionally, the differences between the experimental velocities and velocities predicted by Handy's equation were more obvious if the porosity and permeability of cores decreased. With


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the introduction of high-tech equipment, some scholars studied the imbibition behavior of different pore-throats by means of NMR and CT. Liu et al

52

and Meng et al53 adopted NMR

technology to monitor the process of spontaneous imbibition in shale samples. The results of Liu et al52 showed that water initially imbibed into the core in larger pores and later into the smaller pores, while the water imbibition velocity was higher for cores with higher permeability. However, Meng et al53 (from the same research group) reported the opposite conclusion. The data were not consistent with the spontaneous imbibition theory of Washburn41. Jabbari et al

54

assumed that the experimental data might have been affected by some unexplainable factors. Several studies are found that experimentally address different factors effecting the imbibition of unconventional reservoirs, such as low permeability pores, tight sandstone, and shale. Those papers focused on measuring the recovery percentage and presented a summary of the experimental laws. Conversely, deep analysis of micro influencing mechanism was rarely conducted, which could potentially lead to the misunderstanding the mechanism of oil recovery by imbibition and the ambiguity of the conditions to be applied for unconventional reservoirs. In this paper, experiments of imbibition and displacement based on NMR and high-pressure mercury injection are conducted, the change in imbibition quantity and rate for different types of pore throats of hydrophilic tight sandstone reservoirs are studied, and the contribution to displacement is also analyzed.

2 EXPERIMENTAL Four different experiments were performed as part of this study, namely imbibition, water flooding (displacement), the high-pressure mercury injection, and the NMR experiments.


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2.1 Experimental protocol 2.1.1 Imbibition experiments The rock samples saturated with simulated oil were immersed in the imbibition fluid. The imbibition instrument with imbibition fluid and rock samples was placed in the incubator. By the volumetric method or NMR analysis, the volume of oil recovered by imbibition was measured at different times. This was used to calculate imbibition velocity and recovery percentage. 2.1.2 Water flooding experiments Displacement refers to the process in which one-phase fluid is injected into the rock by an external driving force to displace the fluid originally existing in. In laboratory, water is usually injected into the pores at either constant pressure or constant flow rate. The volume of fluid collected at the exit was used to calculate the oil production velocity and recovery under different displacement modes. 2.1.3 High pressure mercury injection experiments Mercury injection is a measure of the “pore-body-weighted pore-throat distribution”. The pore structure of rocks is extremely complex, and it can be viewed as a series of interconnected capillary network. The capillary force exerted by mercury injection and pore-throat radius can be determined using equation (1) ： pc =

2σ cos θ 0.735 ≈ r r

Where Pc is the capillary pressure and r is the pore throat radius. 2.1.4 Pore structure characterization using NMR According to the basic principle of nuclear magnetic resonance. The T2 time in single pore 100% saturated water can be expressed as 55：


(1)

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1 1 1 1 = + + T2 T2bulk T2surface T2diffusion

(2)

In equation (2): 1 T2surface

D ( γ GTE ) S 1 =ρ 2 ， = V T2diffusion 12

2

(3)

For a water-wet rock, the value of T2bulk can be ignored. The T2diffusion can also be ignored according to the established experimental methodology (G and TE are small) 55-57 . Therefore, Equation (3) is simplified to Equation (4), the T2 in single pore is proportional to the surface-to-volume ratio of the pore, which is a measure of the size of the pore. Thus, the observed T2 distribution of all the pores in the rock represents the pore-size distribution of the rock. S 1 = ρ2 T2 V

The relationship between the specific surface area and pore radius satisfy the equation 57-59

(4)

S FS = V rcn

. So, we can get:

T2 =

rcn ρ 2 Fs

It is difficult to measure ρ2 and Fs, due to which, it is impossible to transform T2 distribution to distribution curves of the pores using Equation (5). However, the pore radius is equal to the product of throat radius and pore-to-throat ratio, namely rc=c1rt. Substitute rc=c1rt into Equation(5). The relationship between the T2 and the pore-throat radius is given by Equation (6).


(5)

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T2

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(c r ) = 1t

n

ρ 2 Fs

(6)

1

Let

( ρ F )n C = 2 s ，then: c1

1

rt = CT2n The T2 distribution of core with 100% saturated water can be transformed into pore-throat radius distribution curve only if the values of C and n are obtained. The general NMR T2surface in a single pore at a mixed saturation is affcted by the water saturation and the wettability for pore-body-size rc. The wettability is assumed to be 1 when the core is hydrophilic, and not be changed after oil saturated and aging. It is assumed that the original saturated fluid in the pore can be completely displaced by the subsequent fluid during imbibition or displacement. Therefore, the water saturation in a single pore is 100% or 0% when oil and water coexist in the core, and the effect of water saturation in a single pore on the NMR test can also be ignored at a mixed saturation. 2.2 Experimental equipment Figure. 1 shows the schematic of the manufactured imbibition instrument. Compared with the conventional one, three holders were added at the bottom to ensure that the core entirely contacts with the imbibition fluid. The division value was 0.005 mL, which is more suitable for unconventional rocks.


(7)

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Figure. 1 Imbibition instrument The experimental setup mainly used for displacement experiment were equipped with high-precision pump having constant velocity and pressure, and could work under the temperature and pressure of reservoir. The instruments for NMR analysis was measured by MicroMR 12-025V||12MHz manufactured by Shanghai Niumag Technology Company while the high pressure mercury injection were analyzed by the AutoPore IV9510. 2.3 Experimental samples and conditions The experimental samples were obtained from reservoir of Mesozoic Yanchang Formation in Ordos basin, China. The parameters such as porosity, permeability and contact angle of the samples are presented in Table 1. Permeability and porosity were measured based on pressure decay method and Boyle's Law method, respectively. Contact angle were obtained from the Kruss DSA-100.

Table 1. Various parameters of samples core

length(cm)

diameter(cm) porosity(%)

permeability(10-3µm2) contact angle(°)

M1

2.360

2.508

0.150

9.81


75.05

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L1

2.306

2.506

8.49

0.139

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69.38

The rock type of the two samples are lithic quartz sandstone. The sandstone is moderately sorted, consisting mostly of clastic particles. These two samples consists of a relatively high abundance of interstitial materials, and their types are diversified, mainly the authigenic clay minerals (illite and chlorite) and carbonate cement (calcite and dolomite). The cementation type is mainly porous style. Intergranular pores, the pores formed by dissolution of feldspar and rock debris and a small amount of intercrystal pores are developed in the two samples. The temperature of imbibition and displacement experiments was 60 °C same as the reservoir temperature, while the temperature of NMR was 30 °C. The water used in the experiment was the simulated formation water of CaCl2 with the salinity of 22.11 g/L, density (1.003 g/cm3)and viscosity ( 0.523 mPa·s) at 60 °C. The oil used in the experiments was the customized simulated oil without hydrogen, which ensured that only the proton 1H signal of water will be detected. The density and the viscosity of the oil at 60 °C were 1.800 g/cm3 and 2.454 mPa·s, respectively. The viscosity was close to that of formation oil, ensuring that the oil-to-water viscosity ratio in the experiments was consistent with the one under reservoir conditions. 2.3 Experimental process The whole experimental process is shown in Figure. 2, whereas the specific experimental procedure is as follows. (1) After the core was washed of oil and dried, its dry weight was measured. The dimensions of the core were also measured. The porosity and permeability of the core were determined using N2 .


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(2) The core was placed in the vacuum saturator having vacuum of 10-3 Pa, and then saturated simulated formation water under 20 MPa (formation pressure). Its wet weight was measured, and the porosity of fluid was determined. (3) The core with 100% saturated simulated formation water was placed in the NMR core analysis meter. Carre-Purcelle-Meiboome-Gill (CPMG) sequence was selected as the pulse sequence. The waiting time (TW) (6000ms), echo numbers (8000), scanning times (256), echo spacing (TE) (0.2ms) and other key parameters were selected according to industrial standard SY/T 6490-2014. (4) The core was put into the core-holder with annular pressure applied. It was displaced with simulated oil until the bound water saturation was established under formation conditions. After 24 hours of aging, the core was taken out for NMR measurements. The test parameters were the same as listed in step (3). (5) The core was placed in the imbibition instrument filled with the imbibition fluid (The imbibition fluid and the imbibition instrument were put in the incubator for 2 h at 60 °C to minish error). The imbibition quantity was obtained at regular intervals, and then, the core was taken out to measure the weight and the relaxation time spectra T2, until the weight and the NMR porosity became stable. (6) Steps (1) - (4) were repeated, and the core, which has already completed imbibition experiment were placed in the core-holder with annular pressure applied. The core was displaced by simulated formation water (0.05 mL/min), and then, taken out to perform the NMR measurements when displaced to varying degrees. The test parameters were kept the same as quoted in step (3).


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(7) The core that have finished the above experiments were washed, dried and placed in high-pressure mercury injection apparatus for mercury injection experiment to obtain the capillary force curve .

Saturated water

Saturated Oil Imbibition ( simulated oil NMR NMR without water Swc Sw=100% hydrogen)

Total pore space

Pore space for movable fluid

NMR Sw1

Water flooding

Pore space for spontaneous imbibition

NMR Sor

Mercury injection

Pore space for water flooding

Figure. 2 Flow diagram of experiment

3 RESULTS AND DISCUSSIONS 3.1 Pore-throat distribution curves obtained from NMR analysis Because the geometrical morphologies of the pore distribution as reflected from mercury injection and the experiment of NMR for the core with 100% saturated water are the same 4, 60- 62. The cumulative distribution curves of NMR T2 and pore-throat radius with mercury injection were drawn in the same coordinate system in order of value, form large to small (Figure. 3 (a)). For any cumulative distribution frequency S(i)( S(i)≤SHgmax), there were a rt(i) in the cumulative distribution curve of pore-throat radius with mercury injection and a T2(i) in the NMR T2 cumulative distribution curve satisfy the Equation (7). Equation 8 shows the logarithm of both the sides of Equation (7) 1 ln rt = ln C + ln T2 n


(8)

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According to the principle of linear least square method, the values of fitting parameters C and 1   n in Equation (8) were obtained by solving the equation L = ∑ i =1  ln C + ln T2 ( i ) − ln rt ( i )  n  

2

m

for the minimum value. Figure. 3(b) shows the fitting result of pore-throat radius of core with mercury injection and NMR T2 relaxation time.

（a） The cumulative distribution curves of NMR relaxation time T2 and the pore-throat radius of high-pressure mercury injection

（b） Fitting result of pore-throat radius with mercury injection and NMR T2 Figure. 3 Transformation of the NMR T2 and pore-throat radius

Figure.4 Comparison of the pore-throat radius distributions by NMR and mercury injection


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Figure. 4 shows the comparison of the pore-throat cumulative distribution by NMR T2 converted and mercury injection. The two curves showed good consistency in terms of form and range, indicating that the method is reliable.

Figure. 5 Distribution of the pore-throat converted from NMR T2 Figure. 5 shows the distribution of the pore-throat converted from T2 spectra for cores M1 and L1 with 100% saturated water. The porosity component is defined as the ratio of the pore volume with a certain radius to the core surface volume, whereas the total of the porosity components is the porosity of the core. It can be seen that the data of the pore-throat distribution converted from T2 significantly increase as the range of the pore size, which shows the advantage of NMR in reflecting the distribution of tiny and complex pores. The NMR pore-throat distribution of cores M1 and L1 shows two peaks, indicating strong heterogeneity of pore distributions in cores. Although the porosity and permeability of cores M1 and L1 are nearly the same, there is a significant difference in the pore-throat distribution, where the right peak is higher than the left one in the core M1. However, the left peak is higher in core L1, indicating that the percentage of pore with bigger size is larger than the one with smaller size in core M1, which is opposite in core L1.


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3.2 Research of imbibition behavior 3.2.1 Fluid distribution in cores at different imbibition times

Figure.6 Fluid distribution in cores at different imbibition times The distribution of pore-throat occupied by water in cores M1 and L1 at different imbibition times are shown in Figure. 6. The water porosity component is defined as the ratio of the pore volume occupied by water in a certain scale pore to the core surface volume. The total water porosity component of the different pore size is the porosity obtained by NMR. Since the curve of core at bound water state represent the distribution of immobile water, the area between the two curves of core at the state of saturated water and bound water shows the distribution of movable fluid, and the area between the curves of core at the state of bound water and the abscissa shows the distribution of immobile fluid. Compared to the curve of core at the state of saturated water, the curve at the state of bound water has significantly declined. The right peak decreased significantly near to the horizontal coordinates, while the left peak declined to half of the one for the state of saturated water. These results indicate that the fluid in pores with bigger size was nearly movable, and only a small part was immovablly affected by the pore


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surface while the fluid in pores with smaller size was hardly able to move due to the large capillary and viscous forces. The water porosity component in pores with different sizes was increased with the imbibition time extension. Longer the imbibition time and the difference between the two curves will be smaller. Until the 5th day of imbibition, the volume of water in core did not increase significantly with the imbibition time extension. Referring to the pore classification in petroleum geology, it can be divided into nano-pore (less than 0.1 µm), sub-micro pore (0.1 - 1 µm), and micro pore (greater than 1 µm)63, 64. The sub-micro pore was the most widely distributed (accounting for 53.37% and 45.12% of the total, respectively) in cores M1 and L1, followed by nano-pore (accounting for 39.47% and 42.94% of the total, respectively), and the micro pore (accounting for 7.17% and 11.94% of the total, respectively). For different imbibition times, the water porosity component in nano-pore was the largest, followed by the sub-micro pore, and the micro pore. Based upon the fact that cores M1 and L1 were weak hydrophilic and the capillary force was the driving force for imbibition, the smaller the pore size, the larger the capillary force was, and hence, the imbibition power was greater. Therefore, the water porosity component was smaller in widespread micro pore but larger in nano-pore .


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(a) The distribution of nano-pore, sub-micro pore and micro pore in core M1

(b) Change of water porosity component in pores of different sizes at different imbibition times in core M1

(c) The distribution of nano-pore, sub-micro pore and micro pore in core L1

(d) Change of water porosity component in pores of different sizes at different imbibition times in core L1

Figure. 7 Comparison of water porosity component in pores of different sizes at different imbibition times


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3.2.2 Change in imbibition quantity and velocity in pore-throats with different sizes Figure. 8 shows the changes in imbibition quantities of total pore, micro pore, sub-micro pore, and nano-pore in cores M1 and L1. The variation in imbibition quantities with the imbibition time extension in different pores presented the same tendency. At the beginning of imbibition, the imbibition quantity rapidly increased. As the imbibition time extended, the increasing tendency gradually slowed down. At the later stage of imbibition, the imbibition quantity tended to stabilize and no longer changed with the imbibition time.

Figure. 8 Change in imbibition quantity of pores with different sizes with time The imbibition velocity of total pore was close to that of nano-pore with larger imbibition in core M1 and L1, indicating that imbibition of hydrophilic tight sandstone was mainly affected by the nano-pore. The imbibition velocity of nano-pore for the two cores decreased with the imbibition time extension, while that of sub-micro pore and micro pore presented different variation tendencies. Theoretically, the imbibition rate depends on the net effect of capillary pressure and the viscous resistance to flow6,65. The nano-pore shows high imbibition velocity due to the smaller size, larger capillary force and higher imbibition driving force. With the progress of imbibition, the water saturation in the nano-pore increased, causing the capillary force to drop rapidly and the imbibition rate to decrease. In the overall imbibition process, the capillary force


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was the main driving force for imbibition of nano-pore. However, at the beginning of imbibition, the imbibition processes of sub-micro and micro pore were controlled by the capillary force, and the imbibition velocity showed declining tendency with the increase in imbibition time. After a certain period of imbibition, due to the high saturation of water in the pores, the capillary force decreased. Additionally, the increase in water saturation may influence the water-rock interface interaction, thus enhancing the hydrophilicity of the rock’s wall-surface, which further leads to the increase in water flow in pores that increases the imbibition velocity with imbibition time. When imbibition goes on, due to the decrease in capillary pressure driving force that is greater than that of the increased easiness to water flow, the imbibition velocity begins to decrease with the imbibition time extension. The imbibition velocities of sub-micro and micro pore in cores M1 and L1 changed in different ways with the change in time, which may be have been caused by the distribution of pores in two cores and the connection of pore-throats with different sizes.

Figure. 9 Change in imbibition velocities of pores with different sizes with time


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3.3 Comparison of displacement and imbibition

3.3.1 Fluid distribution in cores at different displacement times

Figure. 10 Fluid distribution of core M1 at different displacement times Figure. 10 shows the distribution of water in core M1 at different displacement times. Compared with imbibition, the processes and results of displacement have significant differences for core M1. (1) In the water distribution for core M1 at different imbibition times, the left peak is higher than the right one, which is opposite during displacement. The main driving force for imbibition was the capillary force, and the smaller the pore size, the larger the capillary force. Therefore, water was easier to get into the pores with smaller size during imbibition. The driving force for displacement was the extra differential pressure. However, the flow resistance in pores with larger size was small, water was easier to get in and replace the oil. There are more large pores and less small pores in core M1. Therefore, the water distribution shows the form of right peak being higher than the left one during water flooding. (2) After the 5th day of imbibition, the water porosity changed slightly with the imbibition time extension, and the fluid distribution at the 5th, 7th, and 10th days of imbibition basically coincided with others. After 10 hours of displacement, the increase in water porosity component in cores stabilized with the displacement


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time. It indicates that imbibition is a slow process compared to displacement. Therefore, to fully understand imbibition and displacement of oil, a longer soaking time is needed to achieve the sufficient oil-water replacement and enhance the produced quantity of imbibition. (3)Compared with the final moments of imbibition, the water saturation after displacement was higher and therefore, more oil was produced, indicating that the water flooding effect was better than that of imbibition.

3.3.2 Comparison of the recovery and residual oil distribution The water distribution curves of cores M1 and L1 at the state of 100% saturated water, bound water, imbibition completed and displacement completed are shown on the same coordinate system (Figure. 11). The distribution of pores represented by the area enclosed by the curve of saturated water and abscissa (the sum of the red, green, yellow and blue parts). The area enclosed by the curve of bound water and abscissa (the red area) shows the bound water distribution. The area between the two curves of imbibition and bound water (the green area) shows the increasing of water phase caused by imbibition. The area between the two curves of imbibition and displacement (the yellow area) shows the distribution of extra water phase in core under the effect of displacement comparing with imbibition effect. The sum of the yellow area and the blue area was the distribution of the residual oil in cores after imbibition, whereas the blue area was that after displacement.


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Figure. 11 Distribution of bound water, produced oil and residual oil in cores Imbibition can replace the oil in pores with different sizes in core M1 and L1. The proportion of the produced oil by imbibition in pores of small size was higher. Compared with imbibition, all the water contained raised in the pores with different sizes in both cores after displacement, indicating that displacement is better than imbibition and the oil recovery of displacement is higher than that of imbibition. The extra produced oil mainly distributed in the sub-micro and micro pores. Additionally, in the distribution curve of water after displacement, the right peak was higher than the left one, illustrating that the oil recovery in pores with larger size was higher by displacement. The relative recovery percentage was calculated using the ratio of produced oil to the saturated oil in the pores, thus representing the difficulty of producing oil in the pores with a certain size (Table 2).

Table 2. Oil recovery and relative recovery percentage in pores with different sizes after imbibition and displacement Oil recovery/ Production Core Relative recovery modes percentage(%)

Nano-pore

Sub-micro pore

Micro pore

＜0.1µm

0.1 µm~1 µm

＞1 µm


Total pore

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imbibition

11.55

8.62

1.93

22.10

displacement 17.53

38.68

7.75

63.96

33.96 Relative recovery imbibition percentage displacement 51.53

14.80

24.89

-

66.42

100.00

-

6.53

1.93

21.34

displacement 16.23

15.94

11.14

43.31

40.26 Relative recovery imbibition percentage displacement 50.68

12.09

13.75

-

29.54

79.52

-

Oil recovery M1

imbibition

12.89

Oil recovery L1

The recovery of displacement for core M1 with a higher right peak in curves of pore distribution was higher than core L1. The recoveries of displacement in two cores were about 40% and 20% higher than those for imbibition. Moreover, the recovery of displacement in nano-pore, sub-micro pore and micro pore were higher than those for imbibition. The relative recovery percentage of nano-pore with larger capillary force and micro pore with smaller flow resistance were higher for imbibition, while that for sub-micro pore was relatively lower. There is more residual oil in the sub-micro and micro pores after imbibition (the sum of the blue and yellow areas in Figure. 11). Larger the sizes of pores were, higher the relative recovery percentage was during displacement. The oil in the micro pore of core M1 can almost be entirely extracted, and there was more residual oil distributed in the nano-pore and sub-micro pore after displacement (the blue area in Figure. 11).


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3.3.3 Contribution of imbibition to displacement in pores with different sizes

Figure. 12 Contribution of imbibition to displacement in pores with different sizes In the development of oil field, the process of imbibition and displacement always exist simultaneously. The contribution rate of imbibition to displacement is defined as the ratio of recovery by imbibition to the one by displacement in pore with a certain. The contribution rate of imbibition made to displacement in nano-pore of cores M1 and L1 were the highest (65.90% and 79.43%, respectively), followed by the that for sub-micro (22.29%, 24.89%, respectively) and micro pore-throats (40.94% and 17.29%, respectively). The contribution rate of imbibition made to displacement in total pore were 34.56% and 49.28%, respectively. The contribution rate of imbibition made to displacement in core L1 was higher, which has a higher left peak in pore distribution curve. In this core, the pore with smaller size was more distributed, and under the same experimental conditions, the effect of imbibition was stronger. It illustrates that for hydrophilic reservoirs with low permeability, the contribution of imbibition made to displacement cannot be ignored. Moreover, smaller the pore radius, higher was the contribution rate of imbibition made to displacement. Therefore, in the development of


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hydrophilic reservoirs with low permeability, especially for the fracturing reservoirs with low permeability and tiny pores, the effect of imbibition should be given full attention.

4 CONCLUSIONS In this paper, the hydrophilic tight sandstone samples from Yanchang formation of Ordos Basin (China) were taken as examples. The conversion from NMR T2 curves of cores M1 and L1 with saturated water to pore-throat distribution curves were completed. On this basis, the imbibition and displacement experiments were conducted, the change in imbibition quantity and rate for different kinds of pores were studied, and the contribution of imbibition to displacement was also analyzed. The results are of great guiding significance to the exploitation of hydrophilic tight sandstone reservoirs. (1) Although the porosity and permeability of cores M1 and L1 were nearly the same, the pore-throat distribution exhibited large differences. The right peak was higher than the left one in core M1, indicating that the distribution of pore with bigger size is larger than the one with smaller size, which is opposite in core L1. (2) By comparing the water distribution of cores M1 and L1 at the state of fully saturated water and bound water, it can be found that, the movable fluid was mostly distributed in the pores with larger size, while the immobile fluid mostly existed in the pores with smaller size and on the wall surface of the pores with bigger size. (3) The variation in the imbibition quantity with imbibition time extension in different pores of cores M1 and L1 basically presented the same tendency: At the beginning of imbibition, the imbibition quantity rapidly increased, then the increasing tendency gradually slowed down, and then the quantity of imbibition tended to stabilize and no longer changed with the change in imbibition time (about 5 days later).


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(4) The imbibition process of hydrophilic tight sandstone was mainly affected by the nano-pore. The imbibition velocity of nano-pore for the two cores decreased with the imbibition time extension, while that of sub-micro pore and micro pores presented different variation tendencies. (5) Compared with imbibition, displacement process was faster and had a better oil displacement efficiency. The extra produced oil through displacement was mainly in the sub-micro and micro pores. The relative recovery percentage in the pores with smaller size was higher after imbibition. For displacement, the larger the size of the pore-throats, the higher the relative recovery percentage would be. (6) The contribution rate of imbibition made to displacement in nano-pores was the highest, followed by the sub-micro and micro pores. For cores M1 and L1, the contribution rate of imbibition made to displacement was higher in core L1 with a higher proportion of small pores.

AUTHOR INFORMATION Corresponding Author

*Email: [email protected]

Notes

The authors declare no competing finanical interest.

ACKNOWLEDGMENT

This work has been funded by the National Natural Science Foundation of China (No. 51774308 , No.51674280 and No.51274226).


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NOMENCLATURE pc—capillary force, MPa; θ—contact angle between mercury and rock surface, °; σ—the surface tension of mercury and air systems, N/m; r—capillary radius, µm;

T2 — transverse relaxation time of the pore fluid as measured by a CPMG sequence, ms; T2bulk—T2 relaxation time of the pore fluid, ms; T2surface—T2 relaxation time of the pore fluid resulting from surface relaxation, ms; T

2diffusion—T2

relaxation time of the pore fluid as induced by diffusion in the magnetic field

gradient, ms;

ρ2 — T2 surface relaxivity (T2 relaxing strength of the grain surfaces) which varies with mineralogy, µm/ms;

S/V —ratio of pore surface to fluid volume, µm2/µm3; D—molecular diffusion coefficient, µm2/ms; γ—gyromagnetic ratio of a proton, rad·s-1·T-1;

G—field-strength gradient, gauss/cm; TE—inter-echo spacing used in the CPMG sequence, ms; rc—pore radius, µm; n—power exponent, non-dimensional; Fs—shape factor of pore, non-dimensional; c1—average pore-throat ratio, non-dimensional; rt—throat radius, µm.


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Fig. 1a 69x273mm (144 x 144 DPI)


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Fig. 1b 46x61mm (220 x 220 DPI)


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Fig. 2 976x281mm (144 x 144 DPI)


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Fig. 3a 89x63mm (300 x 300 DPI)


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Fig. 3b 89x63mm (300 x 300 DPI)


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Fig. 4a 89x63mm (300 x 300 DPI)


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Fig. 4b 89x63mm (300 x 300 DPI)


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Fig. 5 89x63mm (300 x 300 DPI)


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Fig. 6a 89x63mm (300 x 300 DPI)


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Fig. 6b 89x63mm (300 x 300 DPI)


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Fig. 7a 89x63mm (300 x 300 DPI)


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Energy & Fuels

Fig. 7b 89x63mm (300 x 300 DPI)


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 7c 89x63mm (300 x 300 DPI)


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Energy & Fuels

FIg. 7d 89x63mm (300 x 300 DPI)


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 8a 89x63mm (300 x 300 DPI)


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Energy & Fuels

Fig. 8b 89x63mm (300 x 300 DPI)


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 9a 89x63mm (300 x 300 DPI)


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Energy & Fuels

Fig. 9b 89x63mm (300 x 300 DPI)


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 10 89x63mm (300 x 300 DPI)


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Energy & Fuels

Fig. 11a 89x63mm (300 x 300 DPI)


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 11b 89x63mm (300 x 300 DPI)


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Energy & Fuels

Fig. 12 89x63mm (300 x 300 DPI)


Study of the Imbibition Behavior of Hydrophilic Tight Sandstone

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