Determination of full-scale pore size distribution of Gaomiaozi bentonite and its permeability prediction

Jingfeng Liu ,Shuibing Song ,Xulou Co ,Qingbin Meng ,b,Hi Pu ,Ynggung Wng ,Jinfeng Liu

a State Key Laboratory for Geomechanics and Deep Underground Engineering,School of Mechanics and Civil Engineering,China University of Mining and Technology,Xuzhou,221116,China

b Key Laboratory of Deep Earth Science and Engineering,Ministry of Education,Sichuan University,Chengdu,610065,China

Keywords:Gaomiaozi(GMZ)bentonite Pore size distribution(PSD)Pressure-controlled porosimetry(PCP)Rate-controlled porosimetry(RCP)Permeability High-level radioactive waste

A B S T R A C T Gaomiaozi(GMZ)bentonite is a potential buffer/backfill material for a deep geological disposal of highlevel radioactive waste.It has a wide pore size distribution(PSD)with sizes ranging from several nanometers to more than one hundred microns.Thus,properly characterizing the pore structures of GMZ bentonite is a challenging issue. In this study, pressure-controlled porosimetry (PCP), ratecontrolled porosimetry(RCP),and scanning electron microscopy(SEM)were used to investigate the PSD of GMZ bentonite.The results indicate that each method has its limitation,and a combined use of PCP and RCP is suitable to obtain the full-scale PSD of GMZ bentonite.Moreover,we also compared the full-scale PSD with nuclear magnetic resonance(NMR)result.It is found that there is no significant difference in the range of PSD characterization between NMR and mercury intrusion method(PCP and RCP).However,in a certain range,the detection accuracy of NMR is higher than that of mercury injection method.Finally,permeability prediction based on PCP and SEM data was conducted,and both of the two methods were found to be able to predict the permeability.The combined method is effective to obtain the full-scale PSD of GMZ bentonite,which is the key to estimation of the sealing ability of bentonite buffer.

1. Introduction

Bentonite has low permeability (when completely or near completely water-saturated)and good swelling abilities,which is considered as a potential buffer/backfill material for high-level and long-lived radioactive waste repository(Komine,2010;Wang et al.,2013;Niu et al.,2019;Wei et al.,2019).A number of studies have been performed with respect to various properties of bentonite or bentonite-based materials,such as swelling properties(Mishra et al.,2011;Cui et al.,2012;Wang et al.,2012;Liu et al.,2014a;Cui,2017;Yang et al.,2018;Tang et al.,2019),water transport properties(Cui et al.,2008;Komine,2010;Wang et al.,2013;Ye et al.,2014;Chen et al.,2015;Camillis et al.,2016),and gas migration properties(Harrington and Horseman,2003;Arnedo et al.,2008;Davy et al.,2009;Gutiérrez-Rodrigo et al.,2014;Liu et al.,2014b,2015; 2016; Xu et al., 2017; Yang et al.,2019).Regarding the permeability and swelling characteristics of bentonite,pore structure is a decisive factor,and pore size distribution (PSD) is a critical parameter in pore structure characterization.

Currently,there exist different techniques to measure PSD,such as mercury intrusion porosimetry(MIP),nitrogen adsorption(NA),nuclear magnetic resonance(NMR),scanning electron microscopy(SEM),and X-ray computer tomography(CT).All these methods have some limitations in characterizing PSD.For instance,CT fails to characterize the pores smaller than 50 nm and its application is of high cost(Blunt et al.,2013;Zhao et al.,2015).NA can merely recognize a narrow range of PSD,primarily nanopores(Zhang et al.,2016).MIP is a well-known technique adopted to measure the PSD of GMZ bentonite(Schanz and Al-Badran,2014;Chen et al.,2016;Liu,2016;Ye et al.,2009).It is acknowledged that this method may affect the accuracy of the size of small pores due to particle breakage and opening of closed pores at high pressures(Penumadu and Dean,2000;Kuila and Prasad,2013).Conventional MIP(pressure-controlled porosimetry(PCP))may also decrease the number of large pores because of the shielding effects of small pores(Kaufmann et al.,2009;Yao and Liu,2012).Then,a new approach was introduced to calculate the fine-scale pore structures of reservoir rocks as an alternative to PCP,known as rate-controlled porosimetry(RCP)(Yao and Liu,2012).The basic principle is that the injected mercury pressures fluctuate with variation of pore structure(Fig.1),with which the pores and throats information can be distinguished on the pressure oscillations.

In general,the PSD results obtained by different characterization methods vary significantly.To the best of the authors’knowledge,systematical investigation is rarely reported on the differences in pore structure characterization of bentonite using the results obtained by different test methods.Therefore,the innovation of this study is to provide an indirect method to characterize a full-scale PSD of bentonite,which can accurately characterize the pores from nano-to micro-scale. Finally, permeability based on the Winland model(Kolodzie,1980)from PCP data and a simplistic equation from SEM image analysis was calculated and compared with the measured value.The proposed method can effectively characterize the pore structure of bentonite and further predict its permeability,which is important for the evaluation of the sealing ability of bentonite barrier.

2. Materials and experimental methods

2.1. Materials

GMZ bentonite used in this context is sampled from Inner Mongolia Autonomous Region,northern China,where is currently selected as a buffer material for radioactive waste disposal(Chen et al., 2012, 2017). The main mineral components of GMZ bentonite are clay minerals,of which montmorillonite accounts for 98% (Liu et al.,2018).The PSD curves of GMZ bentonite powder are shown in Fig.2.The powder was pre-conditioned in a desiccator with relative humidity(RH)of 43% and temperature of 22°C until a constant mass was obtained.The prepared powder was compacted in a dedicated steel cylindrical mold to obtain a cylinder sample with 10.28% water content and 1.7 g/cm3dry density.The dry density has a close relationship with the swelling pressure(Kaufhold et al.,2015).The swelling pressure imposed by bentonite should be in a reasonable range,otherwise damage caused by swelling pressure to the surrounding rocks will be induced;it should not be too small,which will result in poor sealing effect.More details can be found in previous studies(Komine,2004;Villar and Lloret,2008;Zhang et al.,2010;Ye et al.,2014;He et al.,2016,2019;Liu et al.,2018).

Fig.1.Schematic diagram of the constant-rate mercury injection process:a,b and c are throats;1 and 2 are pores(Zhu et al.,2015).

Fig.2.PSD curves of GMZ bentonite powder.

2.2. Experimental methods

Four samples were dried in an oven at 105°C.Then,two samples were taken out from the oven and cooled down at room temperature,and then were put in an AP-608 automated porosimeterpermeameter(porosity)to measure the porosity and gas permeability.The other two samples were used for SEM and NMR tests,respectively.Then,the first two samples were taken out from the AP-608 porosimeter-permeameter to perform PCP and RCP tests.The experimental procedure is presented in Fig.3.

Fig.3.The experimental procedure used in this study.

2.2.1. Mercury intrusion porosimetry(MIP)

The basic principle of MIP is to promote mercury into the pores of the sample under increasing pressure.The mercury intrusion and extrusion curves are acquired by recording the intruded volume at each pressure(p)step;the pressure can be converted into the equivalent pore size(r)by means of the Washburn(1921)equation:

where θ is the contact angle(assumed to be 140°in the test)and σ is the mercury surface tension(σ=0.48 N/m).After the substitution of θ and σ,Eq.(1)can be re-written as

In this study,both PCP and RCP methods were adopted.PCP was performed with an Autopore IV 9505 porosimeter.The sample was first placed in an oven at 105°C for drying until the mass was stable.The length of the samples is 2 cm.The maximum intrusion pressure is 200 MPa.For PCP tests,both intrusion and extrusion curves were obtained.RCP was performed with a Coretest ASPE370 porosimeter.To keep a quasi-static injection rate (5 ×10-5mL/min), the maximum intrusion pressure was 6.2 MPa(corresponding to a pore throat radius of 0.12 μm).Prior to the RCP test,we firstly performed a calibration test with a stainless steel non-porous blank to obtain the pressure-volume curve.Afterwards,this curve can be used to calibrate the RCP data.

2.2.2. Nuclear magnetic resonance(NMR)

Low-field NMR technology uses hydrogen or nucleus in water or water to resonate in a magnetic field and generate signal characteristics to detect oil,gas,water and their distribution,as well as physical properties of the medium.In the NMR process,the relaxation time reflects the pore size.Because clay particles in bentonite will expand when exposed to water and cause pore structure deformation,we used kerosene as the fluid medium.Therefore,the transverse relaxation time T2spectrum was used to show the PSD of the sample.The larger the pore size,the longer the corresponding relaxation time.The T2spectrum and the sample pore size have the following relation:

where ρ is the surface relaxivity(μm/ms);S is the pore surface area(μm2);V is the pore volume(μm3);and F is the geometrical form factor,and it equals 3 and 2 for spherical and columnar pores,respectively.In this study,spherical pores were chosen for equivalence.The surface relaxivity was taken as 0.05 μm/ms.

2.2.3. Scanning electron microscopy(SEM)

A small piece(e.g.10 mm×5 mm×5 mm)was broken off from the regular cylindrical sample.The sample pore structure was characterized at different magnifications from×1000 to×10,000 using an FEI QuantaTM 250 field-emission microscope.Regarding the PSD determination and permeability calculation,the format of the image was firstly changed into 8-bit greyscale.Next,we set the scale of the image according to the known distance.Subsequently,the threshold,which can distinguish the pore and the particle,is set.We first calculated the porosity based on the SEM image by different algorithms and then compared it with NMR results.For comparative analysis, a suitable thresholding algorithm was selected for SEM image segmentation.Finally,the pore structure information(e.g.radius,area and porosity)can be retrieved from the grey-level images and the permeability can be predicted based on the pore structure information.

2.2.4. Establishment of comparison standard

When calculating the frequency(fq1)of PSD,we divided the mercury intrusion volume(Vp)at each mercury intrusion pressure by the total mercury intrusion volume(Vm):

However,the mercury intrusion saturation of PCP and RCP is very different(95.95% vs.42.51% ).To facilitate the comparison between the PCP and RCP results,we chose the total pore volume(Vt)to calculate the frequency(fq2):

This method is also applicable to NMR technology.The total pore volume is calculated by multiplying the helium porosity by the bulk volume.

3. Results and discussion

3.1. PCP results

The PCP intrusion curves of GMZ bentonite sample are presented in Fig.4 and the corresponding parameters are tabulated in Table 1.From this figure,there exists a horizontal period of the intrusion curve with intrusion pressure ranging from 0.007 MPa to 0.67 MPa,which corresponds to a highly porous region.Mercury started to enter the sample under entry pressure of 0.007 MPa.The displacement pressure can represent the size and distribution of the maximum connected pores,which has a good correlation with permeability.This value is equal to 1.36 MPa,equivalent to the maximum pore-throat radius of 0.54 μm.The maximum mercury intrusion saturation is 95.95% (at 124 MPa).Despite the large value of intrusion saturation,the residual mercury saturation is only 60.72% when the pressure drops to the atmospheric pressure,i.e.a portion of injected mercury is still trapped in the pore network.This phenomenon implies the relatively poor pore network connectivity and the existence of inkbottle-shaped pores(Kaufmann et al.,2009;Zhao et al.,2015).Since the capillary pressure is not large enough to extrude mercury,some pores with wide bodies and narrow necks are still filled with mercury in pores when extruding mercury.In addition,the non-wetting fluid is difficult to form a continuous flow in the pore network due to poor connectivity.As a result, this phenomenon leads to a lower mercury extrusion efficiency.

Fig.4.Intrusion and extrusion curves obtained by PCP.

Table 1 Key parameters for PCP and RCP.

Fig.5 shows the PSD measured by PCP over the size range from 0.003 μm to 53.667 μm.The pores with a radius larger than 1 μm are rarely observed,while the pores with radii between 0.03 μm and 0.3 μm account for more than 50% of the total pores.According to the classification standard suggested by Loucks et al.(2012),nanopores are within the range from 1 nm to 1 μm,micropores within the range from 1 μm to 62.5 μm,and mesopores within the range from 62.5 μm to 4 mm.The pores investigated in this study are mainly composed of nanopores.In addition to this method,International Union of Pure and Applied Chemistry(IUPAC)has also proposed a PSD classification method,in which micropore are less than 2 nm,mesopores are within range of 2-50 nm,and macropores are larger than 50 nm(Rouquerol et al.,1994).

Fig.5.PSD curve obtained by PCP.

3.2. RCP results

A RCP curve is presented in Fig.6,and the corresponding parameters are tabulated in Table 1.The displacement pressure is 2.17 MPa,corresponding to the maximum pore-throat radius of 0.34 μm.The tendency of the total intrusion curve is almost in accordance with that of the throat intrusion curve.The pore mercury saturation is less than 1% for the whole stage.The final mercury intrusion saturation of the throat is 42.18% ,which is much larger than that of pore space(0.32% ).The total mercury saturation of RCP is 42.51% ,which is much lower than that of PCP(95.95% ).The difference is related to the maximum intrusion pressure of RCP,which is only 6.12 MPa(corresponding to a pore size of 0.12 μm).As a result,RCP cannot characterize the pores less than 0.12 μm,which occupy a large part of the total pores.

Fig.7a reveals only a narrow range of throat size distribution,from0.118μm to9.42μm.There are two peaks:a right mainpeak and a left subsidiary peak.From 1 μm to 9.42 μm,the radii of most pores(or throats)range between 5 μm and 9.42 μm,with a peak value of 7.46 μm.From 0.1 μm to 1 μm,most pores are between 0.26 μm and 0.3 μm,with a peak value of 0.29 μm.As mentioned previously,a large number of pores(＜0.12 μm)cannot be characterized by the RCP method due to the low maximum intrusion pressure.

The pore distribution ranges from 100 μm to 170 μm,with two peak values(140 μm and 160 μm)(Fig.7b).However,the frequency of the large pores is very low when compared with those of the throats(Fig.7c).It should be noted that when calculating the distribution frequency of pore(throat),the denominator is only the volume of pore(throat).When the distribution frequency of pore and throat is superposed on the same image,the denominator is the sum of pore and throat volume.In addition,the pores ranging from 10 μm to 100 μm are missing and the pores larger than 100 um are very few,which means that RCP has poor characterization effect on large pores.

An SEM image(Fig.8a)shows that most of the pores have a size of approximately 0.1 μm,which is in accordance with the PCP result.The large pores can reach 10.71-12.5 μm.These large pores are usually distributed among some large solid particles,but with limited amount(Fig.8b).

Fig.6.Intrusion and extrusion curves obtained by RCP.

Fig.7.Distribution of the characteristic parameters in RCP:(a)Throat,(b)Pore,and(c)Throat+pore.

3.3. Comparison of PCP and RCP results

Fig.8.(a)PSD histogram of GMZ bentonite analyzed by SEM image;and(b)SEM image of GMZ bentonite.

In fact,both of the PCP and RCP methods reflect the identical physical mechanism of mercury injection.Overall,the mercury intrusion curves measured by the two techniques match well,with some discrepancies at the low injection pressure stage(Fig.9).The intrusion saturation of PCP at 6.2 MPa(i.e.the maximum intrusion pressure for RCP)is smaller than that of RCP.The discrepancies between the two methods range from 0.4% to 16% .Regarding the discrepancies,some factors can affect the shift of the MIP curve.First,the compression of grains due to high intrusion pressure for PCP can affect the pore structure of the sample,and in turn affect the mercury intrusion curve.In addition,a correction curve was acquired by performing RCP test on a stainless steel blank,while no similar calibration test was performed for PCP.Third,for RCP,the contact angle and interfacial tension are constant.This is mainly due to the quasi-static constant value of the intrusion velocity.However,those values are varying for PCP because of a high mercury intrusion velocity(Clarkson et al.,2013;Zhao et al.,2015). As a result, mercury cannot enter the small pores(or throats)easily due to the variations in contact angle and interfacial tension.Therefore,the intrusion mercury saturation of PCP is smaller than that of RCP.

3.4. Determination of full-scale PSD

Fig.9.Comparison of PCP and RCP tests on GMZ bentonite.

Despite some discrepancies between the two methods,the intrusion curves measured by the two methods can still be considered identically.As described above,it is inappropriate to obtain the full-scale PSD of GMZ bentonite using a single method due to the wide PSD range.RCP cannot characterize pores with a radius smaller than 0.12 μm,because the mercury cannot enter these pores at the low injection pressure.For the pores ranging from 2.26 μm to 9.1 μm and that higher than 100 μm,PCP fails to identify these pores;however, they can be measured by RCP(Fig.10a).The purpose is not to correct the PSD curve,but to obtain the full-scale PSD of GMZ bentonite.Therefore,the PCP and RCP methods can be combined based on the intersection(i.e.at a pore radius of 2.26 μm,9.1 μm and 100 μm).

As shown in Fig.10b,the red part was characterized by PCP and the blue part by RCP.The full-scale PSD of GMZ bentonite is a polymodal curve with pore size ranging from 0.003 μm to 170 μm.Two peaks exist when the pores are less than 1 μm,with values of 0.01 μm and 0.12 μm,respectively.In contrast,there exist several peaks when pore radii are higher than 1 μm.As shown in Fig.11,the GMZ bentonite exhibits a multi-scale porosity:inter-laminar pore,intra-aggregate pore and inter-aggregate pore.The inter-laminar pores and intra-aggregate pores are usually less than 0.1 μm and cannot be observed in the SEM image.The inter-aggregate pores are in the range from 0.1 μm to 100 μm and can be observed by SEM image directly.The pores larger than 100 μm are possibly the residual inter-particle pores or microcracks.According to the pore size classification proposed by Loucks et al.(2012),the distribution frequencies of nanopores,micropores and mesopores are 71.74% ,7.27% and 0.92% ,respectively(Fig.12).Nanopores and micropores are the main pore size types,of which nanopores are the dominant.This constitution is favorable for the sealing behavior of GMZ bentonite.From high suction(low RH)to low suction(high RH),some micropores and mesopores can be filled by the swollen clay aggregates when they absorb water(Fig.13).As a result,sealing can be achieved.

3.5. Comparison with NMR result

At present,NMR is widely used to characterize pore structures,especially to determine the PSD,because of its nondestructive properties.Therefore,we further compared the PSD curves obtained by PCP-RCP with that obtained by NMR.As shown in Fig.14a,it is found that NMR technology can well characterize the pores in the range of 0.54-6.17 μm,while MIP is not effective in detecting this size range of the pores.Similarly,we cut the curve at values of 0.54-6.17 μm to obtain a new full-scale PSD curve(Fig.14b).When combined with MIP,the range of characterization remained unchanged.Only in a certain region,the detection accuracy of NMR is higher.

Analysis result shows that PCP and RCP can better characterize the pores in the whole scale.In particular,the range of PSD characterized by PCP is wider.If combined with NMR technology,the pore size in the 0.54-6.17 μm interval can be better characterized.PCP technology is preferred if experimental conditions are limited.

In this study,we focused on the acquisition of full-scale pore size of dry samples.However,in practical engineering,most of the soil/rock mass is in unsaturated or saturated state.If ovendrying is used,the pore structures may be destroyed.Therefore,it can be freeze-dried and the proposed method can be adopted.

3.6. Permeability prediction based on MIP data and SEM image

3.6.1. Winland model

Permeability prediction is of great importance for sealing estimation of the buffer/backfill materials.PCP is frequently used in combination with the investigation of permeability.Several models have been proposed to predict permeability based on some parameters,e.g.porosity,pore connectivity,pore size and grain surface(Kolodzie,1980;Pittman,1992;Rezaee et al.,2006).Among these models,the Winland model(Kolodzie,1980)is commonly used to predict the permeability:

Fig.10.PSD curves obtained by combination of PCP and RCP:(a)Original curve,and(b)Full-scale curve.

Fig.11.Multi-scale pore structure of GMZ bentonite(Le Pluart et al.,2004;Agus et al.,2010).

where k is the permeability(mD);a1,a2and a3are the empirical variables;φ is the porosity;and R35is the pore-throat radius that corresponds to a mercury saturation of 35% .Winland calibrated his model with a series of tests on 82 samples(56 sandstones and 26 carbonates)and further with 240 samples(Pittman,1992).The calibration test gave the following values of the empirical variables:a1=49.4,a2=1.7 and a2=1.47.Using these parameters,the permeability for GMZ bentonite is calculated equal to 2.1 ×10-16m2, which is very close to the measured values(2.58×10-16m2and 1.38×10-16m2,see Table 1).Although the unknown parameters are calibrated with sandstones and carbonates,it is found that these parameters can be used to predict the gas permeability of GMZ bentonite very well.

3.6.2. SEM imaging

Complementary to the permeability obtained from MIP based on Winland model, the SEM images can also determine the permeability merely based on geometrical information(Guo et al.,2019;Song et al.,2019).The pores in the SEM image can be simplified as a system of ducts having varied cross-sectional area Ai(Fig.15),and the total cross-sectional area is A.In the case of filtration,the total flow rate Q perpendicular to the cross-section equals the sum of elementary flow rates Qithrough the individual ducts:

From the Darcy’s law,we have

where μ is the viscosity of the fluid,and i is the hydraulic gradient.Combining Eqs.(7)and(8),we have

According to Hagen-Poiseuille equation describing flow transport in a tubular duct(Landau and Lifshitz,1987),a flow rate Qithrough an elementary duct i can be expressed as

Fig.12.PSD histogram of GMZ bentonite obtained by a combination of PCP and RCP.

Fig.13.SEM images of GMZ bentonite at different RH values.

Fig.14.PSD curves obtained by a combination of PCP,RCP and NMR:(a)Original curve,and(b)Full-scale curve.

where Riis the radius of circular cross-section of a duct i.

After substituting Eq.(10)into Eq.(9),the following relationship is obtained:

The pore structure information(Aiand Ri)was extracted from the SEM image.To avoid the influence of the computational domain,the box counting method was applied.We chose five different positions(center,top left,top right,bottom left and bottom right)and extended the computational area until stable value was obtained(Figs.16 and 17).Using this method,the calculated permeability was determined as 6.89 ×10-15m2,which is apparently higher than the measured values(2.58×10-16m2and 1.38×10-16m2).When compared with Winland model,its deviation is larger,as shown in Fig.18.For Eq.(11),we did not consider the effect of tortuosity.In addition,SEM image is two-dimensional,thus it cannot reflect the tortuosity of the pore structure in the Z-direction. As a result, there is a difference between calculated and measured results.Further,we can reconstruct the three-dimensional pore structure of GMZ bentonite based on FIB/SEM or CT technology and calculate the permeability with the pore structure information.Overall,the predicted values based on Winland model and SEM imaging match well.Therefore,these two approaches are feasible to predict the gas permeability of GMZ bentonite when experimental conditions are limited.

Fig.15.Total flow rate Q perpendicular to a flat segment of GMZ bentonite as the sum of the elementary flow rate Qi through individual duct.

Fig.16.Computational area and box counting.

Fig.17.Permeability of GMZ bentonite calculated based on the SEM image.

Fig.18.Comparison of the gas permeability between predicted(kSEM and kWinland)and measured values(kNo.2 and kNo.2).

4. Conclusions

In this study,we attempted to combine PCP and RCP techniques to characterize the overall PSD of GMZ bentonite. The major concern is to merge the PSD at where they overlap.Additionally,NMR can detect the pores in the range of 0.54-6.17 μm with a high accuracy,which can be considered as a supplementary method to the PCP-RCP measurement.In addition,GMZ bentonite has a multiscale porosity:inter-laminar pore,intra-aggregate pore and interaggregate pore. Only inter-aggregate pores can be observed directly by SEM image.Based on the pore size classification,the main pore types are the nanopores and micropores,among which the nanopores are dominant.

The Winland model based on PCP data and a simple equation based on the SEM image were adopted to predict the permeability of GMZ bentonite.Such an estimation procedure of the permeability was found to be an alternative when experimental conditions are limited. For the SEM imaging technology, any empirical variable is not required,as it is based on the pore structure information. However, there exist some differences between the calculated and measured results.This deviation is related to some limitations of these technologies,e.g.tortuosity of the pore structure in Z-direction,and empirical variables used in the model.

In further study,we would adopt a similar method to obtain the full-scale PSD of other materials(e.g.sandstone and shale)by combination of PCP and RCP,and predict the gas permeability using SEM image and PCP data.This prediction is important for the estimation of the sealing ability of GMZ bentonite,and also for the storage capacity evaluation of tight oil reservoirs(e.g.sandstone gas and shale gas).

Declaration of Competing Interest

The authors wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgments

The authors are grateful to the support of the National Natural Science Foundation of China(Grant Nos.51809263)and the Open Fund of Key Laboratory of Deep Earth Science and Engineering(Sichuan University)(Grant Nos.DESE201906 and DESE201907).