Comparison of CO2 Flow Behavior Through Intact Siltstone Sample Under Tri-Axial Steady-State and Transient Flow Conditions

applied sciences

Article Comparison of CO2 Flow Behavior through Intact Siltstone Sample under Tri-Axial Steady-State and Transient Flow Conditions

Chengpeng Zhang 1 ID , Ranjith Pathegama Gamage 1,* ID and Mandadige Samintha Anne Perera 2 ID 1 Deep Earth Energy Laboratory, Department of Civil Engineering, Monash University, Building 60, Melbourne, VIC 3800, Australia; [email protected] 2 Department of Infrastructure Engineering, The University of Melbourne, 209B, Building 175, Melbourne, VIC 3010, Australia; [email protected] * Correspondence: [email protected]; Tel.: +61-3-9905-4982

Received: 20 March 2018; Accepted: 27 June 2018; Published: 5 July 2018

Abstract: With its low viscosity properties, CO2 has much greater penetration capacity into micro-fractures, and therefore has more potential to create expanded and effective fractures in shales during the hydraulic fracturing process. However, the feasibility of this technique is dependent on the accurate prediction of formation flow characteristics, given the high leak-off of CO2 at deep depths. The aim of this study is therefore to understand the flow behavior of CO2 in deep shale plays. A series of tri-axial permeability tests was conducted under both steady-state and transient conditions. The test results show much lower permeability values for liquid CO2 than gaseous CO2, and the permeability under transient conditions is much lower than that under steady-state conditions, due to the combined effects of the reduced slip-flow effect under low pressures and the temperature variation influence under steady-state conditions. Under steady-state conditions, unstable flow behavior occurred at higher injection pressure (≥9 MPa) possibly due to the fine mineral particle migration and the deposition of small drikold particles, which indicates the serious error in permeability calculation under steady-state conditions. Importantly, a greater than 1 effective stress coefficient (χ) for permeability in tested siltstone was observed, confirming the greater sensitivity of CO2 to pore pressure than confining pressure.

Keywords: CO2 apparent permeability; CO2 phase transition; siltstone; steady-state conditions; transient conditions

1. Introduction Being a green energy source, natural gas has recently attracted increased scientific and industrial interest, and shale gas accounts for more than 63% of the total global sources of unconventional gas [1]. The economic exploitation of shale gas therefore has the ability to satisfy the increasing world energy consumption [2]. Although the extremely low permeability of the shale matrix obstructs gas migration from the matrix to the production wells, some reservoir-enhancement techniques, such as hydro-fracturing, can significantly enhance permeability by creating a fracture network between the production wells and the shale matrix, that eventually enhance shale gas productivity [3–5]. For the hydraulic fracturing process, water-based fracturing fluids are currently used. However, this has raised many issues, including formation damage, long clean-up times, excessive water consumption and wastewater generation [6–9]. Liquid CO2 with low viscosity can be used as an alternative to water-based fracturing fluids [10], which avoids most of the issues created by water-based fluids. The use of CO2 as a fracturing fluid

Appl. Sci. 2018, 8, 1092; doi:10.3390/app8071092 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 1092 2 of 26

also contributes to CO2 geo-sequestration, which has already been successfully verified in some shale formations [11]. During the fracturing process, CO2 is often injected into reservoir formations in its liquid or super-critical state in a short time, and high pressurized CO2 can fracture the shale matrix or open up existing fractures [12]. However, the low viscosity of CO2 and its high penetration capacity cause very fast leak-off rates [13], and insufficient leak-off control can cause unacceptably high injection rates and excessive CO2 consumption, challenging the capacity of the fracturing pump. Consequently, treatment using CO2 may not be applicable to relatively high permeable reservoirs for hydraulic fracturing. After the completion of the fracturing process, CO2 flows from the shale matrix to the wellhead through the fracturing wells, where CO2 is easily subjected to phase transition among gaseous, liquid and super-critical states because the physical properties of CO2 are highly pressure- and temperature-dependent [14]. The huge pressure gradient induced near the fracture points upon the release of injection pressure may cause fine particle migration, which can move from the reservoir to the well along the CO2 flow [15]. Furthermore, since injecting CO2 into depleted oil and gas reservoirs and saline aquifers also contributes to the geological storage of CO2, the safe storage of injected CO2 in these formations depends on the ultralow permeable rock layers lying above the formation [16,17]. As the primary security key for CO2-based hydraulic fracturing and the associated geological storage of CO2, a full understanding of CO2 flow behavior in low permeable formations under different in situ environments is therefore essential, otherwise, erroneous leak-off rate estimations based on a vague understanding of CO2 flow behavior in gas reservoirs can lead to inaccurate estimation of total CO2 usage and prediction of the CO2 injection rates required for fracturing. On the other hand, the complicated thermodynamic properties of CO2 increase the complexity of precisely estimating the apparent permeability of shale for CO2. Various methods have been developed to measure the permeability of reservoir rock with ultralow permeability and studies have been performed under both steady-state and transient conditions [18]. For steady-state conditions, the downstream pressure can be controlled to achieve a specific pressure gradient along the sample, and many tests under steady-state conditions have been achieved by opening the downstream to the atmosphere, offering atmospheric downstream pressure conditions, and flow rates are measured when the pressure distribution along the sample reaches equilibrium. However, this fails to secure super-critical or liquid CO2 flow downstream, resulting in phase variation of CO2 throughout the sample [19]. These issues can be overcome by using transient tests, in which the downstream outlet is closed, giving the opportunity for downstream pressure development [20]. However, the calculation of transient permeability is much more complicated than the steady-state calculation, and researchers have used downstream pressure development curves for this purpose [21]. Depending on the experimental conditions, transient tests and steady-state tests closely correspond to the CO2 injection process and the CO2 clean-up process, respectively. In theory, the apparent permeability for CO2 through sample is independent of different measurement techniques. Existing research shows that permeability results using transient techniques may be up to twice greater than permeability calculated using steady-state approaches in low permeable rocks, due to the many assumptions made in transient calculations [21]. Rushing et al. [18] found five times greater permeability using the transient approach compared to the steady-state approach. This exhibits differences among permeability calculations under steady-state and transient conditions [22]. Importantly, permeability calculation under both conditions may have considerable errors if the possible CO2 phase transition through the rock mass is not considered under steady-state conditions [23]. As a result, precise knowledge of the liquid CO2 flow behavior in the reservoir rock mass is vital. Zhang et al. [24] proposed a new method to calculate the apparent permeability for gaseous and liquid CO2 under steady-state conditions, and speculated that the permeability for liquid CO2 at higher than 12 MPa calculated by the traditional method can deviate greatly from the actual value. This study therefore attempts to distinguish the flow behavior of CO2 at higher pressures considering the CO2 phase transition between liquid and gaseous phases, and to identify the difference between Appl. Sci. 2018, 8, 1092 3 of 26 steady-stateAppl. Sci. 2018, 8 and, x FOR transient PEER REVIEW conditions, following a comprehensive set of permeability experiments3 of on 26 siltstone based on different confining and injection pressures at room temperature. 2. Experimental Methodology 2. Experimental Methodology 2.1. Sample Description 2.1. Sample Description Since siltstone is one of the primary rocks in many shale formations, and both siltstone and shale haveSince similar siltstone mineral is compositions one of the primary and pore rocks structures in many shale[25], formations,siltstone sample and bothwas siltstoneused in this and study shale haveas an similar alternative mineral to compositions shale samples and to pore investigate structures the [25 CO],2 siltstoneflow behavior sample in was shale used formations. in this study The as ansiltstone alternative outcrop to shale sample samples was collected to investigate from the COEidsvold2 flow formation, behavior in Queensland, shale formations. Australia, The siltstoneand the outcroptotal porosity sample of wasthe dry collected siltstone from measured the Eidsvold using the formation, mercury Queensland,intrusion method Australia, was around and the 19.5 total%, porositywhich is ofhigher the dry than siltstone that of measured most shale, using but thestill mercury available intrusion in some methodshale formations was around [26 19.5%,], and whichthe bulk is higherdensity than was thataround of most 2.24 g shale,/mL. The but stillpore available size can be in calculated some shale by formations measuring [ 26the], pressure and the bulk and volume density wasof injected around mercury 2.24 g/mL. [27], The and pore the pore size candistribution be calculated of the by tested measuring sample the is plotted pressure in and Figure volume 1. This of injectedsiltstone mercury has very [27 tiny], and pores, the poreand the distribution median pore of the diameter tested sample is around is plotted 625 nm in Figureand 171..2 This nm siltstonein terms hasof pore very volume tiny pores, and andarea, the respectively. median pore This diameter pore structure is around was 625 then nm validated and 17.2 nmby performing in terms of a pore CT volumescanning and test area, on a respectively.sample with Thisa diameter pore structure of 13 mm, was as thenCT scanning validated can by offer performing non-destructive a CT scanning three- testdimensional on a sample imaging with a of diameter the interior of 13 mm, structure as CT (see scanning Figure can 2 offerand non-destructiveFigure 3). The porosity three-dimensional obtained imagingthrough CT of the testing interior was structure 15.4% calculated (see Figures based2 and on3 the). The watershed porosity algorithm obtained through[28,29], which CT testing is slightly was 15.4%lower calculatedthan the value based obtained on the watershedfrom mercury algorithm intrusion [28 testing.,29], which There is slightlyare many lower pores than with the varying value obtainedsizes in the from siltstone, mercury although intrusion only testing. a limited There number are many of pores pores are with of the varying order sizesof magnitude in the siltstone, of 100 althoughµm and most only of a the limited pores number are of the of order pores of are 1 µm of the (see order Figure of magnitude2). 3-D CT images of 100 canµm be and reconstructed most of the poresby superimposing are of the order CT ofslices 1 µm and (see only Figure show2). 3-Dthe CTpore images structure can (see be reconstructed Figure 3), where by superimposing tiny pores are CTevenly slices distributed and only and show connected the pore with structure each other (see Figurethrough3), small where pore tiny throats. pores are Regarding evenly distributedthe mineral andcomposition connected of with the each tested other siltstone, through according small pore to throats. XRD analysis, Regarding the the tested mineral dry siltstone composition is mainly of the testedcomposed siltstone, of quartz according (43%) to andXRD kaolinite analysis, the(40%), tested and dry the siltstone tiny kaolinite is mainly particles composed (<2 of µm quartz) separate (43%) andquartz kaolinite-quartz (40%),particle and contacts the tiny and kaolinite segment particles the space (<2 formedµm) separate by quartz quartz-quartz particle skeletons particle [30 contacts]. As a andresult, segment the high the clayspace content formed in by the quartz tested particle siltstone skeletons sample [30 contributes]. As a result, significantly the high clay to content this pore in thenetwork tested [31,32 siltstone]. This sample overall contributes pore structure significantly governs to this the pore low network permeability [31,32 of]. Thisthis sedimentaryoverall pore structuresiltstone [ governs33]. the low permeability of this sedimentary siltstone [33].

Figure 1 1.. Pore size distribution defined deﬁned by incremental pore volumevolume and pore areaarea [[2424].]. Appl. Sci. 2018, 8, 1092 4 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 26

Figure 2. CT images of cylindrical siltstone sample with diameter of 13.0 mm and height of 13.5 mm Figure 2. CT images of cylindrical siltstone sample with diameter of 13.0 mm and height of 13.5 mm Figure(black cavities 2. CT images represent of cylindrical pores). siltstone sample with diameter of 13.0 mm and height of 13.5 mm (black cavities represent pores). (black cavities represent pores).

Figure 3. Reconstructed 3-D CT images of pore structure with sample size of 6 mm × 7 mm × 7 mm Figure 3. Reconstructed 3-D CT images of pore structure with sample size of 6 mm × 7 mm × 7 mm Figure(pores are 3. Reconstructed shown in blue). 3-D CT images of pore structure with sample size of 6 mm × 7 mm × 7 mm (pores are shown in blue). (pores are shown in blue). 2.2. Experimental Procedure 2.2. Experimental Procedure A sample of dry siltstone 38 mm in diameter and 76 mm in height was first prepared in the Deep EarthA Energy sample Researc of dry siltstoneh Laboratory 38 mm at inMonash diameter University, and 76 mm and in the height detailed was first prep preparedaration procedure in the Deep is Earthreported Energy by Ranjith Researc andh Laboratory Perera [34] at and Monash Zhang University, et al. [24]. and the detailed preparation procedure is reportedIn the by present Ranjith study,and Perera permeability [34] and testsZhang were et al. performed [24]. under both steady-state and transient tri-axialIn the conditions present atstudy, room permeability temperature tests (stabilized were performed at 22 °C) by under injecting both CO steady2 with-state 99.95% and purity. transient To tri-axial conditions at room temperature (stabilized at 22 °C) by injecting CO2 with 99.95% purity. To Appl. Sci. 2018, 8, 1092 5 of 26

2.2. Experimental Procedure A sample of dry siltstone 38 mm in diameter and 76 mm in height was first prepared in the Deep Earth Energy Research Laboratory at Monash University, and the detailed preparation procedure is reported by Ranjith and Perera [34] and Zhang et al. [24]. In the present study, permeability tests were performed under both steady-state and transient ◦ tri-axial conditions at room temperature (stabilized at 22 C) by injecting CO2 with 99.95% purity. To avoid the effect of sample variance on the permeability results, only one dry sample was used. After each confining pressure from 10 MPa to 40 MPa became constant, permeability testing started. Sub-critical CO2 was injected into the siltstone sample, maintaining the injection pressure at a value of less than 90% of confining pressure to avoid possible CO2 leak-off through the sample-membrane boundary. For steady-state tests, the downstream outlet was opened to the atmosphere, and once the CO2 flow rate at the downstream became constant, the injection pressure was increased to the next higher value. Similar tests were conducted for a series of gas injection pressures. Since the expansion of CO2 flow along the sample can absorb heat from the surroundings and temperature fluctuation can affect accuracy in measuring permeability, a thermometer was placed in the tri-axial cell to monitor the temperature change in confining pressure oil during the tests. The temperature in the confinement cell remained steady at 22 ◦C, which indicates the constant ambient temperature around the sample. For transient condition tests, the outlet was closed, and once the downstream pressure reached the injection pressure, both upstream and downstream pressures were released to remove the injected CO2 from the sample, and the pressure release was done at a very slow rate of 0.2 MPa/min controlled by a pump to avoid any sudden CO2 volumetric expansion with the associated temperature change. Once the downstream pressure reached the atmospheric pressure and the flow rate at downstream dropped to zero, the next injection pressure was initiated, and similar tests were conducted for a series of gas injection pressures. Considering the possibility that multiple cycles of pressurization and depressurization may cause serious and irreversible structure damage to the sample, permeability tests at 10 MPa confinement under steady-state conditions were repeated and nearly the same flow rates under the same condition were witnessed. This confirms that the sample was not fatigued in this test, because the maximum confinement pressure and injection pressure applied in this study were much lower than the rock strength and the tested siltstone was still in the elastic stage.

2.3. Permeability Calculation In shale formations or tight formations with ultralow permeability, the flow behavior of gas is affected by the combination of stress effects and the flow regime effect. The flow regime effect cannot be ignored, in particular when the gas pressure is low and the pore throat is small, and the transport of gas is governed by a mixture of Darcy flow, which is caused by the pressure gradient, and Knudsen flow, which is caused by molecular collisions along the walls of the flow channels [35]. Therefore, it is necessary to distinguish the flow pattern of CO2 in siltstone before calculating the permeability. The flow behavior of gas depends on the pore throat, temperature, pressure and the molecular diameter, and can be divided into different flow types at different scales, and the flow regimes can be distinguished by the dimensionless Knudsen number (see Equations (1) and (2)) [3]. According to Heller et al. [3], when the Knudsen number is less than 0.01, the pore size is much higher than the mean free path of gas molecules, and the flow is mainly driven by pressure difference (Darcy flow); in contrast, when Kn > 10, the gas molecules move along the tiny pore throats by the collisions between gas molecules and between the pore wall and gas molecules, and the driving force is mainly caused by the concentration gradient instead of the pressure difference (Knudsen flow), and Darcy’s law is therefore no longer applicable. The flow is in slip flow regime when 0.01 < Kn < 0.1 and in transition flow regime when 0.1 < Kn < 10, which are mainly induced by Darcy flow and Knudsen flow, respectively [3,35]. λ Kn = (1) dp Appl. Sci. 2018, 8, 1092 6 of 26

Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 26 k T λ = √ B (2) 2 where, Kn is the dimensionless Knudsen number,2π dmdPp is the diameter of the pore,  is the mean

−23 2 −2 −1 where,free pathKn is of the CO dimensionless2 molecules, KnudsenkB is the number, Boltzmanndp is the constant diameter (=1.38 of the × pore,10 λmiskgs the meanK ), freeT is path the −23 2 −2 −1 of CO2 molecules, kB is the Boltzmann constant (=1.38 × 10 m kgs K ), T is the temperature (K), temperature (K), dm is the CO2 molecular diameter, and P is the gas pressure. dm is the CO2 molecular diameter, and P is the gas pressure. With the increase of gas pressure, the molecular mean free path of CO2 becomes smaller with With the increase of gas pressure, the molecular mean free path of CO2 becomes smaller with higher gas density (see Figure 4), and the effect of Knudsen flow recedes with the increase of pressure higher gas density (see Figure4), and the effect of Knudsen flow recedes with the increase of pressure (see Figure 5). For example, for a pore with a diameter of 300 nm, the Knudsen number is 0.0139 at a (see Figure5). For example, for a pore with a diameter of 300 nm, the Knudsen number is 0.0139 at pressure of 2 MPa and the flow is in slip flow, while the Knudsen number is 0.0093 at pressure of 3 a pressure of 2 MPa and the flow is in slip flow, while the Knudsen number is 0.0093 at pressure of MPa and the flow is in Darcy flow. When the pressure is higher than 5 MPa, the mean free path is 3 MPa and the flow is in Darcy flow. When the pressure is higher than 5 MPa, the mean free path 1.67 nm, and pure Darcy flow can only happen in pores with diameters greater than 167 nm and slip is 1.67 nm, and pure Darcy flow can only happen in pores with diameters greater than 167 nm and flow in pores between 16.7–167 nm. According to the pore size measured by mercury intrusion slip flow in pores between 16.7–167 nm. According to the pore size measured by mercury intrusion testing, the median pore diameter of siltstone is around 625 nm where the flow mainly belongs to testing, the median pore diameter of siltstone is around 625 nm where the flow mainly belongs to Darcy flow, while there are still many pores with a diameter around 10–300 nm where the slip flow Darcy flow, while there are still many pores with a diameter around 10–300 nm where the slip flow effect also has an important role (see Figure 5), in particular when CO2 is in the gaseous state. Due to effect also has an important role (see Figure5), in particular when CO 2 is in the gaseous state. Due to the smaller molecular diameter and larger mean free path of CO2 compared with CH4, (see Figure 4), the smaller molecular diameter and larger mean free path of CO2 compared with CH4, (see Figure4), slippage effects are slightly greater for CO2, and the apparent permeability for CO2 is slightly higher slippage effects are slightly greater for CO2, and the apparent permeability for CO2 is slightly higher than that of CH4. than that of CH4.

FigureFigure 4. 4.Relationship Relationship between between mean mean free free path path and and pressure pressure at at 22 22◦ C.°C.

TheThe slip-flow slip-flow effect effect was was first first discovered discovered by by Klinkenberg Klinkenberg [[3636],], and and the the effect effect is is expressed expressed as as EquationEquation (3),(3),which whichindicates indicates thatthat thethe slip-flowslip-floweffect effectcan cangreatly greatlyincrease increasethe thepermeability permeabilityfor forgas gas ifif thethe pore pore radius radius and and pore pore pressure pressure are are small. small. b k  k (1b ) (3) k g= k (l1 + ) (3) g l PP

where, k is apparent the permeability for gas CO2, k is the intrinsic permeability of tested where, kg isg apparent the permeability for gas CO2, kl is thel intrinsic permeability of tested siltstone whichsiltstone can which be measured can be measured using liquid using CO liquid2 or CO water,2 or water,b is the b Klinkenberg is the Klinkenberg parameter parameter and P andis the P poreis the pressure. pore pressure. Appl.Appl. Sci.Sci. 20182018,, 88,, 1092x FOR PEER REVIEW 77 ofof 2626

◦ FigureFigure 5.5. DimensionlessDimensionless KnudsenKnudsen numbernumber ofof COCO22 vs.vs. pore pressure forfor differentdifferent porepore sizessizes atat 2222 °C.C.

SinceSince thethe ﬂowflow regime regime mainly mainly belongs belongs to to Darcy Darcy ﬂow, flow, the the permeability permeability of theof the tested tested siltstone siltstone for gasfor injectiongas injection under under various various steady-state steady conditions-state conditions can be calculatedcan be calculated using the using traditional the traditional Darcy equation Darcy (Equationequation (Equation (4)), based (4) on), thebased assumption on the assumption that gas volume that gas changes volume inversely changes inversely proportionally proportionally with gas pressurewith gas atpressure constant at temperatureconstant temperature [37]. [37].

2Qo PoL kg  2Qo PoµL (4) kg = 2 2 (4) AP2i  Po2 A Pi − Po

where, k is the permeability for CO2, Q is CO2 flow rate at downstream,  is its viscosity, L where, kg gis the permeability for CO2, Qo iso CO2 flow rate at downstream, µ is its viscosity, L and A are the length and cross-sectional area of the specimen, P and P are downstream pressure and and A are the length and cross-sectional area of the specimen,o i Po and Pi are downstream upstream pressure. pressure and upstream pressure. However, when the injection pressure is higher than 6 MPa, the gaseous CO2 and liquid CO2 However, when the injection pressure is higher than 6 MPa, the gaseous CO2 and liquid CO2 coco-exist in the sample because CO2 transfers into its liquid state at 6 MPa (data from NIST) [38], and the exist in the sample because CO2 transfers into its liquid state at 6 MPa (data from NIST) [38], and the Boyle’s Law that gas volume is proportional to the gas pressure is assumed to be applicable for the Boyle’s Law that gas volume is proportional to the gas pressure is assumed to be applicable for the gaseous state for simplicity, but not for the liquid state, because this phase transition causes sudden gaseous state for simplicity, but not for the liquid state, because this phase transition causes sudden enhancement of density [39]. For example, when CO2 is in its liquid state, its density increases slightly enhancement of density [39]. For example, when CO2 is in its liquid state, its density increases slightly from 760 kg/m3 at 6.01 MPa to 901 kg/m3 at 15 MPa, which is much higher than 210 kg/m3 at 6.00 MPa. from 760 kg/m3 at 6.01 MPa to 901 kg/m3 at 15 MPa, which is much higher than 210 kg/m3 at 6.00 MPa. Therefore, the Darcy equation for compressed gas is not suitable for this case, and in consideration Therefore, the Darcy equation for compressed gas is not suitable for this case, and in consideration of the slight difference of density in the liquid state, the permeability for the liquid section can be of the slight difference of density in the liquid state, the permeability for the liquid section can be calculated using the method proposed by Zhang et al. [24], utilizing Equations (5) and (6), and the calculated using the method proposed by Zhang et al. [24], utilizing Equations (5) and (6), and the ratio between the length of gaseous CO2 section to sample length is inversely proportional to the ratio ratio between the length of gaseous CO2 section to sample length is inversely proportional to the ratio between the flow rate at an injection pressure of 6 MPa and that at each higher injection pressure. between the flow rate at an injection pressure of 6 MPa and that at each higher injection pressure. QQ6LL Ll = L − Lg = L − 6 (5) Ll  L  Lg  L  Qo (5) Qo Qlµl Ll kl = (6) A(QPil −l LPlt) kl  (6) where, Ll is the length of liquid CO2 in the sample,ALPgi isP thet  length of gas CO2 in the sample, Q6 is the flow rate at 6 MPa injection pressure, kl is the permeability for liquid CO2 at a certain injection pressure where, L is the length of liquid CO2 in the sample, L is the length of gas CO2 in the sample, Q (>6 MPa),lQl is the liquid CO2 flow rate at transition point,g µl is the viscosity of liquid CO2 at room6 temperature,is the flow ratePt atis 6 pressure MPa injection at transition pressure, point kl and is the here permeability it equals 6 MPa, for liquid and PCOi is2 upstreamat a certain pressure. injection

pressure (>6 MPa), Ql is the liquid CO2 flow rate at transition point, l is the viscosity of liquid Appl. Sci. 2018, 8, 1092 8 of 26

For transient conditions, the permeability at speciﬁc pressure was calculated using pulse-decay permeability measurement by the following equations (Equations (7) and (8)) [3]:

−αt ∆P(t) = ∆P0e (7)

kA α = (8) βVdown Lµ where, α is the decay exponent, ∆P0 is the pressure difference between upstream and downstream at time t = 0, ∆P(t) is the pressure difference between upstream and downstream with time, k is the permeability for CO2, β is the CO2 compressibility, Vdown is the volume of the downstream reservoir, µ is the CO2 viscosity, and L and A are the length and cross-section area of the sample, respectively.

3. Results and Discussion

3.1. Permeability Behavior of CO2 under Steady-State Conditions

CO2 was first injected into the same siltstone sample at steady-state conditions under four different confining pressures (see Table1), and the corresponding downstream flow rate was observed and recorded over time. The flow rate development under 20 MPa confinement is shown in Figures6 and7. When the injection pressure is not higher than 9 MPa, the downstream CO2 flow rate gradually reaches a steady state at each injection pressure after around 20 min of injection (see Figure6). However, when the injection pressure goes beyond 9 MPa, although the flow rate increases with increasing injection pressure, obtaining a steady state flow rate condition under each injection pressure condition was quite difficult due to the highly unsteady flow (see Figure7). At each unsteady downstream flow behavior step (relevant to each injection pressure after 9 MPa), the flow rate first increased rapidly followed by a slow reduction, although confining and injection pressures remained steady during each injection process and the possibility of leak-off was excluded. This is possibly because some physical process occurs in the sample with existing high flow rates under greater injection pressures, and fine particle migration is one of the suspected causes. Fine particle migration with the high pressure-driven great advective flux in such situations may be responsible for this phenomenon, and a small quantity of fine particles was seen on the filter paper at the downstream after the permeability tests. The mineral particle distribution is shown in a SEM image and the differentiation of particle radiuses is marked (see Figure8). The size of the kaolinite particles (less than 2 µm in diameter) is much smaller than that of the quartz particles (less than 62.5 µm in diameter), and kaolinite particles therefore normally exist between quartz particles and have a high tendency to occupy the flow path, showing the negative influence of clay content on flow ability or permeability of sample [31,40]. When the injection pressure is higher than 9 MPa, higher advective flux along the rock matrix induces a higher pushing force on some free or loosely-bonded fine particles, extracting them from the rock matrix and mixing them into the fluid flow. While blockage of the available narrow pore throats in the rock sample through fine particle accumulation can cause a significant reduction in flow ability through the rock matrix, once the accumulated pressure at the upstream side reaches a certain value, these blockages can be pushed out by the associated great pushing force, opening the pore throats. This might cause the observed sudden flow rate increments (see Figure9). Another reason for this phenomenon maybe the presence of small drikold particles near the downstream due to the sharply drop of temperature of CO2 flow, which will be discussed in detail in Section 3.2. However, for these complex downstream flow behaviors obtained under high CO2 injection pressure, the average of peak points was taken as the steady-state downstream flow rate to calculate the permeability. These observed flow behaviors of CO2 under steady-state conditions exhibited similar patterns under the greater confinements of 30 and 40 MPa. The flow rates obtained under each test condition are shown in Figure 10, which confirms the linear variation between the flow rate and injection pressure. Therefore, Darcy’s equation was used to calculate the permeability for CO2 in dry siltstone under each test condition. Appl. Sci. 20182018,, 88,, xx FORFOR PEERPEER REVIEWREVIEW 99 of 2626

2 thethe permeability permeability.. These observed flow behaviors of CO2 under steadysteady--statestate conditions conditions exhibited exhibited similarsimilar patternspatterns underunder thethe greatergreater confinementsconfinements ofof 30 and 40 MPa. The flow rates obtained under each test condition are shown in Figure 10,, whichwhich confirmsconfirms thethe linearlinear variationvariation betweenbetween thethe flowflow raterate 2 Appl.and Sci. injection2018, 8, 1092pressure. Therefore, Darcy’s equation was used to calculate the permeability for CO9 of2 26 inin dry siltstone under each test condition.

Table 1. Steady-state permeability test conditions for the same sample. Table 1.. Steady--statestate permeabilitypermeability testtest conditionsconditions forfor thethe samesame sample.sample.

InjectionInjectionInjection Pressure Pressureressure (MPa) (MPa)(MPa) ConﬁningConfining Pressure(MPa) Pressure(MPa)ressure(MPa) GaseousGaseous State Statetate Liquid Liquid S Statetatetate 10 3, 4, 5, 6 7, 8, 9 1010 3,3 4,, 4 5,, 65, 6 7, 7, 8, 8, 9 9 20,20, 30, 4030, 40 3,3, 4, 4, 5, 65, 6 7, 7, 8, 8, 9, 9, 10, 10, 12, 12, 14, 1616

FigureFigure 6. 6..Flow Flow rate rate development development with with time time when when injection injection pressure pressure is is not not higher higher than than 9 9 MPa. MPa.

FigureFigure 7. 7..Flow Flow rate rate development development with with time time when when injection injection pressure pressure is is higher higher than than 9 9 MPa. MPa. Appl. Sci. 2018, 8, 1092 10 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 10 of 26

Figure 8. SEM image of tested siltstone sample with varisized particles. Figure 8 8.. SEM image of tested siltstone sample with varisized particles. Figure 8. SEM image of tested siltstone sample with varisized particles.

Figure 9 9... SchematicSchematic diagram diagram of effect effect of of fine fine particle particle migration migration on on permeability permeability (solid (solid circles circles represent represent Figuremineral 9. Schematic and finefine particles;particles; diagram dashedofdashed effect circlescirclesof fine representrepresentparticle migration movingmoving fine fineon permeability particles).particles). (solid circles represent mineral and fine particles; dashed circles represent moving fine particles).

Figure 10.. Flow rates for different injection pressures. FigureFigure 10 10.. FlowFlow rates rates for for different different injection injection pressures. pressures.

Appl. Sci. 2018, 8, 1092 11 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 26

TheThe permeability permeability of of the the siltstone siltstone was was then then calculated calculated using using the the traditional traditional Darcy Darcy equation equation for for gasgas (see (see Equation Equation (4) (4)),), and and Figure Figure 11 11 shows shows the the calculated calculated permeability permeability values values for for each each injection injection pressure. When the whole sample is filled with gaseous CO2, the siltstone’s permeability increases pressure. When the whole sample is filled with gaseous CO2, the siltstone’s permeability increases with withincreasing increasing injection injection pressure, pressure, regardless regardless of confinement. of confinement. For example, For example, increasing increasing the injection the injection pressure pressurefrom 3 from to 6 MPa 3 to 6 causes MPa causes the sample the sample permeability permeability to increase to increase from from 0.00457 0.00457 mD mD to 0.00654 to 0.00654 mD mD and and0.00264 0.00264 mD mD to 0.00439 to 0.00439 mD at mD 10 MPa at 10 and MPa 40 MPa and confining40 MPa confin pressures,ing pressures, respectively. respectively. This permeability This permeabilityincrement may increment be related may to be the related effective to the stress effective effect. stress Increasing effect. theIncreasing injection the pressure injection expands pressure the expands the rock pore throats, even opening some new flow paths for CO2, which contributes to the rock pore throats, even opening some new flow paths for CO2, which contributes to the reduced reduced tortuosity for CO2 movement along the sample. This trend of permeability increase appears tortuosity for CO2 movement along the sample. This trend of permeability increase appears to change to change with the phase transition, which occurs in CO2 after around 6 MPa and continues, and with the phase transition, which occurs in CO2 after around 6 MPa and continues, and permeability permeabilityfirst slowly firstreduces slowly with reduces increasing with injection increasing pressure injection up pressureto around up 10 to MPa around (from 10 0.00654 MPa (from mD to 0.006540.00601 mD mD to and0.00601 0.00439 mD and mD 0.00439 to 0.00413 mD mD to 0.00413 at 10 MPa mD andat 10 40MPa MPa and confining 40 MPa confining pressures). pressures). After that Afterpermeability that permeability is surprisingly is surprisingly subjected subjected to a sudden to a increment. sudden increment.

FigureFigure 11 11.. RelationshipRelationship between between permeability permeability of of siltstone siltstone under under different different injection injection pressures pressures (traditional(traditional method). method).

This permeability reduction is due to fact that after 6 MPa at 22 °C, CO◦2 transfers into the liquid This permeability reduction is due to fact that after 6 MPa at 22 C, CO2 transfers into the state from the gaseous state. As a result, the presence of liquid CO2 in the siltstone sample (at the liquid state from the gaseous state. As a result, the presence of liquid CO2 in the siltstone sample upstream(at the upstream side) causes side) this causes opposite this opposite permeability permeability trend. The trend. lower The permeability lower permeability for liquid for liquid CO2 compared to gaseous CO2 in the siltstone sample is due to the slip-flow effect. The reduction of CO2 compared to gaseous CO2 in the siltstone sample is due to the slip-ﬂow effect. The reduction permeability for liquid CO2 compared with gaseous CO2 is related to the slip-flow effect, as gas of permeability for liquid CO2 compared with gaseous CO2 is related to the slip-ﬂow effect, as gas moleculesmolecules with with higher higher compressibility and and lower lower viscosity viscosity have have greater greater potential potential to slip to through slip through narrow narrow pore throats [36,41]. In addition, liquid CO2 with higher viscosity meets much higher pore throats [36,41]. In addition, liquid CO2 with higher viscosity meets much higher resistance than resistance than gaseous CO2, and very tiny pore throats are impenetrable for liquid CO2. Although gaseous CO2, and very tiny pore throats are impenetrable for liquid CO2. Although the permeability theat permeability higher injection at higher pressures injection is much pressures lower is than much that lower for the than gaseous that for state, the gaseous the leak-off state, rate the may leak be- off rate may be much higher than that for gaseous CO2 because of its greater density. Importantly, much higher than that for gaseous CO2 because of its greater density. Importantly, this shows the thiscalculation shows the of calculation permeability of permeability based on Darcy’s based equation on Darcy’s for equation gas is not for accurate gas is not for accurate the prediction for the of prediction of the permeability of samples under these two-phase CO2 conditions (liquid at upstream the permeability of samples under these two-phase CO2 conditions (liquid at upstream and gas at and gas at downstream). Further, there is a sharp rise in viscosity when the CO2 transfers into the downstream). Further, there is a sharp rise in viscosity when the CO2 transfers into the liquid state liquidat 6 MPa statefrom at 6 MPa 18.19 fromµPa ·18.19s to 66.15 μPa·sµ Pato ·66.15s, and μPa·s, the use and of the the use traditional of the traditional Darcy’s equation Darcy’s withequation mean withviscosity mean inviscosity the gaseous in the stategaseous causes state some causes errors, some because errors, thebecause basic the assumption basic assumption of Darcy’s of Darcy’s equation equationfor gas, that for gas,viscosity that is viscosity nearly independent is nearly independent on the pressure on the variation, pressure is no variation, longer applicable is no longer when applicableboth liquid when and both gas liquid co-occur and in gas the co sample.-occur in This the issample further. This highlighted is further byhighlighted the sudden by permeabilitythe sudden permeability increment after 12 MPa, caused by the abrupt change of the mean viscosity after 12 MPa (see Figure 12), and it is likely that the greater portion of liquid CO2 in the sample at greater pressure Appl. Sci. 2018, 8, 1092 12 of 26

Appl.increment Sci. 2018 after, 8, x 12FOR MPa, PEER caused REVIEW by the abrupt change of the mean viscosity after 12 MPa (see Figure12 of 12 26), and it is likely that the greater portion of liquid CO2 in the sample at greater pressure signiﬁcantly significantlyincreases this increases error. This this is error. conﬁrmed This is by confirmed Table2, which by Table shows 2, which that when shows the that injection when the pressure injection is 2 pressuregreater than is greater 6 MPa, than liquid 6 MPa, CO2 isliquid present CO in is the present sample, in the and sample, the proportion and the is proportion around 25% is ofaround the whole 25% ofsample the whole at 7 MPa sample injection at 7 MPa pressure injection and pressur arounde 80% and ataround 16 MPa 80% injection at 16 MPa pressure. injection This pressure. suggests This that suggests that the higher the injection pressure, the greater the proportion of liquid CO2 in the sample the higher the injection pressure, the greater the proportion of liquid CO2 in the sample for liquid 2 forCO 2liquidinjection. CO injection.

Figure 12 12.. Relationship between CO 2 viscosityviscosity at at different different injection pressures.

This was then considered by recalculating the permeability for liquid CO2 injection (>6 MPa) This was then considered by recalculating the permeability for liquid CO2 injection (>6 MPa) ususinging the proposed method (see Equation (6) (6)),), which separates the gaseous and liquid section along the tested sample, and the results are shown in Figure 13.. ThisThis proposedproposed method divides the liquid and gaseous states of CO2 in the sample to apply the corresponding Darcy equation for the gas and and gaseous states of CO2 in the sample to apply the corresponding Darcy equation for the gas and liquid portions, respectively. The newly-calculated permeability values corresponding to liquid CO2 liquid portions, respectively. The newly-calculated permeability values corresponding to liquid CO2 injections are much lower than those for the gaseous CO2 section (see Figure 13). For example, when injections are much lower than those for the gaseous CO2 section (see Figure 13). For example, when the theinjection injection pressure pressure increases increases from from 6 MPa 6 MPa to 7 MPa,to 7 MPa, the permeability the permeability drops drops sharply sharply from 0.00564 from 0.00564 mD to mD0.00244 to 0.00244 mD at amD confinement at a confinement of 20 MPa, of 20 and MPa, the suddenand the permeabilitysudden permeability reductions reductions are around are 63%, around 57%, 63%, 57%, 39% and 52% under 10, 20, 30 and 40 MPa confinements, respectively. For the liquid CO2, 39% and 52% under 10, 20, 30 and 40 MPa confinements, respectively. For the liquid CO2, although althoughthere is a there little fluctuationis a little fluctuation in permeability in permeability with injection with injec pressure,tion pressure, its permeability its permeability increases increases slightly withslightly the with increase the increase of injection of injection pressure, pressure, due to the due decrease to the decrease of effective of effective stress. Overall, stress. theOverall, range the of range of variation of apparent permeability for liquid CO2 is much smaller than that for gaseous CO2. variation of apparent permeability for liquid CO2 is much smaller than that for gaseous CO2.

Table 2. Proportion of liquid CO2 length in sample calculated using Equation (5) (%). Table 2. Proportion of liquid CO2 length in sample calculated using Equation (5) (%). Confining Pressure (MPa) Injection Pressure (MPa) Conﬁning Pressure (MPa) Injection Pressure (MPa) 10 20 30 40 7 1023.96 2026.74 34.18 30 28.99 40 78 23.9640.16 26.7441.67 47.47 34.18 45.56 28.99 89 40.1648.59 41.6749.60 54.78 47.47 53.33 45.56 9 48.59 49.60 54.78 53.33 10 56.55 60.00 58.12 10 56.55 60.00 58.12 1212 70.0070.00 68.48 68.48 67.33 67.33 1414 75.2975.29 76.79 76.79 77.31 77.31 1616 79.0079.00 80.74 80.74 81.15 81.15 Appl. Sci. 2018, 8, 1092 13 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 26

FigureFigure 13.13. RelationshipRelationship betweenbetween apparentapparent permeabilitypermeability ofof siltstonesiltstone underunder different injectioninjection pressurespressures (proposed(proposed method).method).

InIn addition addition to to the the injection injection pressure, pressure, reservoir reservoir depth depth or confining or confining pressure pressure also significantly also significantly affects theaffects flow the behavior flow behavior in any reservoir in any [42 reservoir,43], because [42,43 increased], because confining increased pressure confining causes pressure shrinkage causes in theshrinkage pore structure in the pore in the structure formation in the rock formation matrix. Thisrock wasmatrix. investigated This was forinvestigated the tested for siltstone the tested and siltstone and Figure 14 shows the observed axial deformation variation of the sample with increasing Figuresiltstone 14 and shows Figure the 14 observed shows the axial observed deformation axial deformation variation of variation the sample of the with sample increasing with increasing applied applied confining pressure. There is a non-linear relationship between axial deformation and confiningapplied confining pressure. pressure. There is Therea non-linear is a non relationship-linear relationship between axial between deformation axial deformation and confining and confining pressure, and the increasing rate of axial deformation decreases with increasing confining pressure,confining and pressure, the increasing and the increasing rate of axial rate deformation of axial deformation decreases de withcreases increasing with increasing confining confining pressure pressure (see Figure 14), because most of the shrinkable pores have already shrunk with the increase (seepressure Figure (see 14 Figure), because 14), because most of most the shrinkableof the shrinkable pores pores have have already already shrunk shrunk with with the the increase increase of of confinement. This shrunken pore structure under high confining pressures results in the reduction confinement.of confinement. This This shrunken shrunken pore pore structure structure under under high high confining confining pressures pressures results results in in the the reductionreduction of flow paths for CO2 movement, and the rock permeability therefore decreases with the increasing of flow paths for CO2 movement, and the rock permeability therefore decreases with the increasing confinement. This is confirmed by Figure 15, which shows that CO2 downstream flow rates decrease confinement. This is confirmed by Figure 15, which shows that CO2 downstream flow rates decrease with increasing confining pressure. withwith increasingincreasing confiningconfining pressure.pressure.

Figure 14.14. Vertical displacementdisplacement atat differentdifferent conﬁningconfining pressures.pressures. Appl. Sci. 2018, 8, 1092 14 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 14 of 26

Figure 15.15. Relationship between permeability of siltstone at different conﬁningconfining pressures.pressures.

3.2.3.2. Considering Thermodynamic PropertiesProperties VariationVariation ofof COCO22 FlowFlow TheThe results results analysisanalysis and and discussion discussion inin SectionSection 3.1 3.1 areare premised premised on on the the condition condition that that the the temperaturetemperature of of both both sample sample and and flow flow fluid fluid was was kept kept at room at room temperature temperature invariably. invariably. While in While reality, in reality,although although the temperature the temperature recorded recorded by the by thermometer the thermometer in the in tri the-axial tri-axial cell kecellpt kept constant, constant, the thetemperature temperature variation variation inside inside the sample the sample during during CO2 expansion CO2 expansion with the with decrease the decrease of pressure of pressure along alongsample sample cannot cannot be ignored be ignored.. According According to the to first the law first of law thermodynamics of thermodynamics [44] [(44see] (seeEquation Equation (9)), (9)), the thevolume volume work work done done by bygas gas expansion expansion is iscompensated compensated by by its its internal internal energy energy and and the the heat transferred intointo thethe system.system. TheThe heatheat exchange,exchange, duedue toto thethe temperaturetemperature differencedifference betweenbetween COCO22 flowflow andand samplesample matrix,matrix, cancan reducereduce thethe raterate ofof COCO22 internalinternal energyenergy decline.decline. However, consideringconsidering that muchmuch energyenergy consumedconsumed forfor thethe fastfast COCO22 volumevolume expansionexpansion and thethe lowlow thermalthermal conductivityconductivity ofof siltstonesiltstone samplesample maymay failfail toto transmittransmit enoughenough energyenergy toto maintainmaintain thethe temperaturetemperature ofof COCO22 flowflow atat roomroom temperaturetemperature alongalong thethe sample,sample, thethe premisepremise conditioncondition forfor permeabilitypermeability calculationcalculation underunder steady-statesteady-state conditionsconditions thatthat COCO22 flowflow along the sample maintained at room temperaturetemperature isis thereforetherefore questionable.questionable. dU W Q (9) dU + δW = δQ (9) where, dU is the change in the internal energy of the system, W is work done by the system where,and dUQ isthe the heat change transferred in the internal to the system. energy of the system, δW is work done by the system and δQ the heatThe transferred temperature to variation the system. of CO2 flow is closely related to its flow rate, thermal conductivity of rock,The CO temperature2 phase transition variation and ofsoCO on.2 Higherflow is closelyflow rate related and lower to its flowthermal rate, conductivity thermal conductivity of siltstone of rock,can promote CO2 phase temperature transitionand variation so on. Higher of CO2flow flow. rate In and particular lower thermal when liquidconductivity CO2 evaporates of siltstone into can promotegaseous temperatureCO2, the heat variation of vaporization of CO2 flow. can In greatly particular decrease when the liquid temperature CO2 evaporates of both into liquid gaseous and COgaseous2, the CO heat2, of because vaporization much canenergy greatly is needed decrease to the do temperature the volume of work both during liquid theand rapid gaseous volume CO2, becauseexpansion much process energy. The is standard needed to enthalpy do the volume change work of vaporization during the at rapid liquefaction volume expansionpoint (22 °C process. and 6 ◦ TheMPa) standard is 6.27 kJ/mol enthalpy, and change it is much of vaporization higher than atthe liquefaction heat capacity point of gaseou (22 Cs and and 6 liquid MPa) isCO 6.272 which kJ/mol, are ◦ andaround it is much36.6 J/mol·°C higher than and the133.8 heat J/mol·°C capacity, respectively. of gaseous and In liquidother words, CO2 which if the are heat around exchange 36.6 J/mol between· C ·◦ andthe CO 133.82 flow J/mol and C,rock respectively. matrix was In not other considered words, if and the heatCO2 exchangeflow was betweenin an adiabatic the CO condition2 flow and ( rock matrix was not considered and CO2 flow was in an adiabatic condition (δQ = 0), 6.27 kJ is needed to = 0), 6.27 kJ is needed to evaporate each mole of CO2, which can decrease the temperature of gaseous◦ evaporate each mole of CO2, which can decrease the temperature of gaseous and liquid CO2 by 171.3 C and liquid CO2 by 171.3 °C and 46.9 °C, respectively. The standard enthalpy change of vaporization and 46.9 ◦C, respectively. The standard enthalpy change of vaporization can increase to 12.22 kJ/mol can increase to 12.22 kJ/mol at −20 °C and 2 MPa, which can absorb more heat from the surroundings. at −20 ◦C and 2 MPa, which can absorb more heat from the surroundings. The evaporation of liquid The evaporation of liquid CO2 can greatly decrease the temperature of adjacent liquid CO2 and evaporated CO2, and even solid carbon dioxide can be formed at the liquefied interface [45]. According to Figure 16, with the decrease of temperature of liquid CO2, the pressure at evaporating Appl. Sci. 2018, 8, 1092 15 of 26

CO2 can greatly decrease the temperature of adjacent liquid CO2 and evaporated CO2, and even solid carbon dioxide can be formed at the liquefied interface [45]. According to Figure 16, with the decrease of temperature of liquid CO2, the pressure at evaporating point also decreases, which indicates the liquid CO2 length in sample is longer than predicted and the higher density of liquid CO2 can lead to much higher flow rate compared with that at constant room temperature. Due to much energy being consumed for the vaporization process when the injection pressure is higher than 6 MPa, the temperature of gaseous CO2 at the liquefied interface will definitely be lower than the room temperature. Besides the temperature variation around the liquefied interface, the gaseous CO2 volume expansion with the decrease of pore pressure can also decrease its temperature. Although the rate of gas volume expansion is much lower than that in the evaporation process, higher gaseous CO2 flow rate can also absorb much energy. If there was no heat exchange between CO2 and the rock matrix in the ideal condition, the gaseous CO2 flow was assumed to be at adiabatic condition and its entropy kept constant. Considering that the temperature of gaseous CO2 at the liquefied interface was lower than room temperature and it is difficult to determine its accurate value when the injection pressure is higher than 6 MPa, only the injection cases, where the injection pressure is not higher than 6 MPa, are used to analyze the CO2 thermodynamic property evolution along the sample. According to Figure 17, with the decrease of pore pressure, the temperature decreases sharply. For example, when the injection pressure equals 5 MPa, its temperature can decrease to liquefaction ◦ point at −40.12 C at 1 MPa. With the decrease of both temperature and pressure, the CO2 level tends to be close to the triple point (−56.6 ◦C and 0.52 MPa). With the further decrease of pore pressure down to the atmospheric pressure, much heat is obtained from the solidification process, and CO2 can be transferred into solid phase. For the ideal steady-state tests, the flow rate and pore pressure along the sample tend to be equilibrate state and the temperature maintains a constant (dU = 0). However, in the real experiments, the temperature variation can also lead to the adjustment of flow behavior. Therefore, the flow rate, pore pressure and fluid temperature gradually reach a steady state with time, where continuous and stable heat was transferred from outside to the CO2 flow through siltstone matrix, which indicates that the real condition is between two ideals conditions which are under constant temperature (dU = 0) and under adiabatic conditions (δQ = 0), respectively. For the complex flow system, it is difficult to accurately assess the flow behavior evolution along the sample, because these variables are interdependent with each other. The heat exchange rate, which is dependent on the thermal conductivity of siltstone, is therefore crucial to the CO2 flow behavior. If the heat exchange rate is much lower than that needed for high CO2 flow rate under high injection pressure, the presence of drikold particles in sample matrix can greatly disturb the steady-state flow, because it can block the flow channels for gaseous CO2 flow. The forming and disappearing of drikold partials is more likely responsible for the unsteady flow rate at downstream at injection pressure higher than 9 MPa. In conclusion, the temperature variation can influence the flow behavior to some extent. The longer length of liquid CO2 along the sample than expected can greatly increase the flow rate due to its much higher density than gaseous CO2. Furthermore, unlike the idea of gas at constant room temperature, where gas volume is inversely proportional to its pore pressure, there is a non-linear relationship between pore pressure and gas volume at adiabatic condition, which is presented by the polytropic process equation in Equation (10) [46]. The higher density along the sample than that predicted at room temperature can also lead to slightly higher flow rate at downstream. The temperature variation, due to the unique thermodynamic properties of CO2, therefore can result in the inaccuracy of permeability calculation under steady-state conditions, and it highlights the necessity of permeability calculation under transient conditions, where the thermodynamic heat exchange is negligible because of much lower pressure variation and flow rate.

γ γ PV = P0V0 = C (10) Appl. Sci. 2018, 8, 1092 16 of 26

Appl.where, Sci. P2018is, the 8, x gasFOR pressure,PEER REVIEWV is the gas volume, γ is the heat capacity ratio (approximately equals16 of to26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 16 of 26 1.3 for CO2) and C is constant.

Figure 16 16.. The phase diagr diagramam of CO 2 ((datedate were were obtained obtained from from REFPROP REFPROP Database [ [38]]).). Figure 16. The phase diagram of CO22 (date were obtained from REFPROP Database [38]).

1010

Liquid Saturation Line Liquid Saturation Line

1 1 Initial conditions: Initial conditions: 1MPa, 22°C 1MPa, 22°C 2MPa, 22°C 2MPa, 22°C 3MPa, 22°C Pressure (MPa) Pressure 3MPa, 22°C Pressure (MPa) Pressure 4MPa, 22°C 4MPa, 22°C 22°C 5MPa, 22°C 22°C 5MPa, 22°C 6MPa, 22°C 6MPa, 22°C 0.10.1 -60-60 -40-40 -20-20 00 2020 4040 6060 TemperatureTemperature (°C)(°C)

FFigureigure 17.17. IsentropicIsentropic plots plots of of pure pure CO22 forfor different different initial initial conditions conditions ( (datedate were obtained from Figure 17. Isentropic plots of pure CO2 for different initial conditions (date were obtained from REFPROP Database [ 38]]).). REFPROP Database [38]).

33.3..3. Permeability Permeability B Behaviorehavior of CO 22 underunder Transient Transient Conditions 3.3. Permeability Behavior of CO2 under Transient Conditions The complex gas/liquid permeability characteristics observed in the rock sample during liquid TheThe complexcomplex gas/liquidgas/liquid permeabilitypermeability characteristicscharacteristics observedobserved inin thethe rockrock samplesample duringduring liquidliquid CO22 injectioninjection indicate indicate the the importance importance of of checking checking the the different different permeability characteristics characteristics of of the the CO2 injection indicate the importance of checking the different permeability characteristics of the tested siltstone siltstone under pure gas and and liquid liquid CO CO2 movementmovement using using transient transient tests. tests. Here, Here, the the permeability permeability tested siltstone under pure gas and liquid CO2 movement using transient tests. Here, the permeability was calculated using Equations (7) and (8), considering the long time of injection under steady-state waswas calculatedcalculated usingusing EquationsEquations (7)(7) andand (8)(8),, consideringconsidering tthehe longlong timetime ofof injectioninjection underunder steadysteady--statestate flow conditions, as longer time is expected under transient conditions, the transient test conditions flowflow conditions,conditions, asas longerlonger timetime isis expectedexpected underunder transienttransient conditions,conditions, tthehe transienttransient testtest conditionconditionss used for the study are therefore down-sized (see Table3). usedused forfor thethe studystudy areare thereforetherefore downdown--sizedsized (see(see TableTable 33)).. The downstream pressure development relevant to each injection under 20 MPa confining pressure Table 3. Transient permeability test conditions. is shown in Figure 18. Here,Table the 3 time. Transient taken permeability to reach the test injection conditions. pressure value at downstream decreases with increasing injection pressure, exhibiting a weakened flow behavior at lower injection InjectionInjection PPressureressure (MPa)(MPa) pressures through theConfiningConfining rock sample. PPressureressure For (MPa)(MPa) example, at 20 MPa confining pressure, the time taken to GaseousGaseous SStatetate LiquidLiquid SStatetate 1010 3,3, 66 99 20,20, 30,30, 4040 3,3, 66 9,9, 12,12, 1515 Appl. Sci. 2018, 8, 1092 17 of 26 reach injection pressure level at downstream pressure is around 11 h, 6.4 h and 2.6 h at 3 MPa, 9 MPa, and at 15 MPa injection pressure, respectively. This is mainly due to the accelerated advective flux, Appl. Sci. 2018, 8, x FOR PEER REVIEW 17 of 26 which creates a greater pushing force under the existing greater initial pressure gap between the injecting pointThe downstream and the rock pressure matrix pore development space. Figure relevant 19 tocompares each injection the time under taken 20 to MPa achieve confining 5.5 MPa (CO2 stillpressure in gaseous is shown state) in pressureFigure 18 at. Here, downstream the timeunder taken various to reach injection the injection (6–15 pressure MPa) and value confining at Appl. Sci. 2018, 8, x FOR PEER REVIEW 17 of 26 (10–40downstream MPa) pressures. decreases The with time increasing taken to injection reach the pressure, 5.5 MPa exhibiting at 6 MPa a weakened injection flow pressure behavior condition at decreaseslower by injection 57%The with downstream pressures the increase through pressure of injectionthe development rock sample. pressure relevant For to toexample, 9 MPaeach injection at at 10 20 MPa MPa under confining confining 20 MPa pressure,confiningpressure, andthe the time takentime taken atpressure 6 MPa to reach is injection shown injection in pressureFigure pressure 18. reduces Here,level theat by downstream time 75%, taken 78% to pressure and reach 83% th ise with injectionaround increased 11 pressure h, 6.4 injection h value and 2.6 at pressure h at downstream decreases with increasing injection pressure, exhibiting a weakened flow behavior at to 15 MPa3 MPa, at 9 20, MPa, 30 andand 40at 15 MPa MPa confinement, injection pressure, respectively respectively. (see FigureThis is mainly19). due to the accelerated advectivelower flux, injection which pressures creates through a greater the pushing rock sample. force For under example, the existingat 20 MPa greater confining init pressure,ial pressure the gap time taken to reach injection pressure level at downstream pressure is around 11 h, 6.4 h and 2.6 h at between the injecting point and the rock matrix pore space. Figure 19 compares the time taken to 3 MPa, 9 MPa, and at Table15 MPa 3. injectionTransient pressure, permeability respectively. test conditions.This is mainly due to the accelerated achieve 5.5 MPa (CO2 still in gaseous state) pressure at downstream under various injection (6–15 advective flux, which creates a greater pushing force under the existing greater initial pressure gap MPa) betweenand confining the injecting (10–40 point MPa) and pressures. the rock matrix The time poreInjection takenspace. toFigure Pressure reach 19 the compares (MPa) 5.5 MPa the at time 6 MPa taken injection to pressureachieve condition 5.5Confining MPa decreases (CO Pressure2 still in by gaseou (MPa)57% withs state) the pressure increase at downstream of injection under pressure various to injection 9 MPa at(6 – 1015 MPa Gaseous State Liquid State confiningMPa) pressure, and confining and the(10 –time40 MPa) taken pressures. at 6 MPa The injection time taken pressure to reach reduces the 5.5 byMPa 75%, at 6 78% MPa and injection 83% with increasedpressure injection condition pressure decreases10 to 15 byMPa 57% at with20, 30 the and increase 3,40 6MPa of confinement, injection pressure respectively 9 to 9 MPa (see at 10 Figure MPa 19). confining pressure,20, and 30, the 40 time taken at 6 MPa injection 3, 6 pressure reduces 9,by 12,75%, 15 78% and 83% with increased injection pressure to 15 MPa at 20, 30 and 40 MPa confinement, respectively (see Figure 19).

Figure 18. Measurement of downstream pressure at different CO2 injection pressures under 20 MPa FigureFigure 18. Measurement 18. Measurement of downstream of downstream pressure pressure at atdifferent different CO 2 injectioninjection pressures pressures under under 20 MPa 20 MPa confining pressure. 2 conﬁningconfining pressure. pressure.

Figure 19. Time for downstream pressure up to 5.5 MPa at different injection pressures and confining pressures.

FigureFigure 19. 19Time. Time for for downstreamdownstream pressure pressure up to up 5.5 to MPa 5.5 at MPa different at differentinjection pressures injection and pressures confining and conﬁningpressures. pressures. Appl. Sci. 2018, 8, 1092 18 of 26

When the injection pressure is 3 MPa and 6 MPa, a steady-state downstream pressure development over time up to the injection pressure can be seen (see Figure 18). Interestingly, this downstream pressure development changes after 6 MPa at greater injection pressures, and the downstream pressure development curves exhibit two steady-state conditions. In other words, in addition to the final steady-state condition (closer to the injection pressure value), an intermediate steady-state pressure development may be seen under high injection scenarios (≥9 MPa). Importantly, for each high injection pressure (from 9 MPa to 15 MPa), the intermediate pressure development occurs when the downstream reaches 6 MPa (it converts from gas to liquid at this pressure), due to the quite different physical properties of CO2 in its gas and liquid phases (see Figure 18). Increasing the downstream pressure beyond 6 MPa causes the phase transition of the CO2 there, and therefore in the whole sample, from gas to the liquid state. The associated sudden increment in CO2 density (increasing from 210 kg/m3 in the gaseous state to 760 kg/m3 in the liquid state) and the reduction in adiabatic compressibility (0.154 (1/MPa) in the gaseous state to 0.009 (1/MPa) in the liquid state) are due to the phase transition. For this liquidation process, a certain amount of CO2 must be aggregated in the downstream, until which time the downstream pressure development occurs only at a slower rate, showing an almost steady-state condition closer to 6 MPa. This is because pressure development in the gaseous state requires a large gas volume in constant space, due to its high compressibility characteristics, and when it converts to the liquid state, the associated huge compressibility reduction and density enhancement cause much quicker pressure development. In other words, downstream pressure closer to 6 MPa means the sample has almost liquid CO2 throughout and is continually sending out CO2 to downstream, which therefore creates an almost steady pressure holding period until the downstream CO2 converts to its liquid state. The duration of this downstream pressure holding is therefore dependent on the advective flux rate through the sample pore space, which is proportional to the pressure difference between the injection point and the holding pressure. In such situations, greater injection pressures create more accelerated advective flux, causing much shorter pressure holding periods. For example, the pressure holding times for 9, 12 and 15 MPa injection pressures are around 2.24 h, 1.05 h and 0.51 h, respectively. Interestingly, once the downstream begins to increase again after the phase transition, the pressure development at downstream initiates after the holding period, and the pressure development seems to be even greater than the pressure development rate experienced during primary pressure development (0 to 6 MPa), which confirms the superior dense and incompressible characteristics of liquid CO2 compared with its gaseous state (see Figure 18). For example, CO2 compressibility reduces from 0.255 (1/MPa) to 0.00457 (1/MPa) with increasing pressure from 3 MPa to 12 MPa, and the possible pressure increment upon the addition of 1% by volume of CO2 is around 0.039 MPa and 2.19 MPa at 3 MPa and 12 MPa, respectively. This shows that, although there is a much slower flow rate in the liquid state, the CO2 pressure can be significantly changed from an additional CO2 drop, which guarantees a high injection pressure of CO2 during the fracturing process. The permeability of the siltstone was then calculated using pulse-decay permeability measurement (Equations (7) and (8)), and Figure 20 shows the logarithmic decay of the difference in pressure between upstream and downstream at 3 MPa injection pressure and 20 MPa confinement. Here, in order to reduce the influence of pore pressure on the permeability calculation, only the tail end of the development of the downstream pressure is used, and for each injection condition, the start time of the pulse decay permeability measurement begins when the pressure difference between upstream and downstream drops to 0.2 MPa (see Figure 20). In this case, the pore pressure approximates the injection pressure. There is a linear relationship between the logarithms of the pressure difference between upstream and downstream with time, and the slope of the straight line is the decay exponent α in Equation (7) (see Figure 21), and the permeability of the siltstone sample at different injection pressures can be calculated from Equation (8). Appl. Sci. 2018, 8, 1092 19 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 19 of 26 Appl. Sci. 2018, 8, x FOR PEER REVIEW 19 of 26

Figure 20. Development of downstream pressure with time at 3 MPa injection pressure under 20 MPa FigureFigure 20. 20. DevelopmentDevelopment of of downstream downstream pressure pressure with with time timeat 3 MPa at 3injection MPa injection pressure pressureunder 20 MPa under confinement. 20confinement. MPa conﬁnement.

Figure 21. Logarithmic decay of difference between upstream pressure and downstream pressure at Figure 21. Logarithmic decay of difference between upstream pressure and downstream pressure at Figure20 M 21.Pa Logarithmicconfinement. decay of difference between upstream pressure and downstream pressure at 2020 MPa MPa confinement. confinement. The calculated permeability values for each injection pressure condition are shown in Figure 22, The calculated permeability values for each injection pressure condition are shown in Figure 22, which shows that the permeability decreases from 0.00061 mD to 0.000433 mD with increasing whichThe calculated shows that permeability the permeability values decreases for each from injection 0.00061 pressure mD to condition 0.000433 are mD shown with increasingin Figure 22 , injection pressure from 3 MPa to 6 MPa at 20 MPa confinement, due to the reducing slip flow with whichinjection shows pressure that the from permeability 3 MPa todecreases 6 MPa at from20 MPa 0.00061 confinement, mD to 0.000433 due to the mD reducing with increasing slip flow injection with increasing pressure, and gaseous CO2 with lower compressibility has high penetration capacity pressureincreasing from pressure, 3 MPa to and 6 MPa gaseous at 20 MPaCO2 with confinement, lower compressibility due to the reducing has high slip penetration flow with increasingcapacity through pore throats. In the case of liquid CO2 injection, when the injection pressure is 9 MPa, the pressure,through and pore gaseous throats. CO In 2thewith case lower of liquid compressibility CO2 injection, has when high the penetration injection pressure capacity is through9 MPa, the pore permeability drops to the lowest point of around 0.000270 mD, recalling the conclusion that the throats.permeability In the case drops of liquid to the CO lowest2 injection, point whenof around the injection 0.000270 pressure mD, recalling is 9 MPa, the the conclusion permeability that drops the permeability for liquid CO2 is much lower than that for gaseous CO2.under steady-state conditions. to thepermeability lowest point for liquid of around CO2 is 0.000270 much lower mD, than recalling that for the gaseous conclusion CO2.under that the steady permeability-state conditions. for liquid With further increase of injection pressure, the permeability starts to slightly increase up to 0.000295 COWithis much further lower increase than of that injection for gaseous pressure, CO the.under permeability steady-state starts conditions. to slightly increase With further up to increase0.000295 of mD2 at 15 MPa, which is mainly related to 2the reduced effective stress effect in rock pores. In this injectionmD at pressure,15 MPa, which the permeability is mainly relate startsd to the slightly reduced increase effective up tostress 0.000295 effect mD in rock at 15 pores. MPa, In which this is study, the permeability at 9 MPa injection pressure is regarded as the reference liquid permeability, mainlystudy, related the permeability to the reduced at 9effective MPa injection stress pressure effect in rockis regarded pores.In as this the study,reference the liquid permeability permeability, at 9 MPa because the slippage effect is almost absent, and the permeability fluctuation is small when CO2 is in injectionbecause pressure the slippage is regarded effect is as almost the reference absent, and liquid the permeability, permeability becausefluctuation the is slippage small when effect CO is2 almostis in the fluid phase. The Klinkenberg parameter b can be calculated using Equation (3). For example, at the fluid phase. The Klinkenberg parameter b can be calculated using Equation (3). For example, at absent,20 MPa and confinement, the permeability it equals fluctuation 3.78 MPa isat small3 MPa wheninjection CO pressure2 is in the and fluid 3.61 phase.MPa at The6 MPa Klinkenberg injection parameter20 MPa confinement,b can be calculated it equals using3.78 MPa Equation at 3 MPa (3). injection For example, pressure at and 20 3.61 MPa MPa confinement, at 6 MPa injection it equals Appl. Sci. 2018, 8, x FOR PEER REVIEW 20 of 26 Appl. Sci. 2018 8 Appl. Sci. 2018,, 8,, 1092x FOR PEER REVIEW 2020 ofof 2626 pressure, with an average value of 3.70 MPa, which is consistent with the findings of Tanikawa and pressure,Shimamoto with [41 an]. Accordingaverage value to Equation of 3.70 MPa (3),, thewhich permeability is consistent for with gas COthe 2findings is 0.001265 of Tanikawa mD at 1 MPaand 3.78pore MPa pressure at 3 MPa and injection0.002268 pressure mD at 0.5 and MPa 3.61 pore MPa pressure, at 6 MPa injectionrespectively, pressure, which with is much an average higher value than Shimamoto [41]. According to Equation (3), the permeability for gas CO2 is 0.001265 mD at 1 MPa of 3.70 MPa, which is consistent with the findings of Tanikawa and Shimamoto [41]. According to porethe liqui pressured permeability. and 0.002268 mD at 0.5 MPa pore pressure, respectively, which is much higher than Equation (3), the permeability for gas CO2 is 0.001265 mD at 1 MPa pore pressure and 0.002268 mD at the liquid permeability. 0.5 MPa pore pressure, respectively, which is much higher than the liquid permeability.

Figure 22. Relationship between permeability of siltstone at different injection pressures. Figure 22.22. Relationship between permeability ofof siltstonesiltstone atat differentdifferent injectioninjection pressures.pressures. Similar to the steady-state permeability tests, the confining pressure under transient conditions also plays an important role in permeability evolution. Higher confining pressures cause the natural SimilarSimilar toto thethe steady-statesteady-state permeabilitypermeability tests,tests, thethe confiningconfining pressurepressure underunder transienttransient conditionsconditions micro-fractures or preferential flow paths to shrink, resulting in a significant permeability reduction. alsoalso playsplays anan importantimportant rolerole inin permeabilitypermeability evolution.evolution. Higher confiningconfining pressurespressures causecause thethe naturalnatural With the increase of confining pressure, the times taken for the equilibrium between upstream and micro-fracturesmicro-fractures oror preferentialpreferential flowflow pathspaths to shrink, resulting in a significantsignificant permeability reduction. downstream are increased and the pressure increase rate is decreased (see Figure 23). The tested WithWith thethe increaseincrease ofof confiningconfining pressure,pressure, thethe timestimes takentaken forfor thethe equilibriumequilibrium betweenbetween upstreamupstream andand siltstone permeability decreases with increasing confining pressure (see Figure 22). For example, downstreamdownstream are are increasedincreased andand thethe pressurepressure increaseincrease raterate isis decreaseddecreased (see(see FigureFigure 2323).). TheThe testedtested under 9 MPa injection pressure conditions, increasing the confinement from 10 to 20 MPa, 10 to 30 siltstonesiltstone permeability permeability decreases decreases with with increasing increasing confining confining pressure pressure (see (see FigureFigure 2222).). For example, example, MPa and 10 to 40 MPa causes the siltstone permeability to decrease by 24%, 31% and 37%, underunder 99 MPaMPa injection injection pressure pressure conditions, conditions, increasing increasing the the confinement confinement from from 10 to 10 20 to MPa, 20 MPa, 10 to 10 30 to MPa 30 respectively. andMPa 10 and to 40 10 MPa to causes40 MPa the causes siltstone the permeability siltstone permeability to decrease by to 24%, decrease 31% and by 24%, 37%, respectively.31% and 37%, respectively.

FigureFigure 23.23Measurement. Measurement of downstreamof downstream ﬂuid fluid pressure pressure for CO for2 injection CO2 injection under 3 under MPa injection 3 MPa pressure injection withoutpressure phase without transition phase transition and under and 12 MPaunder injection 12 MPa pressureinjection withpressure phase with transition phase transition (for the effect (for the of Figure 23. Measurement of downstream fluid pressure for CO2 injection under 3 MPa injection conﬁningeffect of confining pressure). pressure). pressure without phase transition and under 12 MPa injection pressure with phase transition (for the effect of confining pressure). Appl. Sci. 2018, 8, 1092 21 of 26

Now, if the steady-state and transient permeability values are compared (Figures 13 and 22), it appears that the permeability calculated under transient conditions is much lower than the steady-state permeability of the tested siltstone. The slip-flow effect is reduced with the downstream pressure development which occurs under the transient test conditions, and for steady-state conditions, the flow behavior of CO2 is mainly dominant at low pore pressure around downstream, where a greater pressure gradient is needed for higher flow rates. Therefore, the slip-flow effect around downstream can result in higher permeability under steady-state conditions compared with transient conditions. More significantly, the temperature variation can greatly change the CO2 flow behavior along the sample and tend to increase the flow rate, which is introduced in detail in Section 3.2. In the field, depending on the flow characteristics of the surrounding rock layers, the flow behavior can be partially steady-state/transient and the permeability behavior can change accordingly, particularly for the gaseous state of CO2. For the fracturing process, the leak-off rate of injected CO2 is more dependent on the flow behavior under transient conditions compared with steady-state conditions.

3.4. Effect of Effective Stress Law on Permeability Behavior of CO2 According to Terzaghi [47], rock deformation is governed by the difference between confining pressure and pore pressure, as in Equation (11), which reveals the opposite effects of confining pressure and pore pressure on the volumetric strain and pore structure. For consolidated rock, the sensitivity of rock deformation to confining pressure and pore pressure is different, and similarly, rock permeability, which is closely related to the pore structure of rock, is affected differently by confining pressure and pore pressure [48]. To describe how permeability varies with confining pressure and pore pressure, the effective stress law is applied, considering an effective stress coefficient (Equation (12)).

σTerzaghi = Cp − Pp (11)

σe f f = Cp − χPp (12) where, Cp is confining pressure, Pp is the pore pressure, χ is the effective stress coefficient for permeability, and σe f f is the effective stress for permeability. The effective stress coefficient for permeability χ indicates the different effects of confining pressure and pore pressure on permeability, and the permeability can be related to single variable parameter σe f f , effective pressure [43]. The effective stress coefficient for permeability can be calculated using the ratio between the sensitivity of permeability to change in pore pressure and confining pressure (see Equation (13)). ∂k/∂Pp χ = − (13) ∂k/∂Cp where, k is the permeability of the sample, and χ indicates the ratio between the relative sensitivity of permeability to changes in confining pressure and pore pressure. Considering the effect of slip-flow on the difference of permeability between gaseous and liquid CO2, only the permeability for liquid CO2 was analyzed for the effective stress coefficient χ. According to Figure 24, there is a linear relationship between permeability and effective stress under steady-state conditions, and χ equals 3.91 in liquid CO2 state, indicating that the permeability of the siltstone sample is more sensitive to change in pore pressure than confining pressure. This result is consistent with many other studies where clay mineral-abundant samples have higher χ values (>1) [49–51], and a similar χ value (2.96) was also calculated for liquid CO2 under transient conditions (see Figure 25). This can be explained by a simplified conceptual model of pore structure proposed by Zoback and Byerlee [49]. The very tiny pore channel for CO2 flow is surrounded by mineral particles, and the quartz particles (accounting for 42% in weight) with a larger diameter and low compressibility make up the skeleton, while many tiny and soft clay particles (accounting for 40% in weight) are present between the quartz particles and tiny pore channels (see Figure 26). The simple conceptual model can be verified by SEM images (see Figure8). In this model, the outer ring is a rigid framework composed Appl.Appl. Sci. Sci. 2018 2018, ,8 8, ,x x FOR FOR PEER PEER REVIEW REVIEW 2222 of of 26 26

conditionsconditions (see (see Figure Figure 25 25).). This This can can be be explained explained by by a a simplified simplified conceptual conceptual model model of of pore pore structure structure proposedproposed byby ZobackZoback andand ByerleeByerlee [49[49].] . TheThe veryvery tinytiny porepore channelchannel forfor COCO2 2 flowflow isis surroundedsurrounded byby mineralmineral particles, particles, and and the the quartz quartz particles particles (accounting (accounting for for 42% 42% in in weight) weight) with with a a larger larger diameter diameter and and lowlow compressibility compressibility make make upup the the skeleton, skeleton, while while many many tiny tiny andand softsoft clay clay par particlesticles (accounting (accounting for for Appl. Sci. 2018, 8, 1092 22 of 26 40%40% in in weight) weight) are are present present between between the the quartz quartz particles particles and and tiny tiny pore pore channels channels (see (see Figure Figure 26 26).). The The simplesimple conceptual conceptual model model can can be be verified verified by by SEM SEM images images (see (see Figure Figure 8 8).). In In this this model, model, the the outer outer ring ring ofisis quartz a a rigid rigid particles framework framework and composedthe composed inner ring of of is quartz quartz composed particles particles of soft and and clay the the minerals. inner inner ring ring When is is compo thecompo confiningsedsed of of softpressure soft clay clay andminerals.minerals. pore pressure When When the the are confining confining applied to pressure pressure the model, and and the pore pore rigid pressure pressure framework are are applied appliedincurs a to to small the the strainmodel, model, which the the rigid rigid has framework incurs a small strain which has limited impact on the thickness of the CO2 2flow channel. limitedframework impact incurs on the a small thickness strain of thewhich CO has2 flow limited channel. impact The on inner theclay thickness mineral of layerthe CO is more flow sensitive channel. toTheThe pore innerinner pressure clayclay mineralmineral because layerlayer the confining isis moremore sensitivesensitive pressure tto iso pore mainlypore pressurepressure supported because because by quartz thethe confiningconfining particles, pressurepressure and pore isis pressuremainlymainly supported supported can produce by by quartz quartz higher particles, particles, strain on and and clay pore pore minerals pressure pressure compared can can produce produce with higher thehigher same strain strain confining on on clay clay pressure,minerals minerals andcomparedcompared the clay withwith mineral the the same same strain confiningconfining can have pressure,pressure, a considerable andand thethe impact clayclay mineralmineral on the thickness strainstrain cancan of have have the aflow a considerableconsiderable channels. impact on the thickness of the flow channels. Therefore, pore pressure has a greater effect than Therefore,impact on pore the pressure thickness has of a the greater flow effect channels. than Therefore, confining pressure pore pressure on the hasflow a behavior greater effect of CO than2 in thisconfiningconfining clay-abundant pressure pressure sampleon on the the flow [flow50]. behavior behavior of of CO CO2 2in in this this clay clay-abundant-abundant sample sample [ 5[500].] .

Figure 24. Permeability versus modified effective stress for liquid CO2 state under steady-state FigureFigure 24.24. PermeabilityPermeability versus versus modified modiﬁed effective effective stress for stress liquid for CO liquid2 state CO under2 state steady under-state steady-stateconditions.conditions. conditions.

Figure 25. Permeability versus modiﬁed effective stress for liquid CO2 state under transient conditions. Appl. Sci. 2018, 8, x FOR PEER REVIEW 23 of 26

Figure 25. Permeability versus modified effective stress for liquid CO2 state under transient Appl. Sci. 2018, 8, 1092 23 of 26 conditions.

FigureFigure 26.26. ConceptualConceptual modelmodel ofof ﬂowflow channelchannel structurestructure inin clay-abundantclay-abundant samplesample [[4949].].

4.4. ConclusionsConclusions

TheThe currentcurrent lacklack ofof understandingunderstanding ofof COCO22 flowflow behaviorbehavior inin deepdeep shaleshale layers,layers, particularlyparticularly withwith itsits expectedexpected phasephase transitiontransition andand usingusing differentdifferent measurementmeasurement techniques,techniques, addsadds manymany complicationscomplications toto thethe prediction of of the the effectiveness effectiveness of of the the fracturing fracturing process. process. The The inte intentionntion of the of thepresent present study study was wastherefore therefore to determine to determine the the flow flow behavior behavior of of CO CO2 in2 in shale shale formations formations and and the the influence influence of of phase phase transitiontransition onon it.it. Further,Further, thethe influenceinfluence ofof utilizingutilizing laboratorylaboratory techniquestechniques (steady-state(steady-state andand transienttransient tests)tests) on on permeability permeability calculation calculation was alsowas examined. also examined. The test The results test enable results the enable following the conclusions following toconclusions be drawn: to be drawn:

(1).(1). Much lower permeability valuesvalues forfor liquidliquid COCO22 comparedcompared toto gaseousgaseous COCO22 were observedobserved underunder transient conditions, due to thethe reducedreduced slip-flowslip-flow effect.effect. ConsideringConsidering thethe significantsignificant differencedifference of density between two phases,phases, the mass flowflow raterate ofof liquidliquid COCO22 isis muchmuch higherhigher thanthan thatthat ofof gaseous CO2.. (2).(2). Under steady-statesteady-state conditions, the heat exchange with the decrease of pore pressure cancan greatlygreatly decrease the flow temperature due to the unique thermodynamic properties of CO2, which can decrease the flow temperature due to the unique thermodynamic properties of CO2, which can liquefy the gaseous CO2 and extend the length of liquid CO2 along the sample, and much higher liquefy the gaseous CO2 and extend the length of liquid CO2 along the sample, and much higher density of liquid CO2 can lead to higher flow rate recorded by flowmeter at room temperature. density of liquid CO2 can lead to higher flow rate recorded by flowmeter at room temperature. Faster temperature variationvariation at at higher higher injection injection pressure pressure than than 9 MPa9 MPa can can results results in in the the presence presence of smallof small drikold drikold particles, particles, which which is responsible is responsible for the for unstable the unstable flow rate flow at higher rate at injection higher pressure. injection (3). Permeabilitypressure. calculated under transient conditions is much lower than that under steady-state (3). conditions,Permeability except calculated the reason under thattransient the slip-flow conditions effect is much under lower steady-state than th conditionsat under steady increased-state conditions, except the reason that the slip-flow effect under steady-state conditions increased the flow behavior of CO2 through the tested sample with ultralow permeability, the influence of temperaturethe flow behavior variation of CO can2 through be excluded the tested under sample transient with conditions ultralow due permeability to its much, lowerthe influence flow rate. of temperature variation can be excluded under transient conditions due to its much lower flow During the field fracturing process, liquid CO2 is injected into the formation matrix at high pore pressure,rate. During and the the field conditions fracturing are closerprocess, to transientliquid CO laboratory2 is injected conditions. into the formation Therefore, matrix the transient at high permeabilitypore pressure, calculation and the conditions approach isare more closer reliable to transient for the shalelaboratory fracturing conditions. process. Therefore, the transient permeability calculation approach is more reliable for the shale fracturing process. (4). The variation of apparent permeability with injection pressure is affected by the combined effects

(4). ofThe slip-ﬂow variation effect, of apparent temperature permeability variation and with effective injection stress. pressure Under is transient affected conditions by the combined without effects of slip-flow effect, temperature variation and effective stress. Under transient conditions any temperature variation, increasing the injection pressure caused an opposite trend of apparent without any temperature variation, increasing the injection pressure caused an opposite trend permeability for gaseous and liquid CO2, because the slip-ﬂow effect dominates the downward of apparent permeability for gaseous and liquid CO2, because the slip-flow effect dominates the of permeability for gaseous CO2 and the effect of effective stress dominates the upward of downward of permeability for gaseous CO2 and the effect of effective stress dominates the permeability for liquid CO2, respectively. However, under steady-state conditions, although upward of permeability for liquid CO2, respectively. However, under steady-state conditions, liquid CO2 showed a similar upward trend to that under transient conditions, gaseous CO2 permeability also exhibited an upward trend with the increase of injection pressure, which is Appl. Sci. 2018, 8, 1092 24 of 26

opposite to that under transient conditions, because the influence of temperature variation becomes stronger with the increase of flow rate and increases the apparent permeability with the increase of injection pressure. (5). Increasing the confining pressure causes the internal natural micro-fractures or preferential flow pathways in the rock matrix to close, which significantly reduces its flow capacity or permeability. A greater than 1 effective stress coefficient (χ) for permeability confirms the greater sensitivity of CO2 to pore pressure compared to confining pressure due to the abundance of clay minerals.

Author Contributions: C.Z. and R.P.G. conceived and designed the experiments; C.Z. performed the experiments; C.Z. and M.S.A.P. analyzed the data and wrote the paper; C.Z. revised the paper according to reviewers’ comments. Funding: This research received no external funding. Acknowledgments: This work was performed in part at the Monash Centre for Electron Microscopy (MCEM). Chengpeng would like to acknowledge the scholarship assistance from China Scholarship Council and Monash University. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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