Critical Conditions for Massive Fines Detachment ... - ACS Publications

Jun 12, 2017 - Australian School of Petroleum, The University of Adelaide, Adelaide, ... ABSTRACT: Fines migration has posed a great challenge to gas ...
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Critical Conditions for Massive Fines Detachment Induced by SinglePhase Flow in Coalbed Methane Reservoirs: Modeling and Experiments Fansheng Huang,† Yili Kang,*,† Zhenjiang You,‡ Lijun You,† and Chengyuan Xu† †

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China Australian School of Petroleum, The University of Adelaide, Adelaide, South Australia 5005, Australia

‡

S Supporting Information *

ABSTRACT: Fines migration has posed a great challenge to gas and water production in CBM reservoirs, resulting not only in dramatic permeability reduction but also in excessive wear on equipment. The objective of this study was to investigate critical flow conditions for massive fines detachment in the dewatering phase, for the purpose of yielding an improved understanding of fines detachment mechanisms and their effective control in the field. First, fines migration experiments under saturated conditions, including effluent concentration and permeability measurements, were conducted at elevated pressure gradients on fractured coal samples with various apertures. Experimental results indicate the existence of a critical pressure gradient (CPG) for massive fines detachment. Second, a mathematical model was developed to describe single particle detachment in the fracture, accounting for the coupling effects of hydrodynamic and extended-DLVO forces. Effects of fines size and fracture aperture on fines detachment were analyzed, and CPGs were determined from the proposed model. Modeling results revealed that the pressure gradient required for fines detachment first decreased with increasing fines size, reached a minimum value, and then increased; these minimum values are defined as CPGs, which exhibit a strong negative correlation with fracture aperture. CPGs obtained from modeling were slightly smaller than those determined from experiments, due to the assumptions of homogeneous surfaces and spherical particles in the model. Finally, the implications of this research on field-scale fines control in coal were thoroughly discussed. precondition of fines migration, is the focus of this work. In the past decades, fines detachment under saturated conditions has been extensively investigated through experiments and theoretical analyses, mainly concentrating on the effects of flow conditions (i.e., flow velocity or pressure gradient), chemical properties of flowing fluid (i.e., pH and ionic strength), and temperature. Experimentally, several researchers have found the presence of a critical salt concentration (CSC) for massive fines detachment.14−20 Above the CSC, fines remain attached to the surface. Below the CSC, mobilization of fines occurs. Additionally, there also exist critical values of flow velocity, pH, and temperature for massive fines detachment, beyond which the attached fines are released, resulting in significant impairment of permeability.19−29 It can be found that previous studies mainly focused on porous media. Nevertheless, coal fines are usually originated from coal fractures.6 Fines detachment in fractured media has seldom been studied so far. Theoretically, some researchers have quantitatively explained the chemical and physical critical conditions for fines detachment using the Derjaguin−Landau−Verwey−Overbeek (DLVO) theory,14,15,20,25 or the coupling effects of extended-DLVO and hydrodynamic forces.18,19,26,28,29 Specifically, if the attaching force/torque exerting on a fine particle is larger than the detaching force/torque, it will remain in an

1. INTRODUCTION Global coalbed methane (CBM) resources (original gas-inplace) ranges from 1300 to 8000 trillion cubic feet (Tcf) ((36.8−226.5) × 1012 m3) approximately, which is a clean, high-efficiency, and low-cost energy fuel that has significant potential for further discovery and development.1 However, due to the natural brittle, low-strength, and weakly consolidated characteristics of coal, large amounts of coal fines with an average size < 50 μm are easily generated during the processes of coalification, tectonic deformation, drilling, hydraulic fracturing, as well as primary and enhanced coalbed methane (ECBM) production.2−9 Numerous experimental and field studies have demonstrated that fines migration triggered by gas and water flow is among the major factors that contribute to the severe reduction of permeability during production of CBM reservoirs, due to fines plugging in cleats and hydraulic fractures, as well as accelerating paraffin and scale formation through acting as nucleation sites.10−12 Additionally, the transport of fines to wellbores can also induce the blockage of CBM wells, premature failure of downhole and surface equipment, operational downtime, and replacement costs.13 For these reasons, it is critical to investigate the transport mechanisms of coal fines and develop a methodology to control fines. Fines migration in porous/fractured media is a process involving fines detachment from the grain/matrix surface, entrainment by fluid, and retention in narrow flow paths or discharged out from the media. Detachment, as the © XXXX American Chemical Society

Received: March 1, 2017 Revised: June 1, 2017 Published: June 12, 2017 A

DOI: 10.1021/acs.energyfuels.7b00623 Energy Fuels XXXX, XXX, XXX−XXX

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Figure 1. Forces acting on a single fine particle adhering to the fracture surface.

attached state; otherwise, the fine particle will be dislodged from the surface. Although modeling results seem to match the critical conditions well, there still exist two main problems requiring further research: (1) Previous researchers often assumed monosized fines in the pores; in fact, the fines sizes range widely from nanoscale to micrometer scale.26,30 Due to the strong dependences of extended-DLVO and hydrodynamic forces on fines size, the critical conditions for fines detachment will change according to fines size. Taking the critical flow velocity (CFV) for example, Bedrikovetsky et al.,28 Sharma et al.,29 and Bergendahl and Grasso31 found that the CFV decreased with increasing fines size, whereas Hayden et al.,32 Shao and Lu,33 Robinovich and Kalman,34 and Dasani et al.35 found that the CFV first decreased with fines size and then increased. Therefore, given that fine particles have distributed sizes within pores or fractures, what are the critical conditions for massive fines detachment? (2) Previous experiments were commonly conducted using homogeneous material and on one sample under specific conditions only, in which the effect of pore structure was not fully investigated. Because pore structure is of crucial importance in affecting the hydrodynamic forces, the critical conditions for fines detachment, especially the CFV, will change with variations in pore structure. Although some researchers have realized the discrepancy in critical conditions among different samples, they did not quantitatively interpret them.16,19 Thus, the effect of pore structure on fines detachment remains largely unknown. The present paper aims to address the above-mentioned questions by examining fines detachment induced by singlephase water flow in coal fractures. Since drainage of CBM wells is usually performed at a constant pressure difference (i.e., the difference between formation and bottom hole pressures), we focus specifically on the critical pressure gradient (CPG) for fines detachment instead of the CFV.6 First, fines migration experiments under saturated conditions, including effluent concentration and permeability measurements, are conducted at varying pressure gradients on fractured samples with different apertures, aiming to obtain the CPGs for massive fines detachment. Second, a mathematical model is developed to describe fines detachment within fractures. The effects of fines size and fracture aperture are analyzed, and the CPGs are determined from the proposed model. Comparisons between modeling and experimental CPGs are also conducted, and discrepancies are interpreted using the characteristics of fractures and fines. Finally, we discuss the implications of this research on field-scale fines control in CBM reservoirs.

2. THEORY OF FINES DETACHMENT Natural fractures in coal are generally considered to be the dominant spaces for the occurrence and transport of coal fines. When fluid flow within a fracture is gradually enhanced, coal fines will be mobilized from fracture surfaces. In order to elucidate fines detachment mechanisms, the main forces acting on an individual fine particle adhering to the fracture surface are analyzed, assuming a homogeneous surface, spherical particle, and Poiseuille flow (Figure 1). These forces can be divided into two groups: the forces encouraging fines mobilization (i.e., drag force Fd due to the pressure gradient of fluid flow and lift force Fl from the fluid velocity gradient normal to the surface), and the forces holding fines on the surface (i.e., adhesive force Fa from the physicochemical interaction, and frictional force Ff due to the bond between fines and the surface). The drag and lift forces can be determined using the expressions of Goldman et al.,36 O’Neill,37 and Saffman,38 and the adhesive force is derived from the extended-DLVO theory.39 The expressions for the above forces can be found in the Supporting Information. It should be mentioned that there also exists gravitational force exerting on fines. However, the gravitational force for particles with radii < 500 μm is negligible if compared to other forces, thus can be omitted from the force analysis.26,40,41 For the same reason, the effect of fracture inclination on fines detachment can also be neglected. On the basis of the above model, fines detachment can be initiated by the incipient motion of fines through three potential mechanisms: rolling, sliding, and lifting. The rolling mechanism occurs when the applied torque caused by hydrodynamic forces exceeds the resistance to motion, while sliding and lifting occur when the encouraging forces are greater than the resisting forces in the tangential and normal directions, respectively. Previous studies have demonstrated that rolling is the primary mechanism for spherical particle mobilization under laminar flow conditions.29,42 The critical condition for rolling is expressed as FdLn = Fna = (Fa − Fl)a

(1)

where Ln [L] is the lever arm of drag force, Fn [MLT−2] is the total force in the normal direction, and the Fa value corresponds to the maximum derivative of the total particle-surface interaction potential;43,44 a [L] is the radius of the particlesurface contact area due to slight deformation of the particle and surface induced by Fn. According to theoretical analysis in O’Neill,37 the drag force Fd acts effectively on the particle at a distance of 1.399r from the fracture surface; thus, Ln = 0.4r + r 2 − a 2 . The value of contact radius can be estimated using the model of Johnson−Kendall−Roberts (JKR).45 Because of no direct physical contact between the B

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Energy & Fuels Table 1. Proximate Analysis and Petrology of the Coal Samplesa proximate analysis (%)

maceral composition (%)

sample

FCad

Vdaf

Aad

Mad

Ro,max (%)

vitrinite

inertinite

exinite

QS 03#

82.23

8.71

8.61

0.45

3.25

74.03

20.23

5.74

Note: FCad is the fixed carbon content; Vdaf is the volatile matter content; Aad is the ash content; Mad is the moisture content; and Ro,max is the maximum reflectance of vitrinite. a

Table 2. Mineral Composition of the Coal Samples sample

quartz (%)

calcite (%)

iron pyrite (%)

ankerite (%)

dolomite (%)

clay (%)

organic matter (%)

QS 03#

0.06

1.11

0.14

0.07

0.76

4.64

93.22

particle and the fracture surface, the value of a at separation should be modified as42,44,46 a = 0.63 × K≡

⎛ 4Fnr ⎞1/3 ⎜ ⎟ ⎝ K ⎠

(2)

4

(

3

1 − v12 E1

+

1 − v22 E2

)

(3)

−1 −2

where K [ML T ] is the composite Young’s modulus; E1, E2 [ML−1T−2] are the Young’s moduli of the particle and the surface, respectively; and v1, v2 [−] are the Poisson’s ratios of the particle and the surface, respectively. It is worth noting that the JKR theory is only valid for soft, highly deformable materials. For stiff materials, the Derjaguin−Muller−Toporov (DMT) theory should be applied.47 Substituting eqs 2 and 3, as well as the expressions for all forces in the Supporting Information, into eq 1, the critical condition for fines detachment, defined using the pressure gradient, is given as ( 1.08ρl0.5 μFa + μ2 rK 0.5 − μr 0.5K 0.25)4/3 Δp = L 9.88ρl2/3 r 2(H − 2r )

Figure 2. Photographs of two fractured coal samples obtained from the Qinshui Basin.

Table 3. Physical Dimensions and Equivalent Hydraulic Aperture (EHA) of the Fractures

(4)

3.1. Sample Preparation. One block of anthracite coal was collected from coal seam No. 3 in the southern part of the Qinshui Basin (China). Petrographic details as well as proximate analysis are given in Table 1. Mineral constituents, determined by X-ray diffraction (XRD), are summarized in Table 2. Cylindrical core samples with a diameter of ∼2.5 cm and a length of ∼5.0 cm were drilled from the coal block perpendicular to the bedding plane. The Brazilian method was utilized to create an artificial fracture parallel to the core axis in each drilled sample.48 Two halves of each core sample, along with the fines produced during core fracturing, were joined together and wrapped with Teflon tape. Two samples having different fracture apertures, hereafter referred to as SY-2 and SY-3, are presented in Figure 2; their physical dimensions are provided in Table 3. The equivalent hydraulic aperture (EHA) of the fracture was estimated using the cubic law through the flow test as described in section 3.249

Δp WH3 12μL 3 −1

core length (cm)

fracture length (cm)

fracture width (cm)

EHA (μm)

SY-2 SY-3

2.50 2.51

5.16 5.72

5.16 5.72

2.43 2.45

16.8 9.6

KCl and distilled Milli-Q water (pH = 5.8). The pH value of the solution was adjusted to ∼7.0 by the addition of KOH and HCl. Prior to use, the electrolyte solution was degassed and filtered through a 0.45 μm membrane to remove any entrained particles with sizes > 0.45 μm. The measured turbidity level of the electrolyte solution of 0.25 NTU was used as the background turbidity level in the following calculations. 3.2. Apparatus and Procedure. Core-scale steady-state flow experiments were conducted to study fines migration in coal fractures under saturated conditions. A schematic of the experimental setup used for flow tests is illustrated in Figure 3. It consists of two ISCO syringe pumps, a core holder, a fraction collector, a glass-tube flowmeter, two pressure transducers, a thermostat, and a data acquisition system (DAS). One ISCO pump was utilized to inject the influent solution through the sample at a constant injection pressure, while the other pump supplied the confining pressure for the core holder. The fraction collector was equipped to collect the effluent solution continuously and was connected in parallel to a flowmeter for measuring output fluxes. Two pressure transducers (0.5% precision over a 60 MPa range) monitored pressures at the inlet and outlet of the sample, respectively. The outlet pressure was always atmospheric. The DAS was used to transfer and digitize pressure and temperature measurements, so that data could be displayed and recorded in realtime. The entire system was placed in a thermostat to maintain a constant temperature (T = 25 °C). Note that all flow elements in the experimental system should be cleaned with alcohol, soapy water, and deionized water prior to flow tests, in order to avoid the effect of residual contaminants.

3. MATERIALS AND METHODS

Q=

sample

core diameter (cm)

(5) −1 −2

where Q [L T ] is outlet flow rate, Δp [ML T ] is the differential pressure across the fracture, μ [ML−1T−1] is the absolute viscosity of fluid, L [L] is the length of the fracture, W [L] is the width of the fracture, and H [L] is the EHA of the fracture. After the fractured cores were dried in an oven at 60 °C for 48 h, samples were preserved in a dry and clean plastic bag for the following fines migration experiments. The background electrolyte solution utilized in this study was 2 wt % KCl (a 1:1 electrolyte), prepared with the analytical reagent-grade C

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Figure 3. Schematic configuration of experimental apparatus for fines migration experiments.

Figure 4. Contour maps of the fracture surfaces with a spatial resolution of 0.1 mm obtained from laser scanner: (a) bottom surface of sample SY-2; (b) top surface of sample SY-2; (c) bottom surface of sample SY-3; and (d) top surface of sample SY-3. Variations in permeability, as a consequence of fines mobilization, should be monitored throughout the tests. Key factors affecting permeability during single-phase water flow are fines migration, stress, clay swelling, and dissolution or precipitation. Results of the XRD analysis have shown that coal samples contained no swelling clay. Also, Guo et al.10 found that mineral dissolution and precipitation were insignificant during water flow. Therefore, in order to evaluate the permeability variation subject to fines migration, stress sensitivity should be eliminated during the entire test period. Nevertheless, previous studies on fines migration in porous media were mostly based on the constant-rate method, and their flow experiments were conducted at a variable effective confining pressure (i.e., the difference between confining and pore pressures), due to the variation in injection pressures caused by released fines plugging the sample.16−19 For this reason, a constant-pressure method was used in this study, and the effective confining pressure was held constant using an automatically controlled syringe pump throughout the tests. The procedure for measuring fines migration and permeability is as follows: (1) The fractured sample was saturated under vacuum for ∼48 h using the filtered and degassed 2% KCl brine solution and was placed in the core holder with an effective confining pressure of 3 MPa. (2) 2% KCl brine solution was injected into the sample at a pressure gradient of 0.01 MPa/cm for several days, in order to ensure stable conditions and determine the initial permeability and EHA. Note that the initial pressure gradient could be properly increased if the fluid is not permeating the sample. (3) Flow tests were sequentially carried out at the following pressure gradients: 0.02, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35,

0.40, and 0.45 MPa/cm. For each case, effluent solutions were continually collected in 5 mL polystyrene tubes with the fraction collector and analyzed for turbidity level using a turbidimeter (2100Q, HACH). Meanwhile, outlet flow rate was also periodically measured using the flowmeter, through switching between Valve 2 and Valve 3 after each interval. (4) A linear calibration curve was established following the procedures described in Chen and Bai,50 to convert the measured turbidity level into a concentration value; then fines concentration, as well as the permeability determined using Darcy’s equation, was plotted versus the volume of effluent. 3.3. Characterization Measurements. 3.3.1. Fracture Characterization. On the basis of the flow experiments mentioned above, the dynamical EHA of the fracture in the coal sample was estimated using eq 5. In order to characterize surface morphologies, fracture surfaces were cleaned up by removing loose particles through airflow and then analyzed using a 3-D laser scanner (TNS-M, CDUT). In order to determine the electrokinetic property of the fracture surface, crushed coal particles were first sonicated for ∼10 min in the background solution, and then samples of the supernatant were taken for electrophoretic mobility measurements using microelectrophoresis (Zeta-PALS, Brookhaven). Measurements were repeated five times at 25 °C, and Smoluchowski’s formula was utilized for converting electrophoretic mobilities into zeta potentials.51 Nevertheless, it is impossible to determine the exact surface potential distribution of the fracture surface due to surface chemical heterogeneities.52 To characterize the surface chemical heterogeneity, one small cylindrical plug (∼4.0 mm in diameter and ∼5.0 mm in length) was prepared from the fractured coal sample. The mineral distribution on the D

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Energy & Fuels Table 4. Surface Roughness Parameters of Fracture Surfaces Obtained from Laser-Scanning Data fracture surface SY-2 SY-3

bottom top bottom top

m (μm)

Rsdr (μm)

Rmax (μm)

Rrms (μm)

SAD (%)

3185 1886 2439 3895

725 510 696 768

8235 6418 8729 8848

878 623 736 811

32.0 27.7 23.8 19.5

fracture surface was examined using a micro-CT scanner (MicroXCT400, Xradia). 3.3.2. Fines Characterization. Electrokinetic properties of coal fines were analyzed using microelectrophoresis (Zeta-PALS, Brookhaven). The electrophoretic mobilities were first measured using effluent fines suspensions, and zeta potentials were then determined from electrophoretic mobilities through Smoluchowski’s formula. Size distribution, geometry, and element compositions of the produced fines were also examined using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX) (Quanta 250, FEI). Prior to the SEM-EDX observation, coal fines were filtered out the effluent solution through a 0.45 μm membrane, and then gold-coated after drying.

4. RESULTS AND DISCUSSION 4.1. Characterization of the Fracture Surface. Figure 4 displays 2-D morphologic images of fracture surfaces contained in samples SY-2 and SY-3. Surface roughness parameters including the mean (m), standard deviation roughness (Rsdr), maximum roughness (Rmax), root-mean-square roughness (Rrms), and surface area difference (SAD) are listed in Table 4. Details on calculating these parameters can be found in Hoek et al.53 The 2-D micro-CT slice images through the fracture surfaces are illustrated in Figure 5. The distribution of mineral

Figure 6. Experimental results of fines concentration and permeability response as a function of effluent volume and pressure gradient for samples (a) SY-2 and (b) SY-3.

rapidly to a low value close to the influent background concentration. In addition, several slight fluctuations in the effluent concentration are also detected. These observations suggest that fines release occurs at each pressure gradient increase, which can be attributed to the existence of finessurface interaction energy distribution due to surface chemical and physical heterogeneities, pore-scale velocity distribution caused by complicated internal fracture structure, and fines size distribution.39,56,57 When comparing the breakthrough curves, abrupt 5- and 7-fold increases in peak values of effluent concentration can be found when pressure gradients increase up to 0.05 MPa/cm for sample SY-2 and 0.20 MPa/cm for sample SY-3, respectively. Such phenomena suggest that there exists a critical pressure gradient (CPG) for massive fines detachment between 0.02 and 0.05 MPa/cm for sample SY-2 and between 0.15 and 0.20 MPa/cm for sample SY-3, beyond which the detaching torque from hydrodynamic forces is sufficient to overcome the attaching torque, resulting in a significant fines release. This is consistent with previous researches, in which a critical flow velocity (CFV) for massive

Figure 5. Slice images through bottom surfaces of the fractures in samples (a) SY-2 and (b) SY-3 using Micro-CT. The white, gray, and black areas represent mineral phases, organic phases, and void spaces, respectively, indicating the surface chemical heterogeneity. These images have a resolution of 1.60 μm.

phases, organic phases, and void spaces, corresponding to white, gray, and black areas, respectively, can be identified based on their different adsorption rates: ∼3000, 1000−1800, and dpore/3, the particle will be captured by the pore.69,70 As shown in Table 3, the EHAs of samples SY-2 and SY-3 are 16.8 and 9.5 μm, respectively; thus it can be found that a significant fraction of produced fines have sizes larger than 1/3 EHA, and some even exceed the EHA. These phenomena can be explained by two aspects: (1) the “golden 1/3 rule of filtration” for porous media may not be appropriate for the fracture, which has been reported by Aadnoy et al.71 and Xu et al.;72 (2) EHA is generally smaller than the mean mechanical aperture, because EHA calculation is based on simple assumptions that the fracture is composed of two smooth parallel plates, neglecting the internal fracture structure heterogeneities.73 Even so, sizes of produced fines are mostly smaller than the initial EHA. It is worthwhile to note that compositions and size distributions of produced fines may change with applied flow conditions,68 but this phenomenon is not investigated in this study.

Figure 7. Total fines produced from fractured cores at different pressure gradients.

sample SY-3 (H = 9.6 μm) is approximately an order of magnitude greater than that of sample SY-2 (H = 16.8 μm); it is mainly attributed to their different fracture properties (e.g., the EHA), which will be further analyzed in next section. The aforementioned effluent fines are the portion of released fines that can reach the outlet, whereas other released fines are captured by the fracture through the mechanisms of straining, reattachment, interception, diffusion, and sedimentation, among which straining can trigger a remarkable permeability response.60 Along with effluent fines concentration, changes in permeability for samples SY-2 and SY-3 are also shown in Figure 6. It can be observed that there exist different degrees of permeability increases at the initial stage of each pressure gradient increase; this phenomenon has also been revealed in Torkzaban et al.61 and Lever and Dawe,14 then explained by Torkzaban et al.61 using the theory of hydrodynamic bridging. Bridging is generally formed by the simultaneous arrival of multiple particles with sizes smaller than the pore size,62,63 some of which can be dislodged by flow interruptions such as flow velocity increases, back-washing, and intermittent flow. After the initial permeability improvement, a gradual permeability reduction happens sequentially during each pressure gradient less than 0.30 MPa/cm for sample SY-2 and 0.40 MPa/cm for sample SY-3, signifying the occurrence and development of clogging induced by the straining of detached fines. Comparing the permeability response curves demonstrates that most reductions in permeability exist at a pressure gradient of 0.05 MPa/cm for sample SY-2 (from 18.7 to 3.9 mD) and 0.2 MPa/cm for sample SY-3 (from 3.0 to 1.1 mD); this can be explained by the accompanied significant fines detachment at these two stages as described above. Nevertheless, no measurable permeability reductions are observed when the applied pressure gradients increase up to 0.30 MP/cm for sample SY-2 and 0.40 MPa/cm for sample SY-3; this phenomenon can be mainly ascribed to the fact that fines F

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Figure 8. Representative SEM images and EDX spectra for each type of coal fines produced from samples SY-2 and SY-3: (a) organic matter; (b) kaolinite; (c) pyrite; and (d) calcite. For comparison, element compositions of background membranes include carbon, nitrogen, oxygen, and calcium.

formulas of Gregory,74 Hogg et al.,75 and Ruckenstein and Prieve,76 respectively. Details on these formulas can be found in the Supporting Information. Under the chemical conditions applied in this study, measured zeta potentials for fines and fracture surfaces are −12.17 and −9.15 mV, respectively. Additionally, a value of 109.58 × 10−21 J for the Hamaker constant is used to represent the fines-water-surface system.10 On the basis of the above parameters, the total fines-surface interaction energies as a function of separation distance are

4.4. Modeling of Fines Detachment. 4.4.1. ExtendedDLVO Interaction Energy Profiles. To gain insight into the mechanism of fines attachment on fracture surfaces, the extended-DLVO theory was applied to calculate the total fines-surface interaction potential energy, which is the sum of van der Waals (VDW) attraction, electrostatic double-layer (EDL) repulsion/attraction, and Born repulsion. For a sphereplate system, the retarded VDW attraction, EDL repulsion/ attraction, and Born repulsion can be determined using the G

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Detachment pressure gradients (DPGs) as a function of fines size and EHA are illustrated in Figure 11. Upon inspection,

Figure 9. Size distributions of fines produced from samples SY-2 and SY-3. Statistical results of fines sizes were obtained from randomly selected 65 and 52 fines for samples SY-2 and SY-3, respectively. Figure 11. Modeling results for the detachment pressure gradient (DPG) of coal fines as a function of fines size and fracture aperture. The theoretical CPG is defined here using the minimum point of the DPG curve. Dashed lines and shaded areas correspond to theoretical and experimental CPGs, respectively.

calculated for the different sizes of fines (d = 0.5, 5.0, 10.0, 20.0 μm), as shown in Figure 10. Calculations reveal that there exist

Reynolds numbers are smaller than 1 under all DPGs. In fractures, water flow is laminar. One of the most important findings is that DPG is highly dependent on fines size: as fines size increases, DPG decreases at first, reached a minimum value, and then increases. In other words, there exists an “optimum” fines size for fines detachment, corresponding to the minimum point of the DPG curve. The “optimum” size strongly depends on fracture aperture and equals 9.5 and 5.5 μm for samples SY2 (H = 16.8 μm) and SY-3 (H = 9.5 μm), respectively. Below the “optimum” size, the decrease of DPG can be attributed to the fact that drag and lift forces increase faster with fines size than adhesive force in this region, whereas the increase of DPG above the “optimum” size is because adhesive force increases faster with fines size than drag and lift forces.29,41,79 These phenomena are consistent with results from Shao and Lu,33 Dasani et al.,35 Kalman et al.,80 and Cabrejos and Klinzing.81 Another important finding is that the DPG curve for sample SY-3 (H = 9.5 μm) is higher than that for sample SY-2 (H = 16.8 μm), indicating the significant effect of fracture aperture on fines detachment. Theoretically, detachment shear rates for same-sized fines are identical. However, due to the effect of fracture aperture on the flow velocity profile, the DPG required will decrease with increasing the EHA according to eq (S-3). DPGs corresponding to the “optimum” fines sizes, defined here as the CPGs described in section 4.2, equal 0.036 and 0.142 MPa/cm for samples SY-2 (H = 16.8 μm) and SY-3 (H = 9.5 μm), respectively, beyond which a massive fines mobilization occurs in the coal fracture. Thus, it can be concluded that there is a strong negative correlation between the EHA and the CPG; that is, the greater the fracture aperture, the easier to bring about massive fines detachment. Comparing experimental results with the model reveals that CPGs predicted by the model are smaller than those obtained from experiments for both samples, as shown in Figure 11. Although the predicted CPG (0.023 MPa/cm) for sample SY-2 is within the experimental range (0.02−0.05 MPa/cm), it is smaller than the mean value of 0.035 MPa/cm and close to the lower bound (0.02 MPa/cm). These prediction errors in CPG

Figure 10. Calculated total interaction energies between various sized fines and coal surfaces.

no energy barriers for fines to deposit in the primary energy minima (i.e., completely favorable chemical conditions), and depths of the primary energy minima increase with fines diameter: ranging from 3165.2 kbT for d = 0.5 μm to 126602.0 kbT for d = 20 μm. 4.4.2. Determination of the Critical Pressure Gradient. Equation 4 is used to predict pressure gradients required to mobilize various sized fines attached to the fracture surface. Input parameters of the model include fines radius r, composite Young’s modulus K, fracture aperture (EHA), adhesive force Fa, water density ρl, and viscosity μ. As described in section 4.3, sizes of produced fines are mostly smaller than EHA; thus, the ratio of fines size to EHA is assumed to range from 0.01 to 0.90. The adhesive force Fa is defined as the maximum value of the derivative in total fines-surface interaction energy. The composite Young’s modulus K is estimated using eq 3, and the ranges of Young’s modulus E and Poisson’s ratio v for anthracite coal are 3.3−8.2 GPa (mean of 5.75 GPa) and 0.15− 0.49 (mean of 0.32), respectively.77,78 Additionally, water density and viscosity at 25 °C are 0.997 g/cm3 and 0.8949 mPa· s, respectively. H

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Energy & Fuels using this model can be attributed to simple assumptions inherent to the model such as spherical fines and smooth surfaces. Produced fines are irregular and present a wide variety of shapes (Figure 8); the shape of fine particles not only influences fines-surface contact forms (e.g., point contact for spherical fines, whereas line or plane contact for nonspherical fines), and hence the adhesive force. Moreover, the shape of fines particles relates directly to the drag and lift forces as well as the complicated flow field. As a result, the pressure gradient required for irregular fines detachment is greater than that for spherical fines. This discrepancy has been verified in Rabinovich and Kalman,34 Hayden et al.,32 Dasani et al.,35 and Gomes and Mesquita.82 Additionally, real fracture surfaces are usually physically heterogeneous (i.e., surface roughness). Surface roughness, including nano- and microscale roughness, has an important effect on the fines-surface interaction energy and lever arms related to the forces acting on fine particles. Under chemically favorable attachment conditions, the magnitude of primary minimum depth can be enhanced by both nano- and microscale surface roughness, although it may also be weakened by nanoscale roughness in some cases.83−85 Besides, nano- and microscale surface roughness can increase the lever arm related to the resisting adhesive forces and reduce the lever arm associated with the hydrodynamic forces by raising rolling point height.44,86 Consequently, the DPG as well as the CPG is increased when surface roughness is taken in account. Despite the distinction between experimental and modeling results, the predicted CPG can be used as the lower bound for fines control, which satisfies engineering demands.

Figure 12. Relationship among cleat spacing, permeability, and aperture based on the parallel-plate permeability model using data obtained from San Juan and Black Warrior Basins (adapted with permission from Laubach et al.89 Copyright 1998, Elsevier).

5. IMPLICATIONS FOR FIELD-SCALE FINES CONTROL Measures for preventing fines migration can be summarized into two major categories: physical methods and chemical methods. For physical methods, in situ fines control is achieved through adjusting flow velocity in the field to be below the CFV.16,21,24,59 Nevertheless, the CPG is applied in this study, due to the fact that a constant pressure difference (i.e., the difference between formation pressure and bottom hole pressure) is usually maintained in the field, and flow velocity is dynamically changing during production.6 Details about determining CPGs for field-scale fines control are described as follows. To the best of our knowledge, this is the first attempt at illustrating field-scale CPGs. Field-scale experiments are different from lab-scale experiments where only a single fracture is used. There exists a discrete fracture network in CBM reservoirs, and fracture aperture-size distribution complies with a power-law scaling.87−89 Laubach et al.89 found that in situ fracture apertures ranged from 3 to 40 μm according to the parallel-plate fracture permeability model, as shown in Figure 12. Thus, in order to solve the fines migration problem, fines present in the 40 μm fractures should be preferentially controlled; this can be attributed to the negative correlation between the CPG and the EHA, as well as the fact that, the larger the fracture’s EHA, the greater its contribution to permeability. Calculated from eq 4, the CPG for the 40 μm fracture is approximately 0.003 MPa/cm (Figure 13); that is, if the bottom hole pressure (BHP) is adjusted to maintain the pressure gradients to be below the CPG of 0.003 MPa/cm, few fines detach during the single-phase flow stage. Nevertheless, due to the strong dependence of CPGs on chemical conditions, it is worth noting that the calculated CPGs in Figure 13 are not appropriate for guiding field-scale fines control; real CPG values should be determined based on the in situ chemical

Figure 13. Detachment pressure gradients (DPGs) as a function of fines size and adhesive force in the widest fracture (EHA = 40 μm). Dashed lines represent CPGs at different adhesive forces (Fa, 2Fa, and 3Fa).

conditions. Furthermore, if field-scale CPGs are obtained, fines production zones can also be approximately derived from the formation pressure profile. The physical method is generally unfeasible for areas near the wellbore due to ultra-high-pressure gradients, unless a chemical method is used simultaneously. For chemical methods, fines control is achieved by injecting fines stabilizers into the formation. Fines stabilizers can significantly enhance the finessurface adhesive force Fa. As shown in Figure 13, when Fa is increased by 2 times, the CPG increases from 0.003 to 0.014 MPa/cm; that is, coal fines become more stable. Commonly used fines stabilizers consist of nanoparticle, zeta potential altering system (ZPAS), and surface tackifying agent (STA). Nanoparticles (NPs), with extremely small sizes (1−100 nm) and ultrahigh surface areas, tend to be strongly attached to fines and the fracture surface, consequently resulting in a notable increase in fines-surface interaction energies.5 Habibi et al.90 performed experiments with three types of NPs, MgO, Al2O3, and SiO2, and found that MgO NPs were the most effective in stabilizing fines. For the ZPAS, the effective constituent is an inner salt of a low-molecular-weight polymer that can alter I

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surface potentials to an optimum range from −20 to +20 mV, thus making for a stronger attraction between fines and the fracture surface.91 In addition, the STA polymer is a highmolecular-weight, hydrophilic polyamide, onto which hydrophobes are grafted. Hydrophilic groups of the STA polymer are prone to be attracted to polar mineral surfaces, resulting in a hydrophobic coating. Due to hydrophobe interactions through VDW bonds, a strong molecular hook-and-latch system is formed between fines and the fracture surface, thus providing an increased adhesive force.92 Several experimental and field studies have demonstrated that chemical methods successfully prevent fines migration, even under high flow rates and flow interruptions, with no observed reduction in permeability.90−97

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yili Kang: 0000-0003-1450-187X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge financial support provided by the National Science Foundation of China (Nos. 51674209, 51604236) and “13th five-year” National Science and Technology Plan Project of China (No. 2016ZX05061003). The authors also thank the CDUT for providing the laser scanner. We would also like to thank Xiangchen Li, Jiang Liu, and Yingqian Tu for their help in collecting effluent samples.

6. CONCLUSIONS Critical pressure gradients (CPGs) for massive fines detachment in coal fractures were investigated in this paper, both experimentally and theoretically. Fines migration experiments under saturated conditions were first performed at elevated pressure gradients in fractured coal samples with various apertures. The purpose was to obtain CPGs at different fracture apertures. A mathematical model was developed to describe fines detachment mechanisms. This made it possible to quantitatively predict theoretical CPGs at different fracture apertures, and effectively guide field-scale fines control. Major conclusions of this contribution are summarized below: (1) Effluent concentrations and permeabilities were significantly increased and reduced, respectively, when pressure gradients increased to 0.05 MPa/cm for sample SY-2 (H = 16.8 μm) and 0.20 MPa/cm for sample SY-3 (H = 9.5 μm), indicating the existence of various CPGs within different fracture apertures. (2) Modeling results indicate that the pressure gradient required for fines release first decreased with the increase of fines size, reached a minimum value, and then increased. For various fines sizes, theoretical CPGs were defined using these minimum values, which produced a strong negative correlation with fracture aperture. (3) The angular shape of fines and fracture surface roughness combined with assumptions of homogeneous surfaces and spherical fines produced inaccurate, but reasonable, CPG estimates. However, modeling CPGs does provide a lower limit on CPGs, which provide guidance for field application. (4) Considering the negative correlation between the CPG and the EHA, as well as that the larger fracture EHA has greater contribution to permeability, coal fines present in the maximum-EHA (∼40 μm) fractures should be preferentially controlled in the field. Additionally, an auxiliary measure (i.e., fines stabilizer) should also be applied to the areas near the wellbore due to the ultrahigh-pressure gradients within these areas.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.7b00623. Additional information about the expressions of forces acting on a single particle attached on the surface (PDF) J

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