SPE-171019-MS

Fracture Conductivity Decrease Due to Proppant Deformation andCrushing, a Parametrical Study

Jiahang Han, Baker Hughes Inc.; John Yilin Wang, The Pennsylvania State University

Copyright 2014, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Eastern Regional Meeting held in Charleston, WV, USA, 21–23 October 2014.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

Sustainable high fracture conductivity is a key to successful stimulation. The reduction of hydraulicfracture conductivity due to proppant deformation and crushing is frequently observed. Previous re-searches are based on laboratory experiments and empirical correlations, which can not fully explainproppant damage in field cases. In this paper, we applied our fully coupled fluid flow and geomechanicalmodel to further understand the proppant pack deformation and crushing.

Parametric studies on wellbore and reservoir pressures, formation properties, and proppant biotconstant were performed to understand proppant deformation and crushing in different conditions.Additionally, an analytical model for avoiding proppant crushing was developed for fractured wells.

Through this research, we found fracture conductivity loss due to deformation and crushing are severerthan laboratory results. Large deformation and high probability of crushing were observed near wellboreaccording to the net pressure. Fast flow back (low bottom hole pressure) would generate large proppantcrushed zone. Various reservoir properties as pressure gradient, formation stiffness, and matrix permea-bility were also investigated. Strong proppant is highly recommended for natural fractures, and hydraulicfracture near well bore especially for tight formations. Small chock size (high BHP) is also recommendedduring early production. Additionally, a simple analytical model is provided, accoding to the parametricalstudies, for operating well without breaking proppant pack.

IntroductionDuring hydraulic fracturing, proppant is used to create conductive channel for oil/gas to flow. The strengthand stiffness of the proppant remains the main concern of the successiveness of the stimulation. Gidleyet al. (1995), and Lacy et al. (1997) pointed out several factors that may severe decrease the proppant packconductivity. Proppant crushing and induced particles could block the fracture channel and decrease thefracture width, resulting in low fracture productivity.

In order to understand the proppant crush resistance, API recommened practice 19C (RP19C, identicalto IS013503-2 standard). Results generated from the 10 inch conductivity cell standard tests may notrepresent field conditions. Palisch et al. (2009) indicated that results from standard tests can deviate fromfield tests at the magnitude of one order. Additionally, the standard lab tests are time consuming. Han etal (2014) developped a numerical model that can quantify the proppant deformation and crushing under

certain assumptions. The model was validated with the conductivity tests. In this paper, this numericalmodel will be used to analized proppant crushing and deformation in reservoir condition and field scale.

Model ConfigurationIn the model Proppant pack and formation rocks were treated as poroelastic media. The poroelasticsimulations estimate 3D compaction related to fracture production by taking subsurface fluid with Darcy’slaw and coupling it to structural displacements with a stress-strain analysis. This model focused on elasticdisplacements brought on by changing fluid pressures when production begins. In order to evaluatefracture conductivity damage due to proppant deformation and crushing, the permeability and porositycubic law is utilized. The porosity change due to proppant deformation and crushing was reflected on thechange of proppant pack permeability. Proppant crushed zone was quantified by Mohr-coulomb failureindex. This coupled finite element model was verified by conductivity tests (Han, Wang, Puri, 2014).

Part of reservoir, which is the fractured area, was simulated. Fracture dimensions are about 500 ft. long,002 ft. wide and 90 ft. high (Fig. 2&3). The fracture was put inside a huge formation block, which is 10ft. wide, 600 ft. long and 100 ft. high (Fig. 3). The reason to simulate part of the reservoir rather thanwhole reservoir area was to save computation load because our research interests are mainly in fractureconductivity. This model can be further connected with production model. The stress loads fromoverburden rocks and in-situ stress were applied. The walls of the fracture can deform freely. The goalwas to solve for the changes in fluid pressure, stress, strain, and displacement of proppant packs due toproduction. Surface between fracture and matrix was set as deformable and permeable. Inputs for themodel are listed on table 1.

Both 2D and 3D views of model are shown in Figs 1 and 2. The fractured zones are meshed in to fineelements while the matrix zone are meshed into larger elements. Hydraulic fractures propagate perpen-dicularly to the minimum in-situ stress, as indicated in Fig.1.

Table 1—Variables for numerical model

Variable Units Description Expression

�m Fractional Porosity of Matrix block 1.00E-01

Cf 1/pa Compressibility of fluid (water) 4.40E-10

Cs 1/pa Compressibility of solid 4.16E�04

Km mD Permeability of matrix blocks 0.1

Kf mD Permeability of proppant pack 10E�05

C Fractional Ratio of �H/�hmin 1.50E�01

� Pa·s Viscosity 1.00E-03

�f lb/ft3 Fluid density 62.43

gradP Psi/ft Pressure gradient 5.00E-01

gradG Psi/ft Overburden stress gradient 9.50E-01

Pr Psi Reservoir Pressure 4.50E�03

Pw Psi Pressure at well bore 5.00E�02

�S lb/ft3 Matrix solids density 125

Vm Fractional Matrix solids Poisson’s ratio 2.20E-01

Bm GPa Matrix solids Bulk modulus 0.7

Gm GPa Matrix solids Shear modulus 4

�p lb/ft3 Proppant density 105

Ef Psi Proppant Young’s modulus 5.00E�06

vf Fractional Proppant Poisson’s ratio 2.50E-01

�f Fractional Porosity of fracture block 3.00E-01

BP GPa Proppant Bulk modulus 1

FCD Fractional Fracture dimensionless conductivity 100

GP GPa Proppant Shear modulus 12

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Figure 1—Top view of the model in 2D (plot in the right side is the geometry after meshing)

Figure 2—3-dimentional view of the model (plot in the right side is the geometry after meshing)

Figure 3—proppant deformation under different reservoir pressure (at t�8 mins)

SPE-171019-MS 3

Where:

(1)

(2)

(3)

Parametrical StudyIn this section, we will study proppant deformation and crushing under different reservoir pressure,flowing bottom hole pressure (FBHP), formation permeability, and proppant pack biot constant.

Effect of Reservoir PressureThe difference of reservoir pressures means the different reservoirs’ depth. Based on pressure gradient 0.5psi/ft and stress gradient 0.95 psi/ft, the reservoir pressure, and in-situ stress accordingly as Equations 1–3.The studied reservoir pressure were assigned from 2000 psi to 6000 psi. Five senarios with 1000 psireservoir pressure incremental were investigates as the following figure.

Figure 3 illustrates proppant pack deformation under five different reservoir pressure. As reservoirpressure increases, more displacement were observed from the simulated results. The results indicate that,large reservoir pressure would decrease more the propped fracture width. Especially for the near wellboreregion, the large difference between wellbore pressure and reservoir pressure can generate large netpressure acting on the proppants, resulting in large proppant deformation as illustrated. For the nearwellbore region, sinario with reservoir pressure of 6000 psi has 5 times more displacement than thereservoir pressure of 2000 psi. In the mean while in the fracture far from wellbore, only 3 times differencewas generated in the proppant pack displacement. These results emphasize the effect of net pressure onproppant deformation. Hence large difference between reservoir pressure and wellbore pressure can causelarge production volume, fast pressure drop in the fracture, and large net pressure on the proppant pack.

We conduct the same parametric study on proppant volumetric deformation. The simulated resultsshow the same trend. For the near wellbore region, Incremental of reservoir pressure from 2000 psi to6000 psi create roughly 5 times difference in volumetric strain, while for zones in fracture away fromwellbore, only less than 3 times difference in proppant pack is found. The net pressure cause a largevolumetric strain in the near wellbore region.

The reservoir pressure would affect the horizontal stress value. Larger reservoir pressure can causelarger horizontal stress based on the concept of the poroelastic medium. The high in-situ stress create moredeformation. It is important to use strong proppant for pressurized reservoir.

Effect of Flowing Bottom Hole PressureDifferent FBHP means different well’s operational conditions. In this parametric study, the wellboreFBHP various from 500 psi to 2000 psi, while the reservoir initial pressure remains at 4500 psi. Four caseswith 500 psi wellbore pressure incremental were built.

Figure 5 shows proppant pack displacement under different wellbore pressure. As wellbore pressuredecreases, more displacement were observed. Smaller wellbore pressure would further decrease thepropped fracture width. Especially for the near wellbore region, the large difference in wellbore pressureand reservoir pressure can create large net pressure acting on the proppants pack, resulting in largeproppant deformation. For the near wellbore region, from 2000 FBHP to 500 FBHP result in 1.3 timesdifference in displacement. In the fracture further from wellbore, no difference was found in the proppantpack displacement, because that of fluid differences in these four cases. These cases enhance ourconclusion on the net pressure effects on the deformation of proppant deformation.

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Parametric studies on proppant volumetric deformation are also examined. The simulated resultsdemonstrate the same result which is small wellbore pressure generate large proppant volumetricdeformation. For the near wellbore region, 1.4 times difference in volumetric strain was generatedcomparing cases with 500 FBHP and 2000 FBHP, while for the fracture far away from wellbore, almostnone difference in proppant pack volumetric deformation is found. The illustrated results point to theeffect of the net pressure on the proppant deformation.

The effects of different wellbore pressure on proppant crushing are also investigated. The proppantcrushing zone under different wellbore pressure are shown on the following Figure 7. Smaller FBHP causelarger the crushed proppant pack zone is. In other word, large chock size would generate large proppedfracture crushing zone. The bottom of the propped area has larger crushed zone than the zone of the upperpart is due to the distribution of the minimum horizontal pressure. The bottom part has larger minimumhorizontal stress than the upper part. Well with a small wellbore pressure will produce at a high production

Figure 4—Proppant pack volumetric strain under different reservoir condition (at t�8 mins)

Figure 5—proppant deformation under different FBHP (at t�8 mins)

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rate and have a large pressure drop which generating large net pressure on the proppant pack. The stresscondition on the proppant pack is investigated to check whether the proppant is under safe condition orcrushed according to the Mohr-coulomb failure criteria

Effect of Formation PermeabilityThree cases of formation permeability of 1 mD, 0.1 mD, and 0.01 mD are analyzed. The simulated resultsof different formation permeabilities are shown in Figure 8.

Figure 8 shows proppant pack displacement under formations of different permeability. As formationpermeability decreases, a higher displacement was observed. The results indicate that formation rockpermeability is inversely related to proppant pack deformation. Especially for the near wellbore region,the effects of formation rock permeability are more obvious. At the near wellbore region, the fracture fluid

Figure 6—Proppant volumetric strain under different well bore pressure (at t�8 mins)

Figure 7—Proppant crushing zone under different well bore pressure (crushed zone are highlighted in red)

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was firstly produced, and then formation fluid would flow into fracture to compensate the pressure dropbetween fracture and formation. When the formation rocks are permeable, the fluid would flow into thefracture easily and help the proppant pack to resist the formation rocks compaction. For the region farfrom wellbore, the fracture pressure was not changed in such a rapid period, and the formation fluid wasn’tflowing to the fracture yet. The formation permeability would affect the rate the fluid flowed from theformation to the fracture. When the formation is permeable, the formation fluid can flow into the fracturemore quickly and easily. The fluid pressure difference between formation and fracture would be small, andless deformation would be expected from the proppant pack.

Same conclusion would be drawn from the propapnt pack volumetric strain as shown in Figure 9.Proppant pack in more permeable formation rocks would have less volumetric strain. The fluid transportedfrom the formation rocks into the fracture would be beneficial for the proppant pack to resist the fractureplanner compaction. Also, the fluid diffusion between formation and fracture would help to balance thefluid pressure difference between formation and fracture.

Effect of Proppant Pack Biot ConstantsThe biot constant of proppant pack mainly depends on solids compressibility, and grain cementing. It isdefined as the following equation.

(4)

Where Kb is the drained bulk modulus of porous rock, and Kg is the bulk modulus of solid grains.represents solid rock without pores. No pressure influence. indicates extremely com-

pliant porous solid. Maximum pore pressure influence.From loosely consolidated sand formation to cemented solids pack, biot constant varies from 0.5 (dry

Fountainebleu sandstone) to 0.9 (dry Ottowa sand) (Zoback, 2007). In this parametric study, we sweepproppant pack biot constant from 0.5 to 0.9 to investigate various packed proppant deformation as thefollowing Figures 10 and 11.

Figure 8—Proppant deformation under different formation permeability (at t�8 mins)

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Figure 9—Volumetric strain under different formation permeability (at t�8 mins)

Figure 10—Deformation of proppant pack with different biot constant (at t�8 mins)

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From Figure 10 and 11, the deformation increases as the proppant pack biot constant increases. Thevalue of biot constant multiply the fluid pressure is the pressure that applied on the solids. The increasedbiot constant can be viewed as increased pressure being applied on the proppant grains which willcompress the solids. Due to the compression of the solids, the proppant pack will deform. Hence, theeffects of different biot constant are more obervious when they are under high pressure.

The effect of various biot constant on proppant crushing is also investigated. The results are demon-strated as the following figure 12.

The figure indicates that the incremental of proppant pack biot will enhance the safety of proppantpack. With high biot number, though solids are of large deformation, they are of less possibility ofcrushing. Due to the use of mohr-coulomb failure as the critera for proppant crushing, the fluid pressurebeing applied on the proppant solids is the minimum stress on the solids. The larger the fluid pressure is,the smaller the mohr circle is. As long as the mohr circle is away from the cretia, the proppant pack willbe safe.

Proppant Pack Damage Analysis PlotBased on the parametric study of the proposed proppant damage analysis numerical model, the sensitivityof some key parameters are investigated. In order to better utilized the methodology in to the field, wedeveloped a practical formalism, Proppant Pack Damage Analysis Plot (PPDA), to predict the potentialof proppant pack damage during field development. The PPDA is designed to integrate relatively simplegeomechanics with the physical state of a reservoir to predict whether proppant pack damage will happenwith time. One import aspect of this study is to analysis the stress condition of proppant pack during thedevelopment of the reservoir. For the settled proppant pack, the stress that being applied are the minimumin-situ stress, which is the �1 on the proppant pack, and the fluid pressure in the fracture, which is the �3

on the pack as Figure 12.

Figure 11—Volumetic strain of proppant pack with different biot constant (at t�8 mins)

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As the conducted parametric study, the potentialof proppant crushing is sensitive to the well borepressure and reservoir pressure. Without integratingthe reservoir parameters, the Mohr-Coulomb modelis difficult for field application. One important com-ponent of this analysis is the change in horizontalstress that related the pressure change during deple-tion. Poroelastic theory is often used for predictingthe changes in magnitude of stresses with depletion.For an isotropic, porous and elastic reservoir that islaterally extensive with respect to its thickness (20:1), the applicable relationship is as following (Segall and Fitzgerald, 1996):

Figure 12—Curshing zone of proppant pack with different biot constant

Figure 13—Mohr-Coulomb failure critaria

Figure 14—PPDA plot

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(5)

where v is Poisson’s ratio and � is the biot coefficient.With production occurs at a low FBHP, decrease of the fluid pressure in facture will decrease the

minimum stress applied on the proppant. The �hmin is also decrease due to the formation pressure decreasein a much slower speed due to its low permeability comparing with fracture. The mohr circle shift left andkeep increasing its area. Once the mohr circle reach the failure line, proppant pack crushing will occur.

The equation of mohr-coulomb failure criteria is , where � is the coefficient of frictionand C0 is the cohesion factor. As the key factor for the proppant pack damage analysis are the �hmin andpf, we want to reformulate the mohr-coulomb failure plot into a new plot with �hmin and pf as the axles.To quantify where the mohr circle reaches the failure envelop is to determine the length of mohr circleradius and distance between the failure line and circle center.

The mohr circle radius:

(6)

Figure 15—PPDA plot application

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The distance between mohr circle center and the failure criteria:

(7)

The coordinates of (x0, y0) are , then

(8)

Set D � Rmor

(9)

The slop of the line would be , and the intersection on the y axle would be as thefollowing figure.

To apply this PPDA plot to the proppant pack damage analysis, the very first step is to determine theinitial �hmin and initial reservoir pressure. The application of the PPDA is demonstrated as the followingcase (Figure 15).

Assume the cohesion factor is negligible, and friction coefficient is 0.6 (applicable for loss cementedsand). And the initial pressure of the sandstone reservoir is 5000 psi and �hmin is 8000 psi as followingfigure. The well initial condition is as point A (5000, 8000). If the well head pressure is set as 600 psi(point C) at the beginning of the well depletion, the link between A and B will cross the failure line, andproppant pack will fail. If the well head pressure is set to be around point B (2800, 8000), as the pressuredeplete, manipulate the well carefully to point D along the failure line without across. The well can besafely produced without breaking the settled proppant pack as the orange line. The time of manipulatingthe well chock would depends on the formation rock permeability, proppant biot constant etc. which arecan affecting the transmissibility of pressure diffusion.

ConclusionA comprehensive study of proppant deformation and crushing under different reservoir conditions isconducted. This research includes parametric studies using a coupled geomechanic and fluid flow model,and an anlytical method for proppant crushing identification. The major conclusions from this work areas follows:

● Largest deformation and highest possibility of crushing were observed near wellbore. Strongproppant was recommended at the last stage of slurry.

● Proppant crushing area is related to the wellbore production pressure. Small chock size isrecommended during wells’ early operation.

● A PPDA plot is developed to properly operate a well without breaking the proppant pack.

Future work can be done for further analysis of the proppant damage phenomenon. Fracture is acomplex system involved with stress, fluid pressure, chemicals, and temperature. Numerical modelingwith the consideration of coupling chemical reaction, fluid transportation, and stress reorientation wouldbe a good approximation of the fracture in the reservoir.

Nonmenclature

�ob, overburden stress, psi.gradG, stress gradient, psi/ft.H, depth, ft.�, biot constant.pr, reservoir pressure, psi.�hmin, minimum insitu stress, psi

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v, poission ratio.�H, maximum insitu stress, psiKb, drained bulk modulus of porous rock, GpaKg, the bulk modulus of solid grains, Gpa�Sh, change of the horizontal insitu stress, psi�Pp, change of the pore pressure, psi�, the coefficient of frictionC0, the cohesion factor.Rmor, radius of mohr circleD, distance between mohr circle center and failure cretariaPf, fluid pressure, psi

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