Simulation of Gel Filter-Cake Formation, Gel Cleanup, and ... - OnePetro

Simulation of Gel Filter-Cake Formation, Gel Cleanup, and Post-Fracture Well Performance in Hydraulically Fractured Gas Wells Sarinya Charoenwongsa, Hossein Kazemi, Perapon Fakcharoenphol, and Jennifer L. Miskimins, Colorado School of Mines

Summary Polymer and gel damage is a major issue in the cleanup of hydraulically fractured gas wells. This paper addresses the issue by using a gas/water flow model that simulates fracture propagation with gel filter cake-formation as mechanical trapping of polymer molecules on the fracture face and filtrate transport into the adjacent matrix. The model accounts for polymer as a chemical component. This approach is different than treating polymer as a highly viscous gel phase, which is the common method in most literature. In this model, the gel filter-cake thickness is calculated on the basis of experimental data. For leakoff, the model allows only the sheared polymer molecules, which are the major cause of formation permeability reduction, to cross the fracture face into the formation and adsorb on the matrix. Other features of the model include water blockage, non-Newtonian flow, non-Darcy flow, and proppant and reservoir compaction. Introduction Research to date has identified various contributing mechanisms that might cause slow cleanup and the associated underestimated productivity of hydraulically fractured gas wells. These mechanisms include water blockage, gel filter-cake formation, unbroken gel residue, viscous fingering, clay swelling, fines migration, proppant compaction, crushing, and embedment. Many laboratory experiments have been conducted to quantify the effects of these individual mechanisms on formation and fracture damage. Several numerical studies have been performed to evaluate cleanup and productivity of hydraulically fractured gas wells. However, the reliability of the published literature’s conclusions remains questionable in some cases because of assumptions, underlying physics, and unrealistic model input data. A comprehensive literature review of damage mechanisms, experimental studies, field observations, and numerical models is presented by Charoenwongsa (2011). Mathematical Formulation To simulate the physical processes occurring in hydraulic fracture creation, cleanup, and production performance, a fracture-propagation model developed by Charoenwongsa (2011) is used (Appendix A). Eqs. 1 through 3 are the governing flow equations used to describe the physical phenomena controlling fluid flow in the reservoir and the hydraulic fracture from the injection through the production periods. Gas saturation equation: v g þ qg q^g ¼ r qg~

@ ½/qg Sg ð1 r ~ u Þ . . . . . . . . . . ð1Þ @t

C 2013 Society of Petroleum Engineers Copyright V

This paper (SPE 150104) was accepted for presentation at the SPE International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 15–17 February 2012, and revised for publication. Original manuscript received for review 30 December 2011. Revised manuscript received for review 4 December 2012. Paper peer approved 16 January 2013.

August 2013 SPE Production & Operations

Water saturation equation: r qw~ v w þ qw q^w ¼

@ ½/qw Sw ð1 r ~ u Þ . . . . . . . . .ð2Þ @t

Polymer concentration equation: v w Cpoly Þ þ qw q^w Cpoly r ðqw~ @ ¼ f½/qw Sw Cpoly ð1 r ~ u Þ þ ð1 /Þqs ag @t

. . . . . . . ð3Þ

Rock displacement equation: u þ ðG þ kÞrðr ~ uÞ Gr2~ ¼ ap frpg ð fw cw þ fg cg ÞrD fw rpcwg g:

. . . . . . . ð4Þ

Eqs. 1 through 3 are used in the reservoir and hydraulic fractureflow modeling components. The solutions to this set of fluid-flow equations give pressure, fluid saturations, and polymer concentrations. Eq. 4 is the rock-mechanics component of the governing equation. Refer to Charoenwongsa (2011) for the detailed mathematical formulation of the fracture-propagation and coupled geomechanics-flow models. Polymer and Gel Damage In this study, polymer in the fracturing fluid is accounted for as a chemical component in the aqueous phase. This approach is different than treating polymer as a highly viscous gel phase (Voneiff et al. 1996; May et al. 1997; Friedel 2004; Friedel et al. 2007; Wang 2008; and Barati et al. 2009). In the following sections, the numerical modeling of polymer and gel damage and the data requirement are discussed. Gel Filter-Cake Formation. A gel filter cake is formed on the fracture face as a result of mechanical trapping of a large fraction of polymer molecules on the fracture face during the leakoff process. During this period, the polymer molecules pass partially through the fracture-matrix interface and are sheared into smaller broken-up molecules. A portion of the polymer molecules remains at the original polymer concentration in the fracture void space, while some polymer molecules are mechanically trapped and left behind, gradually forming the gel filter cake on the fracture face as shown in Fig. 1. The thickness of the gel filter cake (lcake ) is calculated from lcake ¼

^ gel M ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð5Þ qgel Cgel

where qgel and Cgel are the density and polymer concentration of the gel filter cake, respectively. The two parameters can be experi^ gel is the mass of polymer retained at the mentally measured. M ^ gel can be fracture face per unit area. For fracture segment i, M estimated from 235

where Unsheared polymer molecules

Proppant (a)

Sheared polymer molecules

Leakoff

(b) Adsorbed polymer molecules on rock matrix

Retained polymer molecules on fracture face (c)

Fig. 1—Schematic of polymer and gel damage created during leakoff. (a) Fracture open during injection; (b) fluid leakoff, gel filter cake formation, and polymer adsorption; (c) fracture closed and proppant pack partially filled by gel filter cake [modified from Cooke Jr. (1975)].

0

1

N X

v qw sw;m=f Cpoly Dt C B C B n¼0 C ; . . . . . . . . . . . . . . ð6Þ B ^ M gel;i ¼ B C DxDz A @

/cake ¼ f

Vf Vprop Vcake : . . . . . . . . . . . . . . . . . . . . ð9Þ Vf

are the permeability and porosity of a propped kfcake and /cake f fracture in the presence of gel filter cake, respectively. kf0 and /0f are the permeability and porosity of proppant pack in the absence of gel filter cake, respectively. Vf , Vprop ; and Vcake are volumes of the fracture, proppant, and gel filter cake, respectively. Laboratory experiments indicate that a large portion of polymer residue is not displaced from the fracture by production and degrades slowly (Cooke Jr 1975). Only a small amount of polymer residue could be displaced from a hydraulic fracture at extremely high pressure gradients (e.g., 100 psi/ft with gas flow). On the basis of these observations, the permeability reduction caused by gel filter cake is assumed to be permanent in this study. The effect of the breaker can be modeled by including additional equations to account for the transport of breaker and the breaker kinetic model. This is considered as a future research area. Non-Newtonian Flow. Polymer-based fracturing fluid exhibits non-Newtonian flow behavior. Its apparent viscosity depends on the shear stress to which fluid is exposed (Economides and Nolte 2000). In this study, the power-law model is used to capture the non-Newtonian flow behavior of a polymer solution by an apparent viscosity (Friedel 2004). This apparent viscosity reflects the equivalent viscosity of a non-Newtonian fluid moving at the same velocity as its Newtonian fluid counterpart. Because the polymer in the fracturing fluid is treated as a chemical component in the aqueous phase, the equivalent viscosity of the pump-in polymer solution is calculated from Eq. 10.

i

where v is a mechanical retention factor, defined as the ratio of the amount of polymer in the gel filter cake and the amount of injected polymer. This parameter can be experimentally measured. Dt is timestep size, DxDz is fracture face area of fracture segment i, and N is the total number of timesteps from injection to shut-in. sw;m=f is the rate of fluid loss into the formation, which can be computed from a leakoff coefficient (during injection) and from fluid transmissibility mass-transfer function (during shut-in). It should be noted that at the end of pumping, the conventional leakoff function is replaced by the mass-transfer function. Additionally, the flowrate is adjusted to make the rate of fluid loss a continuous function when transitioning from injection to shut-in. In the paper, the normal leakoff formulation is used for simplicity and convenience. However, if the correlation between leakoff coefficient and pressure difference is known for a given reservoir, the pressure-dependent leakoff coefficient can be included in the simulation code. For instance, a simple equation such as Eq. 7 can be used. pf pm CL@lab p ; . . . . . . . . . . . . . . . . . . . ð7Þ CL@pf ¼ Dplab where CL is the overall leakoff coefficient, pf is the computed fracture pressure, pm is the computed matrix pressure, and Dplab is the pressure difference across the core from the leakoff laboratory experiments. A similar equation can be used when the matrix contains microfractures. Assuming that the presence of a gel filter cake reduces the fracture permeability by the loss of porosity, the volume of the gel filter cake can be related to the volume blockage that causes damage to the propped fracture. According to the Kozeny equation (Cooke Jr 1975), a reduction of permeability by porosity blockage as a result of the gel filter cake is defined as kfcake

236

¼

kf0

/cake f /0f

!5 ; . . . . . . . . . . . . . . . . . . . . . . . . . ð8Þ

eff leqv poly ¼ lpoly ½ðrpw cw rDÞ

n0 1 n0

; . . . . . . . . . . . . . . ð10Þ

where leff poly ¼

0 1n0 K0 3 n 9 þ 0 ½721/ðSw Swr Þkkrw 2 : . . . . . . ð11Þ n 12

eff leqv poly and lpoly are the equivalent and effective viscosities of the fracturing fluid, repectively. n0 is the flow behavior index, K 0 is the flow consistency index, and 1 is tortuosity. Here, the power-law model is selected because it is well received by the fracturing service industry to describe the nonNewtonian characteristics of the fracturing fluids. There are significant experimental data of power-law fluid parameters (i.e., K 0 and n0 ) available for a specific fracturing fluid at different conditions. Note that in Eq. 11, k; krw ; / can be properties of either the propped fracture or the reservoir, because this study considers that polymer molecules can exist in both porous media. The equivalent viscosity of the water phase in the presence of polymer (leqv w ) can be approximated from: Cpoly Cpoly eqv l l ; . . . . ð12Þ ¼ þ 1 leqv w Cpoly;inj poly;sheared Cpoly;inj fw

where leqv poly;sheared is the equivalent viscosity of the filtrate containing fragments of the sheared polymer. This parameter can be experimentally measured at the polymer concentration of the pump-in fracturing fluid, lfw is the viscosity of the formation water, Cpoly is the calculated polymer concentration of either the fracturing fluid in the hydraulic fracture or filtrate in the matrix concentration of the pump-in fracturand Cpoly;inj is the polymer Cpoly is very small, providing much less ing fluid. Note that Cpoly;inj Cpoly . For example, from the calculacontribution than 1 Cpoly;inj tion at the very beginning of production, Cpoly in the matrix adjacent to the fracture is only 20 ppm, and Cpoly;inj is 4,200 ppm. This August 2013 SPE Production & Operations

1.0 1

day

Fractional Retained 0 Matrix Permeability, kad /k (–) m m

Adsorbed Polymer, a (μg/grock)

1000 800 0.5

600

400

day

ay

d 0.1 200 0

0.8

0.6

0.4

0.2

0.0 0

400 100 200 300 Polymer Concentration, Cpoly (ppm)

500

0

(a)

400 100 200 300 Adsorbed Polymer, μg/grock

500

(b)

Fig. 2—Examples of experimental data needed for polymer adsorption modeling. (a) Kinetic Langmuir adsorption isotherm of the polymer; (b) retained matrix permeability as a function of adsorbed polymer amount.

Cpoly ¼ 0:0048; making the first term of the right Cpoly;inj side of Eq.12 insignificant compared with the second term of the right side of Eq.12. If one can determine experimentally sheared and unsheared concentration after passing through the filter cake, the following equation can be used to compute the equivalent viscosity of the water phase in the presence of the polymer: means that

leqv w ¼

Cpoly;unsheared eqv lpoly;unsheared Cpoly;inj Cpoly;sheared eqv lpoly;sheared þ Cpoly;inj Cpoly;unsheared Cpoly;sheared lfw ; þ 1 Cpoly;inj Cpoly;inj

. . . . . ð13Þ

where leqv poly;unsheared is the equivalent viscosity of the fracturing fluid containing fragments of the unsheared polymer. Polymer Adsorption. During leakoff, the model allows a small portion of the sheared polymer molecules to cross the fracture face into the formation on the basis of experimental leakoff data. Knowing the transport of sheared polymer molecules, the effect of adsorption of the filtrate polymer on the rock matrix can be accounted for through the loss of formation permeability. In this study, the equilibrium Langmuir model is used to model the retention of the sheared polymer on the surface of the formation rock as a function of polymer concentration of the filtrate (Marczewski 2010).

Fracture face

ad km1

kcake

lcake

Fig. 3—Fracture-face damage from polymer adsorption. Gel filter cake can be captured in the model if polymer adsorption and gel filter cake data are available. August 2013 SPE Production & Operations

ja Cpoly amax ; . . . . . . . . . . . . . . . . . . . . . . . . . . ð14Þ ja Cpoly þ 1

where a is the mass of adsorbed polymer per mass of rock, amax is the adsorption capacity, and ja is the adsorption rate coefficient. Here, the equilibrium Langmuir model is used because of its simplicity and the difficulty in obtaining kinetic, nonequilibrium experimental data (Fig. 2). If such data are available, the adsorption of polymer on the rock surface can be modeled by including the kinetic equations in the simulation code. A nonequilibrium polymer adsorption should be considered as a future research area. The effect of shut in time on production is related to the capillary-gravity segregation issue, not the time-dependent nonequilibrium polymer adsorption. This is consistent with the modeling and field observations reported in Cheng (2012). The loss of the formation permeability caused by polymer adsorption can be expressed as kmad ¼ km0 expðwaÞ; . . . . . . . . . . . . . . . . . . . . . . . . .ð15Þ where kmad and km0 are permeabilities of the formation in the presence and absence of adsorbed polymer, respectively. w is an empirical constant. Fig. 2 shows examples of adsorption isotherms and retained matrix permeability, which can be determined from laboratory experiments. Reduction in Fracture-Face Permeability. Gel filter cake and polymer adsorption also affect the flow at the fracture face (Fig. 3). If the permeability of the gel filter cake and the loss of formation permeability are determined from laboratory experiments, the retained permeability at the matrix-fracture interface as a result of polymer and gel damage can be estimated using the harmonicaveraging technique, as shown in Eq. 16. Dym1 lcake 1 adþcake ¼ ðDym1 þ lcake Þ þ ; . . . . . . . . ð16Þ km1 ad kcake km1

Matrix-tofracture flow Δ ym1

a¼

adþcake where km1 is the retained permeability at the matrix/fracture interface as a result of polymer adsorption and gel filter cake, Dym1 is the grid size in the y-direction of the matrix node adjacent ad is to the fracture node, lcake is the thickness of gel filter cake, km1 the retained permeability at the matrix/fracture interface as a result of polymer adsorption, and kcake is the permeability of the gel filter cake. In summary, to simulate the effects of gel filter-cake formation and polymer adsorption on cleanup and post-fracture performance

237

1,320 ft Well

Matrix 50 ft

Drainage area Fra

x

50

z y

Well re

ctu

0f t

1,320 ft

Fig. 4—Schematic of a quarter of the fluid-flow model of the hydraulically fractured well system. The vertical well is located at the center of the gas reservoir intersected by the vertical hydraulic fracture running along part of the northwest face.

of a hydraulically fractured gas well, additional experimental data are needed. These data include: Density of the gel in the filter cake (qgel ) Concentration of the polymer in the gel filter cake (Cgel ) Gel filter-cake mechanical retention factor (v) Permeability of the gel filter cake (kcake ) Amount of adsorbed polymer on the rock matrix ðaÞ as a function of polymer concentration ðCpoly Þ of the filtrate and exposure time (texp ) ad km as a function of the Retained matrix permeability km0 adsorbed polymerðaÞ Note that these data strongly depend on the surface characteristics of the formation, temperature, type, and amount of polymer added to the fracturing fluids. Example Results: Polymer and Gel Damage From Crosslinked Fluid The numerical modeling of the hydraulically fractured well system is performed on a quarter of the rectangular reservoir with a vertical well at the center and a symmetrical vertical fracture with two wings (Fig. 4). The results are then scaled up to obtain the performance of the whole system. The grid refinement in the x and y directions is applied according to the algorithm proposed by Bennett et al. (1986). The resulting lateral grid size is adjusted to capture the capillary end effect at the fracture face. This method is used because the modeling of this end effect can only be achieved if the proper scaling and rock features are accounted for to represent the interaction of capillary and viscous forces (Pusch et al. 2004). Simulation Cases. Five simulation cases are designed to investigate the effects of polymer and gel damage on cleanup and postfracture well performance following a crosslinked fluid treatment. Table 1 presents the simulation cases. Case 1 is the base case, which considers the combined effects of multiphase flow, capillary end, non-Darcy flow, proppant compaction, and reservoir compaction. For interpretation purpose, Cases 2 through 4 isolate the effects of gel filter-cake formation

on the fracture face, polymer adsorption on the formation rock surface, and non-Newtonian flow of polymer, respectively. Case 5 represents the combined effects of gel filter cake, polymer adsorption, and non-Newtonian flow of polymer. Input data for these cases are provided in Table 2. Reservoir Properties. The reservoir rock is assumed to be an isotropic and homogeneous sandstone with uniform permeability and porosity at initial conditions. The properties of the reservoir rock are based on typical tight sandstone reservoirs in the US (Voneiff et al. 1992). The properties of reservoir fluids are calculated from existing correlations (McCain Jr. 1990; Lee and Wattenbarger 1996). Rock-Fluid Interactions. Water-gas relative permeability and water-gas capillary pressure curves are represented in Fig. 5. These multiphase functions are derived on the basis of experimental results (Ward and Morrow 1987; STIM-LAB 2005a; Ionescu et al. 2006; Bazin et al. 2008). Leakoff. The leakoff coefficient used as the input data for the simulation is from the leakoff data of 40 ppt-guar with breaker (7.5 ppt Viconþ0.5gpt CAT3þ0.1 gpt CAT8) (STIM-LAB 2005b). The data are presented in Appendix B, where it can be seen that the leakoff profiles of different fracturing fluids are essentially a linear function of the square root of time. Treatment Schedule and Fracturing Materials. Each reservoir is different and requires a hydraulic fracturing design tailored to the particular conditions of the formation. In this study, a small fracture treatment is considered sufficient to provide further understanding of damage and cleanup mechanisms in the hydraulically fractured reservoir system. A commercial fracturedesign simulator is used to guide the design of the treatment schedule as well as the selection of fracturing materials. Table 2 shows the types of fracturing fluid and proppant, and Fig. 6a shows the pumping-treatment schedule. Polymer and Gel Damage. Input data for modeling polymer adsorption, gel filter-cake formation, and non-Newtonian flow are presented in Fig. 7 and Tables 3 and 4. Additional Data. Input data for modeling water blockage, non-Darcy flow, and proppant and reservoir compaction are provided by Charoenwongsa (2011).

TABLE 1—SIMULATION CASES Case

Case Description

Features

Legend (Fig. 8)

1 2 3 4 5

Water-only leakoff Gel filter cake Polymer adsorption Non-Newtonian flow Polymer and gel damage

MPþCEþNDþPCþRC MPþCEþNDþPCþRCþPD (cake) MPþCEþNDþPCþRCþPD (ad) MPþCEþNDþPCþRCþPD (nn) MPþCEþNDþPCþRCþPD (all)

MPþCEþNDþPCþRC Case 1þPD (cake) Case 1þPD (ad) Case 1þPD (nn) Case 1þPD (all)

Key: MP ¼ multiphase flow effect, CE ¼ capillary end effect, ND ¼ non-Darcy flow effect (in the hydraulic fracture, reservoir and at the wellbore), PC ¼ proppant compaction, RC ¼ reservoir compaction, PD (cake) ¼ polymer damage from gel filter cake, PD (ad) ¼ polymer damage from polymer adsorption, PD (nn) ¼ polymer damage from non-Newtonian flow, and PD (all)¼ polymer damage from gel filter cake, polymer adsorption, and non-Newtonian flow.

238


TABLE 2—INPUT DATA FOR SIMULATION

0.65 200,000 Fig. 5a Fig. 5b Fig. 5c 0

0.8 0.6 0.4 krg krw

0.0 0.0

0.2 0.4 0.6 0.8 Water Saturation, Sw (–) (a)

1.0

1.0 Capillary Pressure, pcwg (psi)

1.0

0.2

Fracture Propagation and Leakoff Data Closure stress or minimum horizontal stress (psi) Fracturing pressure (psi) Leakoff coefficient (ft/min0.5) Fracturing Fluid Data Crosslinked fluid–35 pptg crosslinked gelled water Polymer concentration of crosslinked fluid (ppm) Fracture and Proppant Data Dimensionless fracture conductivity (FCD) Fracture half-length (ft) Proppant size/type Propped fracture porosity (–) Propped fracture permeability (md) Injection Data Treatment schedule Shut-in Data Shut-in time (day) Production Data Production time (day) Bottomhole pressure

8,000 50 3,600 150 0.08 0.05 0.45 3.0E–06 170 7.3Eþ06 0.15

Relative Permeability, krw or krg (–)

Relative Permeability, krw or krg (–)

Reservoir Data Reservoir depth (ft) Reservoir thickness (ft) Initial reservoir pressure (psi) Reservoir temperature (F) Initial reservoir porosity (–) Initial reservoir permeability (md) Initial water saturation (–) Pore compressibility (psi–1) Rock density (lbm/ft3) Young’s modulus (psi) Poisson’s ratio (–) Formation Fluid Data Specific gravity of gas (–) Salinity of water (ppm) Rock-Fluid Interaction Data Matrix relative permeability Fracture relative permeability Matrix capillary pressure Fracture capillary pressure (psi)

krg

0.8

krw 0.6 0.4 0.2 0.0 0.0

0.2 0.4 0.6 0.8 Water Saturation, Sw (–) (b)

1.0

1400

4,377 4,577 0.0013

4,200 > 10 500 20/40 Brady sand 0.3 311,000 Fig. 6a 1 200 Fig. 6b

km = 0.0005 md km = 0.005 md km = 0.05 md

1200 1000 800 600 400 200 0 0.4

0.5 0.6 0.7 0.8 0.9 Water Saturation, Sw (–) (c)

Fig. 5—(a) Matrix relative permeability, (b) fracture relative permeability, and (c) matrix capillary pressure curves.

30 2.0 1.5

20

1.0 10 0.5

Bottomhole Pressure, psia

2.5

Fracturing Fluid Rate, bpm

Proppant Concentration, ppg

5000

40

3.0

4000

3000

2000

1000

km = 0.05 md 0

0.0 0.0

7.5 2.5 5.0 Injection Time, min (a)

10.0

0 10–2

100 Time, day (b)

102

Fig. 6—(a) Treatment schedule and (b) post-fracture bottomhole pressure. August 2013 SPE Production & Operations

239

25 20 15 10 5 0

0

100 200 300 400 500 600 700 800 900 1000 Polymer Concentration, Cpoly (ppm) (a)

0 Fractional Retained Matrix Permeability, kad m /km (–)

Adsorbed Polymer, a (μg/grock)

30

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

100 200 300 400 500 600 700 800 900 1000 Adsorbed Polymer, a (μg/grock) (b)

Fig. 7—Input data for modeling polymer adsorption. (a) Equilibrium Langmuir adsorption isotherm of the polymer; (b) retained matrix permeability as a function of adsorbed polymer amount. Because of a lack of laboratory data, these data are assumed.

In Table 3, the permeability of the gel filter cake is based on the core analysis of Frontier formations damaged from gel filter cake (Voneiff et al. 1996). This experimental study indicates that fracture-face damage from gel filter cake causes a thin damaged zone with a permeability one-tenth to one-hundredth of the formation permeability. In addition, polymer concentration of gel in the filter cake is based on leakoff experiments (STIM-LAB 2003). From this study, a polymer concentration of leakoff gel of 250 pptg (approximately 30,000 ppm) is measured for a crosslinked 35 lbm CMHPG þ Zr gel system. Because of a lack of data, the density of gel in the filter cake and the mechanical retention factor are assumed. Simulation Results. The simulation results of Cases 1 through 5 are presented in Fig. 8. Gas, water, and polymer production rates, as well as cumulative totals, are provided. Gel Filter Cake. The effect of gel filter cake on cleanup and post-fracture well performance after a crosslinked fluid treatment is studied by comparing the results of Case 2 (represented by red dashed lines in Fig. 8) with those of Case 1 (represented by blue solid lines in Fig. 8). From these figures, it can be seen that gel filter cake decreases gas rate over the entire production period and reduces cumulative gas production. However, gel filter cake has an insignificant impact on water and polymer production. The time evolution of crosslinked-gel filter-cake formation is presented in Fig. 9. It can be seen from Fig. 9a that the thickness of the gel filter cake increases continuously with time, with a thicker layer at the wellbore. From Fig. 9b, the gel filter cake formed on the fracture wall near the wellbore occupies approximately one-half of the average fracture width. Polymer Adsorption. The effect of polymer adsorption on cleanup and post-fracture well performance after a crosslinked fluid treatment is studied by comparing the results of Case 3 (represented by green dotted lines in Fig. 8) with the results of Case 1 (represented by blue solid lines in Fig. 8). From these figures, it can be seen that polymer adsorption has an insignificant impact on production of gas, water, and polymer. The influence of polymer adsorption on the retained matrix permeability is also pre-

sented in Fig. 10. From this figure, it can be seen that the polymer adsorption reduces the original permeability of the reservoir adjacent to the fracture face by up to 8%. However, a large area of the reservoir remains unaffected after 200 days of production. Non-Newtonian Flow. To study the effect of non-Newtonian flow behavior of crosslinked fluid on cleanup and post-fracture well performance after a fracturing treatment, the results of Case 4 (represented by purple dash-dot lines in Fig. 8) and Case 1 (represented by blue solid lines in Fig. 8) are compared. From these figures, it can be seen that non-Newtonian flow behavior has a slight negative impact on gas production but has a significant negative impact on water and polymer production. From Figs. 8a and 8b, it can be observed that non-Newtonian flow behavior delays gas breakthrough time and reduces gas rate for the first 100 days of production. After that period, the effect of non-Newtonian flow on gas rate reduction disappears, as indicated by the collapse of the gas rate with that of Case 1 (without any polymer damage). From Figs. 8c through 8f, it can be seen that non-Newtonian flow behavior significantly reduces rates and cumulative production of water and polymer. Combined Effects. To study the effects of polymer and gel damage on cleanup and post-fracture well performance after a crosslinked fluid treatment, the results of Case 5 (represented by orange solid lines in Fig. 8) are compared with those of Case 1 (represented by in blue solid lines in Fig. 8). From these figures, it can be seen that polymer and gel damage from crosslinked fluid reduces cumulative production of gas by approximately 20%. Cumulative water and polymer are also reduced significantly. Discussion of Simulation Results. A crosslinked fluid treatment creates severe flow impairment. Because of low leakoff and high polymer concentration, crosslinked fluid creates a thick gel filtercake layer (Fig. 9) and a large amount of adsorbed polymer on the rock matrix (Fig. 10). If gel filter cake and adsorbed polymer are not removed, deliverability will remain impaired (Fig. 8). In addition, non-Newtonian flow behavior causes slow cleanup of highly viscous fluid during early production, resulting in delayed gas breakthrough time and reduced water and polymer returns. The effect of non-Newtonian flow gradually disappears when crosslinked fluid in the fracture is cleaned up. In the course of this study, this effect lasts for approximately 100 days of production.

TABLE 3—GEL FILTER-CAKE DATA Density (lbm/ft3) Polymer concentration (ppm) Mechanical retention factor (–) Permeability (md)

240

64.4 30,000 0.3 0.01 km

TABLE 4—NON-NEWTONIAN PARAMETERS Flow consistency index (lbf.sn/ft2) Flow behavior index (–)

3.40E–03 0.8


900 Gas Production Rate, Mscf/D

800 700 600 500 400 300 MP+CE+ND+PC+RC Case 1+PD (cake) Case 1+PD (ad) Case 1+PD (nn) Case 1+PD (all)

200 100 0 10–2

10–1

100 101 102 Production Time, day (a)

Cumulative Gas Production, MMscf

100

70 60 50 40 30

10 0

20

40

60 80 100 120 140 160 180 200 Production Time, day (b)

60 50 40 30

80 70 60 50 40 30

20

20

10

10 10–1

100 101 102 Production Time, day (c)

MP+CE+ND+PC+RC Case 1+PD (cake) Case 1+PD (ad) Case 1+PD (nn) Case 1+PD (all)

90 Water Recovery, %

70

0 10–2

MP+CE+ND+PC+RC Case 1+PD (cake) Case 1+PD (ad) Case 1+PD (nn) Case 1+PD (all)

20

100 MP+CE+ND+PC+RC Case 1+PD (cake) Case 1+PD (ad) Case 1+PD (nn) Case 1+PD (all)

80 Water Production Rate, B/D

80

0

103

90

103

0

140

20

40

60 80 100 120 140 160 180 200 Production Time, day (d)

50 Case 1+PD (cake) Case 1+PD (ad) Case 1+PD (nn) Case 1+PD (all)

120 100 80 60 40

Case 1+PD (cake) Case 1+PD (ad) Case 1+PD (nn) Case 1+PD (all)

45 40 Polymer Recovery, %

Polymer Production Rate, lbm/D

90

35 30 25 20 15 10

20 0 10–2

5 10–1

100 101 102 Production Time, day (e)

103

0 0

20

40

60 80 100 120 140 160 180 200 Production Time, day (f)

Fig. 8—Effects of polymer and gel damage on cleanup and post-fracture well performance after a crosslinked fluid treatment for a 0.05-md-reservoir (a) gas rate, (b) cumulative gas production, (c) water rate, (d) water recovery, (e) polymer rate, and (f) polymer recovery. The combined effects of gel filter cake, polymer adsorption, and non-Newtonian flow behavior of crosslinked fluid significantly reduce rates and cumulative production of gas, water, and polymer.

Even though the effects of various mechanisms affecting cleanup and post-fracture well performance are often discussed separately, it is to be noted that these mechanisms do not occur independently. In fact, they tend to mutually affect each other. For instance, when considering both non-Newtonian flow and polymer adsorption, the latter reduces the effect of non-Newtonian flow behavior because of polymer concentration reduction as a result of polymer adsorption (Fig. 8). Thus, to determine a realistic production forecast from a hydraulically fractured gas well, these mechanisms must be taken into account simultaneously. As August 2013 SPE Production & Operations

shown in Fig. 8, the overall effect is less than the sum of the individual effects. Conclusions In this study, a hydraulic fracture propagation-flow model is developed to simulate the physical processes occurring during the fracture creation, cleanup, and production time frames. The model is used to investigate the effects of polymer and gel damage on cleanup and post-fracture well performance. It is found that 241

0.020

0.5 Injection

End of Shut-i

n

Shut-in

Production

0.4

0.015

km = 0.05 md Width, in.

Gel Filter Cake Thickness, in.

km = 0.05 md

0.010

0.005

End of Inject

ion

0.3

0.2 Average Fracture Width

0.1 Minimum Fracture Width

Gel Filter Cake Width

0.000 0

400 100 200 300 Distance X From Wellbore, ft (a)

500

0.0 1E–3

0.01

1 0.1 Time, day (b)

10

100

Fig. 9—Time evolution of crosslinked-gel filter-cake formation (Case 2). (a) Gel filter cake thickness along the fracture; (b) maximum gel filter-cake width (at the wellbore) and fracture width. The thickness of the gel filter cake increases continuously with time, with a thicker layer at the wellbore (Fig. 9a). At the end of shut-in, the gel filter cake at the wellbore occupies almost one-half of the average fracture width (Fig. 9b).

polymer and gel damage from crosslinked fluid reduces cumulative production of gas by approximately 20% for a reservoir permeability of 0.05 md. Cumulative water and polymer are also reduced significantly. On the basis of the results of this study, it is recommended to conduct additional laboratory experiments to determine the following: 1. Hysteresis of relative permeability and capillary pressure in tight gas formations. 2. Gel filter-cake mechanical retention and permeability of gel filter cake. 3. Polymer adsorption and retained matrix permeability. These laboratory data will provide additional insight into polymer and gel damage mechanisms in hydraulic fracturing stimulations. Specifically, hysteresis is the result of fluid trapping when the flow direction is reversed, for instance, going from injection of the filtrate into the formation as compared to the production of the filtrate. Next, measuring the gel filter-cake mechanical retention factor and permeability of the gel filter cake is an important issue, because these data would allow calculation of the gel filter cake thickness and skin damage on the fracture face. Finally, for more accurate modeling, one should know the effect of polymer km 0 km

103

1

Distance Y From Fracture, ft

0.99 0.98

102

0.97 0.96

101

0.95 0.94

100

0.93 0.92 200 400 600 800 1000 1200 Distance X From Wellbore, ft

Fig. 10—Effect of adsorption of crosslinked polymer (Case 3) on retained matrix permeability after 200 days of production. Polymer adsorption reduces the original permeability of the reservoir adjacent to the fracture face by up to 8%. However, a large area of the reservoir remains unaffected (km /k0m)51. 242

retention on formation-permeability reduction and the viscosity of sheared polymer filtrate. Nomenclature a ¼ mass of polymer adsorbed on the surface of the rock per unit mass of rock amax ¼ adsorption capacity Af ¼ face area of a single wing of the hydraulic fracture, L2 C ¼ polymer concentration in gel filter cake or fracturing fluid (Cgel in mass of polymer per unit mass of cake, Cpoly in mass of polymer per unit mass of fluid) CL ¼ overall leakoff coefficient, L/t0.5 D ¼ depth measured from the datum point, L f ¼ fractional flow FCD ¼ dimensionless fracture conductivity G ¼ shear modulus of rock, M/(Lt2) hf ¼ fracture height, L k ¼ permeability of porous media, L2 krg ¼ relative permeability of gas phase krw ¼ relative permeability of water phase K 0 ¼ flow consistency index, Mtn–2 /L lcake ¼ thickness of the gel filter cake, L Lf ¼ fracture half-length, L ^ gel ¼ mass of polymer retained at the fracture-matrix M interface per unit area, M/L2 0 n ¼ flow behavior index N ¼ total number of timesteps from injection to shut-in p ¼ pressure, M/(Lt2) pcwg ¼ water/gas capillary pressure, M/(Lt2) q^ ¼ fluid source and sink of the well per volume of gridblock, 1/t S ¼ fluid saturation t ¼ time, t texp ¼ exposure time, t ~ u ¼ rock displacement vector ~ v ¼ superficial velocity vector V ¼ volume, L3 wf ;max ¼ maximum total fracture width, L w f ¼ average total fracture width, L x ¼ distance in the x direction, L y ¼ distance in the y direction, L z ¼ distance in the z direction, L ap ¼ Biot’s poroelastic constant or effective stress coefficient Dt ¼ timestep size, t Dx ¼ spatial step size in the x direction, L August 2013 SPE Production & Operations

Dy Dz c 1 ja k l leff leqv n

¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

q¼ rh;min ¼ sw;m=f ¼ t / v w r r @=@t

¼ ¼ ¼ ¼ ¼ ¼ ¼

Subscripts ad ¼ cake ¼ f¼ fw ¼ g¼ gel ¼ i¼ inj ¼ j¼ k¼ m¼ m1 ¼ poly ¼ prop ¼ s¼ sheared ¼ unsheared ¼ w¼ wr ¼

spatial step size in the y direction, L spatial step size in the z direction, L fluid gravity, M/(L2t2) tortuosity adsorption rate coefficient, 1/t Lame’s constant, M/(Lt2) viscosity, M/(Lt) effective viscosity, M/ L1–n equivalent viscosity, M/(Lt) exposure time when fluid has leaked from each small area element of the fracture, t density, M/L3 minimum horizontal stress or closure stress, M/(Lt2) rate of fluid loss into the formation from injection to shut-in, L3/t Poisson’s ratio porosity of porous media gel filter-cake mechanical retention factor empirical constant gradient operator divergence operator time derivative, 1/t

polymer adsorption gel filter cake fracture formation water gas gel filter cake spatial coordinate x pump-in fracturing fluid spatial coordinate y spatial coordinate z matrix matrix node adjacent to fracture node polymer component proppant solid, rock sheared polymer unsheared polymer water irreducible water

Superscripts 0 ¼ initial state (in the absence of polymer and gel damage) ad ¼ in the presence of polymer adsorption cake ¼ in the presence of gel filter cake Acknowledgments This work was supported by the Fracturing, Acidizing, Stimulation Technology (FAST) Consortium and the Marathon Center of Excellence for Reservoir Studies (MCERS), Colorado School of Mines. References Barati, R., Hutchins, R.D., Friedel, T. et al. 2009. Fracture Impact of Yield Stress and Fracture-Face Damage on Production With a Three-Phase 2D Model. SPE Prod & Oper 24 (2): 336–345. SPE-111457-PA. http://dx.doi.org/10.2118/111457-PA. Bazin, B., Bekri, S., Vizika, O. et al. 2008. Fracturing in Tight-Gas Reservoirs: Application of SCAL Methods to Investigate Formation Damage Mechanisms. Presented at the SPE International Symposium and Exhibition on Formation Damage Control, Lafayette, Louisiana, USA, 13–15 February. SPE-112460-PA. http://dx.doi.org/10.2118/112460-MS. Bennett, C.O., Reynolds, A.C., Raghavan, R. et al. 1986. Performance of Finite-Conductivity, Vertically Fractured Wells in Single-Layer Reservoirs. SPE Form Eval 1 (4): 399–412. SPE-11029-PA. http:// dx.doi.org/10.2118/11029-PA. August 2013 SPE Production & Operations

Carter, R.D. 1957. Derivation of the General Equation for Estimating the Extent of the Fractured Area. Appendix I: Optimum Fluid Characteristics for Fracture Extension. In Drilling and Production Practice, G.C. Howard and C.R. Fast, 261–269. New York: American Petroleum Institute. Charoenwongsa, S. 2011. Numerical Simulation of the 3-D Hydraulic Fracturing Process, Cleanup and Relevant Physics. PhD dissertation, Colorado School of Mines, Golden, Colorado. Charoenwongsa, S., Kazemi, H., Miskimins, J. et al. 2010. A FullyCoupled Geomechanics and Flow Model for Hydraulic Fracturing and Reservoir Engineering Applications. Presented at the Canadian Unconventional Resources & International Petroleum Conference, Calgary, 19–21 October. SPE-137497-MS. Cheng, Y. 2012. Impact of Water Dynamics in Fractures on the Performance of Hydraulically Fractured Wells in Gas-Shale Reservoirs. J Can Pet Technol 51 (2): 143–151. SPE-127863-PA. http://dx.doi.org/ 10.2118/127863-PA. Cooke, C.E. Jr. 1975. Effect of Fracturing Fluids on Fracture Conductivity. J Pet Technol 27 (10): 1273–1282. SPE-5114-PA. http:// dx.doi.org/10.2118/5114-PA. Economides, M.J. and Nolte, K.G. 2000. Reservoir Stimulation, third edition. New York: John Wiley & Sons. England, A.H. and Green, A.E. 1963. Some Two-Dimensional Punch and Crack Problems in Classical Elasticity. Math. Proc. Cambridge Philos. Soc. 59 (2): 489–500. http://dx.doi.org/10.1017/S0305004100036860. Friedel, T. 2004. Numerical Simulation of Production From Tight-Gas Reservoirs by Advanced Stimulation Technologies. PhD dissertation, Technischen Universita¨t Bergakademie Frieberg, Frieberg, Germany. Friedel, T., Mtchedlishvili, G., Behr, A. et al. 2007. Comparative Analysis of Damage Mechanisms in Fractured Gas Wells. Presented at the European Formation Damage Conference, Scheveningen, The Netherlands, 30 May–1 June. SPE-107662-MS. http://dx.doi.org/10.2118/ 107662-MS. Ionescu, F.G., Awemo, K.N., and Pusch, G. 2006. Fracture Design Considerations for the Development of Tight Gas Formations. Presented at the SPE Europec/EAGE Annual Conference and Exhibition, Vienna, Austria, 12–15 June. SPE-100231-MS. http://dx.doi.org/10.2118/ 100231-MS. Lee, W.J. and Wattenbarger, R.A. 1996. Gas Reservoir Engineering. Dallas, Texas: Textbook Series, SPE. Marczewski, A.W. 2010. Analysis of Kinetic Langmuir Model. Part I: Integrated Kinetic Langmuir Equation (IKL): A New Complete Analytical Solution of the Langmuir Rate Equation. Langmuir 26 (19): 15229–15238. http://dx.doi.org/10.1021/la1010049. May, E.A., Britt, L.K., and Nolte, K.G. 1997. The Effect of Yield Stress on Fracture Fluid Cleanup. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 5–8 October. SPE-38619-MS. http://dx.doi.org/10.2118/38619-MS. McCain, W.D. Jr. 1990. The Properties of Petroleum Fluids, second edition. Tulsa, Oklahoma: PennWell Publishing Company. Pusch, G., Reitenbach, V., and Ionescu, G.F. 2004. Modelling of the Capillary End Effects in Hydraulically Fractured Tight Gas Reservoirs. Presented at the 66th EAGE Conference & Exhibition: Shared Earth Modelling Session, Paris, France, 7–10 June. STIM-LAB. 2003. Fracturing Fluid Cleanup. Presented at the 2003 STIMLAB Proppant Consortium Meeting, San Diego, California, USA, 10–11 July. STIM-LAB. 2004. Fracturing Fluid Cleanup. Presented at the 2004 STIMLAB Proppant Consortium Meeting, Mesa, Arizona, USA, 24–25 February. STIM-LAB. 2005a. “Multiphase Flow. Presented at the 2005 STIM-LAB Proppant Consortium Meeting, San Diego, California, USA, 21–22 July, 2005. STIM-LAB. 2005b. “Fracturing Fluid Cleanup. Presented at the 2005 STIM-LAB Proppant Consortium Meeting, San Diego, California, USA, 21–22 July. STIM-LAB. 2008. Fracturing Fluid Cleanup. Presented at the 2008 STIMLAB Proppant Consortium Meeting, San Diego, California, USA, 26–27 June. Voneiff, G.W., Holditch, S.A., and Robinson, B.M. 1992. Evaluating the Benefits of Applying New Fracture Technology—Part 3: A Statistical 243

Approach. Topical Report PB-93-158541/XAB, Contract No. GRI5091-221-2129, Gas Research Institute, College Station, Texas (01 December 1992). Voneiff, G.W., Robinson, B.M., and Holditch, S.A. 1996. The Effects of Unbroken Fracture Fluid on Gaswell Performance. SPE Prod & Fac 11 (4): 223–229. SPE-26664-PA. http://dx.doi.org/10.2118/26664-PA. Wang, Y. 2008. Simulation of Fracture Fluid Cleanup and Its Effect on Long-term Recovery in Tight Gas Reservoirs. PhD dissertation, Texas A&M University, College Station, Texas. Ward, J.S. and Morrow, N.R. 1987. Capillary Pressure and Gas Relative Permeabilities of Low-Permeability Sandstone. SPE Form Eval 2 (3): 345–356. SPE-13882-PA. http://dx.doi.org/10.2118/13882-PA.

Mass-Balance Equation and 1D Leakoff Model.

ðt

qinj ¼ 2

dAf CL dAf pffiffiffiffiffiffiffiffiffiffi dn þ w f : . . . . . . . . . . . . . ðA-1Þ dt t n dn

0

Average Fracture Width. (For the PKN fracture geometry shown in Fig. A-1.) p2 wf ¼ wf ;max : . . . . . . . . . . . . . . . . . . . . . . . . . ðA-2Þ 4 Maximum Fracture Width.

Appendix A—Fracture-Propagation Model A fracture-propagation model is used to describe the physical phenomena controlling fracture growth during the injection period of the hydraulic fracturing process. The governing equations are developed from the mass-balance equation and the 1D leakoff model proposed by Carter (1957), and the maximum fracturewidth equation for Perkins-Kern-Nordgren (PKN) fracture geometry (Fig. A-1), proposed by England and Green (1963). The mathematical formation of the fracture propagation model is presented by Eqs. A-1 through A-3.

wf ;max ¼

2ð1 tÞðpf rh;min ÞLf : . . . . . . . . . . . . ðA-3Þ G

The detailed mathematical formulation and numerical approximation of the fracture-propagation model can be found from Charoenwongsa (2011) and Charoenwongsa et al. (2010). Appendix B—Leakoff Data The leakoff data of 40-pptg guar reported by STIM-LAB (2005b, 2005c, 2008) are shown in Fig. B-1. It can be seen that the leakoff

Well

z

Lf

hf

wf

Overburden y Reservoir

x

Underburden

Fig. A-1—Hydraulically fractured reservoir system with a PKN fracture propagating along the x-coordinate, perpendicular to the fracture face in the y-coordinate (Charoenwongsa et al. 2010).

2.0 40 ppt Guar + 1 ppt AP breaker 40 ppt Guar + 2 ppt AP breaker 40 ppt Guar + 1 gpt Fracsal II + no breaker 40 ppt Guar + 1 gpt Fracsal II + 1 gpt CaO2 breaker 40 ppt Guar + 1 gpt Fracsal II + 2 gpt CaO2 breaker 40 ppt Guar + 1 gpt Fracsal II + 5 ppt Vicon breaker 40 ppt Guar + 1 gpt Fracsal II + 10 ppt Vicon breaker 40 ppt Guar + 7.5 ppt Vicon breaker + 0.5 gpt CAT3 + 0.1 gpt CAT4

Leakoff Volume, ml/cm2

1.5

1.0

0.5

0.0 0

2

4 Time0.5, min0.5

6

8

Fig. B-1—Leakoff profiles of different fracturing fluids are essentially a linear function of the square root of time (STIM-LAB 2005b, 2005c, 2008). 244


profiles of different fracturing fluids are essentially a linear function of the square root of time. According to STIM-LAB, the linear relationship suggests that the polymer is being retained in the filter cake.

testing, and improved oil and gas recovery processes. He holds BS and PhD degrees in petroleum engineering from the University of Texas at Austin. Kazemi is a member of the National Academy of Engineering (NAE) and a Distinguished and an Honorary Member of SPE.

Sarinya Charoenwongsa is a petroleum engineer at Chevron Energy Technology Company. She worked as a reservoir engineer for PTT Exploration and Production Company (PTTEP) from 2002–2007 and as a post-doc research scientist at the Colorado School of Mines (CSM) in 2012. She holds BS and MS degrees in chemical engineering from King’s Mongkut Institute of Technology Ladkrabang and Chulalongkorn University, Thailand, respectively, and a PhD degree in petroleum engineering from CSM.

Perapon Fakcharoenphol is a PhD candidate in petroleum engineering at CSM. His research interests include numerical simulation of coupled geomechanics and transport in porous and fractured media. He worked as a reservoir engineer for PTTEP from 2002–2008. Fakcharoenphol holds BS and MS degrees in petroleum engineering from Chulalongkorn University, Thailand, and Imperial College, London, respectively.

Hossein Kazemi is the Chesebro’ Distinguished Professor of Petroleum Engineering at CSM and Co-Director of the Marathon Center of Excellence for Reservoir Studies (MCERS). He retired from Marathon Oil Company in 2001 after serving as the Director of Production Research, Manager of Reservoir Technology, and Executive Technical Fellow. At CSM he teaches graduate courses and supervises research in reservoir modeling, well


Jennifer L. Miskimins is a senior consulting engineer at Barree & Associates and holds an appointment as an associate professor at CSM. She holds a BS degree from Montana College of Mineral Science and Technology and MS and PhD degrees in petroleum engineering from CSM. She served as the Executive Editor for the SPE Production & Operations journal from 2008–2011 and was an SPE Distinguished Lecturer for 2010–2011 and 2013–2014.

245