Research ArticleWell Performance Simulation and Parametric Study for DifferentRefracturing Scenarios in Shale Reservoir

Jing Huang ,1 Lan Ren,1 Jinzhou Zhao ,1 Zhiqiang Li,2 and Junli Wang3

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu,Sichuan 610500, China2School of Petroleum and Natural Gas Engineering, Chongqing University of Science and Technology, Chongqing 401331, China3Shu’nan Gas-Mine Field, PetroChina Southwest Oil and Gas Field Company, Luzhou, Sichuan 646000, China

Correspondence should be addressed to Jing Huang; huangjing_swpi@163.com and Jinzhou Zhao; zhaojz@swpu.edu.cn

Received 8 May 2018; Revised 6 July 2018; Accepted 17 July 2018; Published 23 August 2018

Academic Editor: Mandadige S. A. Perera

Copyright © 2018 Jing Huang et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

Refracturing is an encouraging way to uplift gas flow rate and ultimate gas recovery from shale gas wells. A numerical model,considering the stimulated reservoir volume and multiscale gas transport, is applied to simulate the gas production from arefractured shale gas well. The model is verified against field data from a shale gas reservoir in Sichuan Basin. Two refracturingscenarios: refracturing through existing perforation clusters and refracturing through new perforation zones, are included in thesimulation work. Three years after production is determined to be the optimum time for refracturing based on the evolutionanalysis of reservoir pressure, effective stress, fracture permeability, and gas recovery. The role that the hydraulic fractureconductivity and hydraulic fracture half-length play in gas production for different refracturing cases is explored. Pumpingparameters of the refracturing job in Sichuan Basin are discussed combining with sensitivity analysis, and suggestions forpumping parameters optimization are proposed.

1. Introduction

The gas flow rate of shale wells declines significantly in thevery first years after the initial hydraulic stimulation, andthe large volume of gas still remains in a shale reservoir [1].Some wells might not achieve an economical gas flow ratewhen the initial stimulation is inadequate: small treatmentsize, low proppant concentration, poor proppant distribu-tion, poor fracturing fluid selection, insufficient perforations,and operational problems with completion [2–7]. Refractur-ing is an encouraging way to uplift shale reservoir gas pro-duction and ultimate gas recovery by enlarging fracturegeometry, creating new fractures, improving pay coverage,reinflating natural fractures, increasing proppant conductiv-ity, and restoring fracture conductivity [8–11]. Compared todrilling and completing of infill wells, refracturing is aneconomical alternative to promote well productivity whenthe right candidate is selected [12–16]. The refracturing pro-cess has been developed and applied to Barnett, Haynesville,

Bakken, Fayetteville, Eagle Ford, and Woodford shale reser-voirs in recent years [6, 15].

Gas flow from an ultralow permeability shale reservoirthrough a complex fracture network, stress, and pressurefield change must be modeled so that restimulation designsand completion strategies can be properly evaluated. It isdifficult to predict gas production and improvement inhydrocarbon recovery post refracturing treatment. Severalprevious works developed numerical simulation approachesto model fluid flow, complex fracture networks, and initialhydraulic fractures of refracturing treatment. Tavassoliet al. perform a sensitivity study on the effect of different res-ervoir and hydraulic fracture parameters on refracturing per-formance based on a dual permeability model [11]. Rodveltet al. use an analytical production simulator to forecast theproductivity index and EUR of Marcellus shale wells [8].Haddad et al. use commercial software program to simulatethe gas production of a refractured shale reservoir [16].Urban et al. use a dual permeability simulator that takes into

HindawiGeofluidsVolume 2018, Article ID 4763414, 12 pageshttps://doi.org/10.1155/2018/4763414

account free gas in matrix and fractures and adsorbed gas tosimulate refracturing in the Eagle Ford shale [17]. Huanget al. use a finite element method to evaluate the well perfor-mance under different refracturing designs [18]. However,these models are still not applicable to describe the complexgas flow transport mechanism in shale gas reservoirs due tothe different sorption behavior and flow regimes betweenkerogen pockets and the inorganic solid medium.

In this paper, a numerical model, considering the stimu-lated reservoir volume and multiscale gas transport, isapplied to simulate the gas production from a refracturedshale gas well. The model is verified against field data of arefractured shale horizontal well in Sichuan Basin, Southwestof China. The evolution of effective stress, reservoir pressure,fracture permeability, and gas recovery is analyzed to deter-mine the optimum time for refracturing. Two refracturingscenarios: refracturing through existing perforation clustersand refracturing through new perforation zones, are includedin the simulation work. The role that the hydraulic fractureconductivity and hydraulic fracture half-length play in gasproduction for different refracturing cases is explored. Inaddition, the pumping parameters of the refracturing jobare discussed combined with sensitivity analysis.

2. Governing Equations

A shale reservoir is a triple-continuum formation which con-sists of organic matter, inorganic matrix, and natural frac-tures [19]. During the production process, the gas releasefollows the mechanism: kerogen system-inorganic matrixsystem-fracture system [20]. The effective stress increaseswhile the reservoir pressure depletes, in which, in turn, theporosity and permeability of shale reservoir change due torock matrix deformation. The stress sensitivity will furtherreduce the flow capacity of the fracture system in the stimu-lated area [21], which is a critical factor for productionprediction and optimal designation of restimulation. Theexisting complex fracture network is properly characterizedin this numerical model; in addition, the solid deformationeffect and complex gas flow behavior are taken into consid-eration. Sang et al. presented the model assumptions [22].

2.1. Deformation of Fractured Porous Shale

2.1.1. Constitutive Equation. Considering the kerogen matrix,inorganic matrix, and fractured solid system as linearly elas-tic media, the constitutive equation for fractured porousshale can be generally expressed as

G∇2u + G + λ ∇εv −2G3 + λ ∇εS − αm∇Pm + αk∇Pk+αf∇P f = 0

1

2.1.2. Initial and Boundary Conditions. Assuming that thewell is not disturbed under the original geological state,therefore, the displacement of shale rock is zero and the ini-tial condition can be presented as

ux x, y, t = 0,uy x, y, t = 0

2

The boundary conditions can be presented as

ux∣x=0 = 0 y = 0 ∼ Ye ,ux∣x=Xe

= 0 y = 0 ∼ Ye ,uy∣x=0 = 0 y = 0 ∼ Ye ,uy∣x=Xe

= 0 y = 0 ∼ Ye ,ux∣y=0 = 0 x = 0 ∼ Ye ,ux∣y=Ye

= 0 y = 0 ∼ Xe ,uy∣y=0 = 0 x = 0 ∼ Ye ,uy∣y=Ye

= 0 y = 0 ∼ Xe

3

2.2. Stress-Dependent Porosity and Permeability. The effec-tive pressure of triple-continuum formation can be presentedas [23]

σij′ = σij − αmPm + αkPk + αfP f δij 4

Stress-dependent correlations are used to considerporosity and permeability reduction. Based on experimentaland numerical simulation results [24], power law correla-tions are used to calculate these stress-dependent propertiesas follows:

ϕξ = ϕξ0 exp −cξ σ′ − σ0′ ,

Kξ = Kξ0 exp −cξ σ′ − σ0′5

2.3. Gas Flow

2.3.1. Continuity Equation of Kerogen System. The transportmechanisms in the kerogen system include viscous flow,Knudsen diffusion, and surface diffusion. Regardless of thespace transmission of the gas in kerogen, the continuityequation of the kerogen system can be present as

−σkmρgKkapp Pk − Pm

μg=∂ εkpϕρg

∂t+ ∂ εks 1 − ϕm − ϕf qa

∂t,

6

where qa is the adsorbed gas volume per unit volume kerogenand defined as

qa =ρsVLMg

Vstd

Pk

PL + Pk, 7

where Kkapp is the apparent kerogen permeability anddefined as

Kkapp = Kk0 +εkpϕDkkμgCkZRgT

+εks 1 − ϕm − ϕf DsCμsμgPk

PL + Pk2Ck

,

8

2 Geofluids

where Dkk is Knudsen diffusivity of the kerogen systemand defined as

Dkk =ϕkτ

2rk3

8RTπMg

1/2

9

2.3.2. Continuity Equation of Inorganic Matrix System. Thefree gas transport in an inorganic matrix involves two trans-fer terms. On the one hand, the adsorbed gas diffuses fromthe kerogen system to the inorganic matrix system. On theother hand, the inorganic matrix system supplies gas for thefracture system. Considering the slippage effect, Knudsen dif-fusion, and viscous flow, the gas continuity equation of theinorganic matrix system can be presented as

∇ ⋅ρgKmapp

μg∇Pm +Wkm −Wmf =

∂ 1 − εkp ϕρg

∂t,

10

where Kmapp is the apparent inorganic matrix permeabilityand defined as

Kmapp =ϕm 1 − εkp

τDkmμgCg + Fm

r2m8 , 11

where Fm is the slippage factor and defined as

Fm = 1 +μg

Pmrm

2α− 1 8πRT

Mg0 5, 12

where Dkm is the Knudsen diffusivity of the inorganic matrixsystem and can be defined as

Dkm = 2rm3

8RTπMg

0 5, 13

whereWmf is the transfer term between the inorganic matrixsystem and fractures. It can be presented based on theWarren-Root transfer model:

Wmf =σmfρgKmapp Pm − P f

μg, 14

where σmf is the pseudosteady state shape factor, which canbe defined as [25]

σmf = 4 1L2fx

+ 1L2fy

15

2.3.3. Continuity Equation of Fracture System. The porediameters in the fracture system are equal to the millimeterscale, the Knudsen diffusion in the fracture system is notablysmall, and only viscous flow is taken into account. Therefore,according to the conservation of mass, the continuity equa-tion of the fracture system can be present as

∇ ⋅ρgK fμg

∇P f +Wmf −Qgwell =∂ ρgϕf

∂t, 16

where Qgwell is the production rate of the fracture system andcan be defined based on the Peaceman model [26]:

Qgwell =2πρgK fW f

μgVb

P f − Pwfln re/rw

17

2.3.4. Initial and Boundary Conditions. Assuming that theinitial pressures of the kerogen system, inorganic matrix sys-tem, and fracture system are identical, then the initial condi-tion can be presented as

Pk x, y, t ∣t=0 = Pm x, y, t ∣t=0 = P f x, y, t ∣t=0 = Pi 18

The shale formation is considered a closed unit. The bot-tom hole flow pressure is applied as the inner boundarycondition:

∂P f∂n

∣Γ1 = Pwf 19

The no-flow outer boundary condition is applied:

∂P f∂n

∣Γ0 = 0,

∂Pm∂n

∣Γ0 = 0,

∂Pk∂n

∣Γ0 = 0

20

Start

Grid mesh and parameters input

Time step Δt

Gas flow equation in kerogen system

Gas flow equation in inorganic matrix system

Gas flow equation in fracture system

Solid deformation equation

Volume strain and effective stress calculation

Production calculation at t Time

Time of refracturing?

Simulation time?

End

Yes

Yest1 = t1 + Δt

t2 = t2 + Δt

No

No

Update hydraulic fracture and

reservoir parameters

Update reservoir param

eters

Figure 1: Simulation procedure of modeling initial fracturing andrefracturing job.

3Geofluids

where Γ1 represents the inner boundary of the productionwell and Γ0 represents the outer boundary.

2.4. Simulation Procedure. The finite difference method isused to solve the highly nonlinear mathematical model. Thesimulation procedure is as follows:

Step 1. The stimulated area and hydraulic fractures aremeshed by the nonuniform rectangular grid system.

Step 2. The pressure in the kerogen system, inorganic system,and fracture system is calculated, respectively.

Step 3. The pressure calculated in Step 2 is used to calculatethe volume strain of grid points; after further calculatingthe average effective stress, the reservoir parameters arerenewed and transferred to the gas flow model. The calcula-tion pauses at the time for refracturing.

Step 4. Hydraulic fracture and reservoir parameters areupdated at the time node of refracturing; the iterative compu-tation will stop at the end of simulation time.

The simulation procedure detail is shown in Figure 1.

3. Results and Discussion

3.1. Model Validation against Field Data. A horizontal wellwith multistage hydraulic fracturing is placed in the centerof the reservoir model (500m× 400m× 50m). Reservoirand wellbore geometry parameters similar to shale gas fieldin Sichuan Basin, Southwest of China, are presented inTable 1. 395m of the horizontal wellbore was initially stimu-lated with 6 stages, and the horizontal well achieved an aver-age daily gas flow rate of 2.5× 104m3 during the earlyproduction stage. However, the daily gas flow rate sharplydeclined to less than 0.5× 104m3 after 4 years of production;it cannot meet the critical liquid carrying flow, and the wellwas shut in.

The refracturing job of this well was carried out bygeneral temporary plug and diversion process. The slickwater was firstly pumped through the casing to compen-sate reservoir energy. While the bottom hole pressure(BHP) reached instantaneous shut-in pressure (ISIP) ofthe initial fracturing treatment, the particulate drops werepumped downhole to temporarily block open perforations,and the larger proppant mass treament schedules werefurther pumped. The increased pressure gained withparticulate drops and stages of sand indicating diversioninto new rock. The process was repeated for last 3 stages.The altered stress field leads to the main uncertainty of

Table 1: Reservoir and wellbore geometry parameters for the simulation model.

Parameter Symbol Value Units

Well radius rw 0.1 m

Bottomhole flowing pressure Pwf 15 MPa

Initial reservoir pressure Pi 20 MPa

Transient shape factor σkm 8 1/m2

Pseudosteady state shape factor σmf 1 1/m2

Initial porosity ϕξ0 0.05 —

Natural fracture porosity φf 0.001 —

Portion of kerogen grain volume in total shale core grain volume εks 0.1 —

Inorganic matrix permeability Kmi 1× 10−7 μm2

Elastic modulus E 22 GPa

Poisson ratio ν 0.2 —

Initial conductivity of hydraulic fractures Fcd 0.1 D·cmHydraulic fracture half-length Lf 70 m

Maximum principal stress σH 40 MPa

Minimum principal stress σh 36 MPa

Reservoir thickness H 50 m

Langmuir volume VL 3× 10−3 m3/kg

Langmuir pressure PL 6 MPa

Molecular mass Mg 0.016 kg/mol

Surface diffusion coefficient Ds 1× 10−7 m2/s

Length of horizontal well L 395 m

Reservoir temperature T 85 °C

4 Geofluids

how much of the lateral and which stage were stimulated[27, 28]. Fortunately, the microseismic monitoring dataproved that intervals closer to the heel (equivalent tostages 3 through 6 from the original stimulation treat-ment) were refractured.

For the refracturing work, the hydraulic fracture con-ductivity is promoted from 0.1D∙cm to 0.4D∙cm; the res-ervoir pressure and the adsorption gas content distributionof the simulated reservoir with refracturing treatment areillustrated in Figures 2(a) and 2(b), respectively. Comparedto the stage with restimulation, the reservoir pressure ofstage 5 and stage 6 maintains a higher level after 10years of production due to the depletion of fracture con-ductivity, the recovery of the absorbed gas is very low,and a large amount of absorbed gas still remains in theshale reservoir.

The gas production is increased through refracturingtreatment, as shown in Figure 3. Figure 3(a) shows the fielddata of the gas flow rate for the horizontal well with initialfracturing treatment and refracturing treatment producing

at a constant well pressure. This well was shut in for 7 timesbefore refracturing, which may be one of the main factorsthat lead to history data-matching error. In general, thesimulation results present a good match with the field data,

0

100

200

−100

−200

x/m

y/m

7.5

9.1

10.7

12.3

13.8

15.4

17.0

18.6

20.0Mpa

0 100 200 300 400 500

(a)

0 100 200 300 400 500

0

100

200

−100

−200

x/m

y/m

3.53.63.73.83.94.04.14.24.34.44.5

kg/m3

(b)

Figure 2: Reservoir pressure and reservoir adsorption gas content distribution after refracturing treatment.

Refracturing: gas flow rateNo Refracturing: gas flow rateField data

0Time (yr)

0

1

2

3

4

5

Gas

flow

rate

(104 m

3 /day

)

6

7

8

Shut-in point

1 2 3 4 5 6 7 8 9 10

(a)

0Time (yr)

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

Cum

ulat

ive G

as P

rodu

ctio

n (1

08 m3 )

Refracturing: cumulative gas productionNo Refracturing: dumulative gas productionField data

(b)

Figure 3: Comparison of simulation results with field data: (a) gas flow rate and (b) cumulative gas production.

Wellbore

Existing perforation clusters

Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6

Toe Heel

New perforation zones (creating new fractures)

Figure 4: Different refracturing scenarios: refracturing throughthe existing perforation clusters and refracturing through newperforation zones.

5Geofluids

which has verified the numerical model is capable of model-ing initial fracturing and refracturing of shale formation.

3.2. Parametric Study Hydraulic Fractures. The role that opti-mal refracturing time, hydraulic fracture permeability, andhydraulic fracture half-length play in gas production isexplored in this section. Two cases are considered, as shownin Figure 4. In the first case, the refracturing job is performedthrough the existing perforation clusters. In the second case,the refracturing job is performed through new perforationzones. In addition, the pumping parameters are also dis-cussed combined with sensitivity analysis.

3.2.1. The Optimal Refracturing Time. Finding the optimaltime for refracturing is crucial so as to maximize the perfor-mance of the refracturing job; the flow capacity of hydraulicfracture and cumulative gas production are the importantindicators. The effective stress will increase as the reservoirpressure depletes during the production, and the inducedeffective stress increment will lead to the degrading flowcapacity of the hydraulic fracture, which is one of the majorobstacles for expected shale gas recovery. As shown inFigure 5, during the early production stage, the ratio of thehydraulic fracture permeability after and before production(K f /K f i) decreases sharply, and it presents a linear and stabledecreasing trend after 3 years of production. The gas pro-duction performance is simulated for refracturing at thethird, fourth, and fifth years, respectively. Cumulative gasproduction of 10 years is shown in Figure 6. As shown inthe figure, refracturing at the fourth and the fifth yearsachieves almost the same cumulative gas production, whilerefracturing at the third year achieves a better performancebut not obvious. However, there is an optimum time forrefracturing, according to the research results of Wanget al., waiting too long between initial stimulation andrefracturing results in reduced treatment effectiveness [29].This is because the reservoir pressure continues to decreasewhile the fracture flow capacity presents a stable value.Therefore, it is the optimal time for a refracturing job whenthe flow capacity of the original fractures trends to be stable.

For the horizontal shale gas well in Sichuan Basin, it is betterto perform refracturing work after 3 years of production.

3.2.2. Hydraulic Fracture Conductivity.As shown in Figures 7and 8, the gas production of both refracturing scenariospresents a positive correlation with hydraulic fractureconductivity. Figures 7(a) and 8(a) illustrate that the gas flowrate of refracturing through the existing perforation clusters(4 stages) is higher than that of refracturing through newperforation zones (3 stages). However, refracturing throughnew perforation zones achieves better gas production com-pared to reopening of the original fractures for the consider-ation of every stage contribution. In the case of 0.4D∙cmhydraulic fracture conductivity, the initial average gas flowrate of every stage for refracturing through existing perfora-tion zones is 1.57× 104m3, while the average gas flow rateof every stage for refracturing through new perforation clus-ters is 1.79× 104m3. The average cumulative gas productionof every stage for refracturing through new perforation zonesis higher than that of refracturing through existing perfora-tion clusters, as shown in Figures 7(b) and 8(b). This isbecause the area undrained by the initial hydraulic fractures

0Time (yr)

122

24

26

28

30

32

34

Ave

rage

effec

tive s

tres

s (M

Pa)

Ratio

of f

ract

ure p

erm

eabi

lity

after

and

befo

re p

rodu

ctio

n (K

f/Kfi)

100.5

0.6

0.7

0.8

0.9

Average effective stressRatio of fracture permeability after and before production

2 3 4 5 6 7 8 9

Figure 5: The variation of average effective stress at the well point grid and ratio of fracture permeability after and before production.

0Time (yr)

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

Cum

ulat

ive g

as p

rodu

ctio

n (1

08 m3 )

Refracturing after 3 years of productionNo refracturing

Refracturing after 4 years of productionRefracturing after 5 years of production

Figure 6: Cumulative gas production for different refracturingtimes.

6 Geofluids

maintains relatively higher reservoir pressure, which contrib-utes a higher production pressure drop. As shown inFigures 9 and 10, compared with performing refracturingthrough existing perforation clusters, refracturing throughnew perforation clusters can communicate the area whichthe initial fracturing is unstimulated, expanding the reservoirseepage area and improving the reservoir recovery. It isunlikely that economic success will be achieved simply byrestoring the flow capacity of hydraulic fractures with newproppant. Therefore, higher proppant concentration andlarge-scale treatment size should be applied to increase frac-ture geometry and reservoir contact with the wellbore forboth refracturing scenarios. In addition, refracturing withhigher strength proppant is helpful for hydraulic fracturesto maintain long-term conductivity due to the increment ofeffective stress [29], as shown in Figure 5.

3.2.3. Hydraulic Fracture Half-Length. In the case of refrac-turing through new perforation clusters, gas flow rate andcumulative gas production for different hydraulic fracturehalf-length are shown in Figures 11(a) and 11(b), respec-tively. Increasing the hydraulic fracture half-length enlargesthe seepage area along the longitudinal direction of the reser-voir as to promote gas production. As shown in Figure 11(b),the cumulative gas production of the well increases from0.48× 108m3 to 0.54× 108m3 while the hydraulic fracturehalf-length increases from 70m to 110m. In addition, thereservoir pressure decreases slower with higher hydraulicfracture half-length, which is beneficial for long-time pro-duction, as shown in Figures 12 and 13. However, in refrac-turing, the fracture does not follow the same path of theinitial fracture due to the change in stress anisotropy; it isnot easy to obtain longer fracture length [14].

No refracturing: fracture conductivity 0.1 D.cmRefracturing: fracture conductivity 0.1 D.cmRefracturing: fracture conductivity 0.2 D.cmRefracturing: fracture conductivity 0.3 D.cmRefracturing: fracture conductivity 0.4 D.cm

0Time (yr)

1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8G

as fl

ow ra

te (1

04 m3 /d

ay)

(a)

No refracturing: fracture conductivity 0.1 D.cmRefracturing: fracture conductivity 0.1 D.cmRefracturing: fracture conductivity 0.2 D.cmRefracturing: fracture conductivity 0.3 D.cmRefracturing: fracture conductivity 0.4 D.cm

0Time (yr)

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

Cum

ulat

ive g

as p

rodu

ctio

n (1

08 m3 )

(b)

Figure 7: Well performance of refracturing through existing perforation clusters: (a) gas flow rate and (b) cumulative gas production.

No refracturing: fracture conductivity 0.1 D.cmRefracturing: fracture conductivity 0.1 D.cmRefracturing: fracture conductivity 0.2 D.cmRefracturing: fracture conductivity 0.3 D.cmRefracturing: fracture conductivity 0.4 D.cm

0Time (yr)

0

1

2

3

4

5

Gas

flow

rate

(104 m

3 /day

)

6

7

8

1 2 3 4 5 6 7 8 9 10

(a)

No refracturing: fracture conductivity 0.1 D.cmRefracturing: fracture conductivity 0.1 D.cmRefracturing: fracture conductivity 0.2 D.cmRefracturing: fracture conductivity 0.3 D.cmRefracturing: fracture conductivity 0.4 D.cm

0Time (yr)

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6Cu

mul

ativ

e gas

pro

duct

ion

(108 m

3 )

(b)

Figure 8: Well performance of refracturing through new perforation zones: (a) gas flow rate and (b) cumulative gas production.

7Geofluids

0

100

200

−100

−200

x/m

y/m

7.5

9.1

10.7

12.3

13.8

15.4

17.0

18.6

20.0Mpa

0 100 200 300 400 500

(a)

0 100 200 300 400 500

0

100

200

−100

−200

x/m

y/m

7.5

9.1

10.7

12.3

13.8

15.4

17.0

18.6

20.0Mpa

(b)

Figure 9: Reservoir pressure distribution: (a) refracturing through existing perforation clusters and (b) refracturing through new perforationzones.

0

100

200

−100

−200

x/m

y/m

3.53.63.73.83.94.04.14.24.34.44.5

kg/m3

0 100 200 300 400 500

(a)

0

100

200

−100

−200

y/m

x/m0 100 200 300 400 500

3.53.63.73.83.94.04.14.24.34.44.5

kg/m3

(b)

Figure 10: Reservoir adsorption gas content distribution: (a) refracturing through existing perforation clusters and (b) refracturing throughnew perforation zones.

0

1

2

3

4

5

Gas

flow

rate

(104 m

3 /day

)

6

7

8

No refracturing: fracture half-length 70mRefracturing: fracture half-length 70mRefracturing: fracture half-length 90mRefracturing: fracture half-length 110m

0Time (yr)

1 2 3 4 5 6 7 8 9 10

(a)

0Time (yr)

1 2 3 4 5 6 7 8 9 100

0.1

0.2

0.3

0.4

0.5

0.6

Cum

ulat

ive g

as p

rodu

ctio

n (1

08 m3 )

No refracturing: fracture half-length 70mRefracturing: fracture half-length 70mRefracturing: fracture half-length 90mRefracturing: fracture half-length 110m

(b)

Figure 11: Effects of hydraulic fracture half-length on: (a) gas flow rate and (b) gas flow rate of refracturing through new perforation zones.

8 Geofluids

3.2.4. Pumping Parameters. The pumping parameters of therefracturing job should be designed for enlarging fracturegeometry, improving pay coverage, and restoring fractureconductivity. The existing fracture network should be takeninto consideration. For the horizontal well discussed in thispaper, the pumping rate of the initial fracturing job is13~14m3/min, due to the existing fracture network andhigher fracturing fluid filtration, and the pumping rateincreased to 14~16m3/min. In addition, the average fluidvolume of every stage increases from 1960m3 to 2490m3,as shown in Figure 14.

100 mesh, 40/70 mesh, and 30/50 mesh ceramic proppantare used for both initial fracturing and refracturing job; theportion of different size ceramic proppant used is shown inFigures 15 and 16. For initial fracturing, only an average vol-ume of 7.5m3 100 mesh proppant is used to polish the frac-ture near the wellbore for every stage treatment, 40/70 meshproppant is mainly used to prop the hydraulic fracture, andan average volume of 9.6m3 30/50 mesh proppant is used toachieve higher fracture conductivity near the wellbore. Thiswell is generally refractured, and the higher proppant is deliv-ered within the limitation of well head pressure (WHP).

Based on microseismic monitoring and pumping data statis-tics, the average volume of 100 mesh proppant is promotedfrom 7.5m3 to 25m3 to keep the narrow fractures createdby refracturing open. 40/70 mesh proppant is also the mainproppant used to restore fracture conductivity.

0x/m

100 200 300 400 500

0

100

200

−100

−200

y/m

7.5

9.1

10.7

12.3

13.8

15.4

17.0

18.6

20.0Mpa

(a)

0x/m

100 200 300 400 500

0

100

200

−100

−200

y/m

7.5

9.1

10.7

12.3

13.8

15.4

17.0

18.6

20.0Mpa

(b)

Figure 12: Reservoir pressure distribution: (a) 90m hydraulic fracture half-length and (b) 110m hydraulic fracture half-length.

0

100

200

−100

−200

x/m

y/m

0 100 200 300 400 5003.53.63.73.83.94.04.14.24.34.44.5

kg/m3

(a)

0

100

200

−100

−200

y/m

x/m0 100 200 300 400 500

3.53.63.73.83.94.04.14.24.34.44.5

kg/m3

(b)

Figure 13: Reservoir adsorption gas content distribution: (a) 90m hydraulic fracture half-length and (b) 110m hydraulic fracture half-length.

Initial fracturingRefracturing

0

500

Flui

d vo

lum

e (m

3 )

1000

1500

2000

2500

3000

Stage 3 Stage 4 Stage 5 Stage 6

Figure 14: Comparison of the total fluid volume of the initialfracturing job and refracturing job.

9Geofluids

The field production data validate that the pumpingparameters for the refracturing job performed through theexisting clusters can effectively restore fracture conductivityas to promote gas flow rate (Figure 3). For refracturingthrough the existing clusters, a higher portion of microprop-pant is helpful to keep the narrow fractures created by refrac-turing open for improving gas production. It is the mostcommon method to promote pumping rate, fluid volume,and proppant concentration in the previous successfulrefracturing jobs [29–32]. On the one hand, a higher pump-ing rate helps to reduce proppant collection at the bottom ofthe wellbore [6]. On the other hand, higher proppant concen-tration and large-scale treatment size are helpful to restore orincrease hydraulic fracture conductivity so as to increase gasproduction, as shown in Figure 7.

4. Conclusion

A numerical model, considering the existing stimulatedreservoir volume and multi-scale gas transport, is applied tosimulate the gas production of the refractured shale well.

The model is verified against field data of the gas flow rate.The optimum time for refracturing is discussed based onthe simulation results. Two refracturing scenarios: refractur-ing through existing perforation clusters and refracturingthrough new perforation zones, are included in the simula-tion work. The role that the hydraulic fracture conductivityand hydraulic fracture half-length play in gas productionfor different refracturing cases is explored, and the pumpingparameters are also discussed. The main observations andconclusions are summarized below:

(1) The simulation results of the gas flow rate present agood match with the field data. It is the optimal timefor the refracturing job when fracture flow capacitytrends to be stable. For the horizontal shale gas wellin Sichuan Basin, it is better to perform the refractur-ing job after 3 years of production.

(2) Production uplift can be achieved by performing therefracturing job both through existing perforationclusters and new perforation zones. Generally, creat-ing new fractures can achieve better gas productioncompared to reopening the original fractures.

(3) The gas production presents a positive correlationwith hydraulic fracture conductivity for both refrac-turing scenarios. It is unlikely that economic successwill be achieved simply by restoring the flow capacityof hydraulic fractures with new proppant. Higherproppant concentration and large-scale treatmentsize should be applied to increase fracture geometryand reservoir contact with the wellbore.

(4) Increasing the hydraulic fracture half-length enlargesthe seepage area along the longitudinal direction ofthe reservoir as to promote gas production. Thereservoir pressure decreases slower with longerhydraulic fracture half-length, which is beneficialfor long-time production.

(5) The field data validate that the pumping parametersfor the refracturing job performed through the exist-ing clusters can effectively restore fracture conductiv-ity as to promote the gas flow rate.

Nomenclature

Cμs: Maximum monolayer adsorbed gas on the kerogensurface (mol/m3)

Ck : The moles of free gas per kerogen organic porevolume (mol/m3)

Cm: The moles of free gas per inorganic matrix porevolume (mol/m3)

Cg: Gas compression coefficient of inorganic matrixsystem (MPa−1)

cξ: Experimental coefficientDkk : Knudsen diffusivity of kerogen system (m2/s)Dkm: Knudsen diffusivity of inorganic matrix system

(m2/s)Ds: Surface diffusion coefficient (m2/s)

0

20

40

60

80

100

120

Stage 3 Stage 4 Stage 5 Stage 6

100 mesh proppant40/70 mesh proppant30/50 mesh proppantTotal proppant

Prop

pant

vol

ume (

m3 )

Figure 15: Proppant parameters of initial fracturing job.

0

20

40

60

80

100

120

Stage 3 Stage 4 Stage 5 Stage 6

100 mesh proppant40/70 mesh proppant30/50 mesh proppantTotal proppant

Prop

pant

vol

ume (

m3 )

Figure 16: Proppant parameters of the refracturing job.

10 Geofluids

Fm: Slippage factorG: Shear modulus (MPa)Kk0: Kerogen intrinsic permeability (μm2)Kmapp: Apparent inorganic matrix permeability (μm2)Kξ: Permeability of shale reservoir during production

(μm2)Kξ0: Initial permeability of shale reservoir (μm2)Rg: Universal gas constant (J/(K∙mol))rm: Pore radius of inorganic matrix (m)Mg: Molecular mass (kg/mol)Pk : Kerogen pressure (MPa)Pm: Inorganic matrix pressure (MPa)P f : Fracture pressure (MPa)PL: Langmuir pressure (MPa)Pi: Initial reservoir pressure (MPa)VL: Langmuir volume (m3/kg)V std: Gas molar volume at the standard condition

(273.15K and 101.325 kPa) (m3/mol)Z: Deviation factorLfx , Lfy: Fracture spacing of x-axis and y-axis,

respectively (m)Wmf : Mass transfer term between inorganic matter and

natural fractures (mol/(m3∙s))Qgwell: Production rate of fracture system (mol/(m3∙s)).

Greek Symbols

αm: Inorganic matrix effective stress coefficientαk : Kerogen effective stress coefficientαf : Fracture effective stress coefficientσij′: Reservoir effective stress (MPa)

σij: Stress tensor (MPa)

σ0′: Initial effective stress (MPa)

σ′: Effective stress during production (MPa)σkm: Transient shape factor (1/m2)σmf : Pseudo-steady state shape factor (1/m2)εν: Volume strainεS: Volume strain induced by gas desorptionεkp: Portion of kerogen pore volume in total interconnected

matrix pore volumeεks: Portion of kerogen grain volume in total shale core

grain volumeϕξ: Porosity during production processϕξ0: Initial porosityϕ: Total matrix porosityϕm: Inorganic matrix porosityϕf : Fracture porosityρg: Gas density (kg/m3)μg: Gas viscosity (mPa∙s)λ: Melanie constantu: Displacement (m)δij: The symbol of Kroneker (if i = j, then δij = 1, else

δij = 0).

Subscripts

k: Related to kerogen

m: Related to inorganic matrixf : Related to fracture0: The reference state.

Data Availability

The basic data in this research article mainly come fromthe published works and a refractured horizontal shalewell in Sichuan Basin, Southwest of China. The productiondata and pumping parameters of the refractured well arecurrently under embargo while the research findings arecommercialized. Requests for data, 12 months after thepublication of this article, will be considered by the corre-sponding author.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors would like to acknowledge the support of theMajor Program of the National Natural Science Foundationof China (51490653) and the National Science and Technol-ogy Major Project of the Ministry of Science and Technologyof China (2016ZX05023005-001-002).

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