SPE-153255-PA (Simulation of Fracturing-Induced Formation Damage and Gas Production From Fractured Wells in Tight Gas Reservoirs)

Simulation of Fracturing-InducedFormation Damage and Gas Production

From Fractured Wells in Tight GasReservoirs

D.Y. Ding and H. Langouet, IFPEN, and L. Jeannin,GDFSUEZ

Summary

Fracturing fluid may jeopardize the production of hydraulicallyfractured tight gas formations. Because capillary forces act stron-ger in low-permeability formations, the invaded fracturing fluid isharder to remove. The increase of water saturation around the frac-tured well affects the mobility of the gas phase, particularly in tightformations where the gas relative permeability declines stronglywhen water saturation increases. This damage might greatlyreduce the gas production in a very long cleanup period. This pa-per presents numerical simulation techniques to account for forma-tion damage with both a near-well model and a full-field model forfractured wells in tight formations. For the full-field model, theskin determined from an inversion is suitable for long-term pro-duction simulations, and a sector model can be used to update thewell skin through a coupled modeling so that the full-field modelcan be used correctly over the whole life of the project.

Introduction

Wells in tight gas reservoirs are generally hydraulically fracturedbecause conventional completion techniques cannot provide eco-nomical gas flow rates. Hydraulic fracturing is designed to increasewell productivities. However, the productivity improvement afteroperations can be disappointing, particularly when fracturing indu-ces damage of petrophysical properties.

Fracturing-fluid invasion of the porous medium leads to anincrease of water saturation in the vicinity of the fractures and adecrease of the effective gas permeability. This hydraulic damage isdifficult to be removed in low-permeability formations because ofhigh capillary pressure and the change of the gas relative permeabil-ity in the invaded zone. The presence of fracturing fluid inside the res-ervoir might greatly reduce the production during a very long period.Besides, because of long-term gas migration, gradual evaporation,and change in pore geometry caused by burial and diagenesis, manytight gas reservoirs are water undersaturatedthat is, the initial watersaturation in the reservoir is smaller than the capillary equilibrium ir-reducible water saturation. The water undersaturated system leads toadditional water blocking andmakes the damagemore severe.

Other causes of deterioration of the well productivity are thedamage inside the fracture, which is related to proppant crushing,proppant embedment, fracture plugging with chemical and poly-mer residues, the inertial non-Darcy flow effect as well as themultiphase flow effect, and the mechanical damage inside the res-ervoir. Mechanical damage effects in the formation are generallycharacterized by a reduction of absolute permeability caused bypolymer solids deposition near the fracture face, clay swelling,and broken gel/fine migration.

We focus the study on hydraulic damage by simulating the fullprocess of fracturing-fluid invasion followed by a cleanup; in addi-tion, the damage inside the fracture and the mechanical damage are

also considered in the numerical simulation. Fracturing-fluid-induced formation damage has been studied in the literature (Hol-ditch 1979; Friedel 2004; Gdanski et al. 2005, 2006; Shaoul et al.2007; Lolon et al. 2007; Ghahfarokhi et al. 2008;Wang et al. 2010).Here, we use a mathematical model based on the polymer flow witha near-well fine-grid system for the formation damage simulation ofhydraulic fractures. Regarding full-field simulations, the main prob-lem is how to account for local phenomena in the vicinity of eachfractured well. Indeed, using a hybrid grid or a local grid refinementaround each well requires too much CPU time and is practicallyunfeasible for real applications. We address, therefore, the model-ing of fractured wells on coarse-grid full-field reservoir simulationsusing skins from the inversion and coupled modeling techniques.

First, we present simulation results concerning fracturing-fluidinvasion and the cleanup process using a very fine-grid near-wellmodel around the fractures. However, this kind of model, takinginto account damage phenomena generally at a scale from severalcentimeters to several meters around the well and fractures, makesthe near-well modeling difficult to integrate information at thereservoir scale. To simulate at full-field scale, coarse grids areusually used with a skin factor for the fractured-well simulation.Several analytical skin formulae are proposed for the fracturedwells in the literature (Mukherjee and Economides 1991; Gdanskiet al. 2006). But these skins are not always accurate for coarse-grid numerical simulations. In this paper, we show a method forthe determination of the numerical productivity index (PI) (orskin) through an inversion procedure, which is appropriate forlong-term predictions. In the last part of the paper, we expose aspecific algorithm for the coupled modeling between a full-fieldreservoir model and near-wellbore models. The coupled modelingprovides time-dependent numerical PI (or skin) for the full-fieldreservoir model. This methodology allows us to simulate correctlythe production behavior in the transient-cleanup period and givesalso a numerical PI (or skin) for long-term production simula-tions. The coupled modeling has been successfully applied to sev-eral cases, including the study of time-dependent productivities ofa multifractured horizontal well in a heterogeneous media.

Simulation of Fracturing-Induced FormationDamageWith a Near-Well Model

Mathematical Equations. The invasion of water-based fractur-ing fluid and its back production are governed by two-phase flowequations in porous media (Mattax and Dalton 1990) as follows:

@

@t/qwSw divqw~uw Qw 0

@

@t/qgSg divqg~ug Qg 0

;

8>:

1

where the Darcy velocity ~um is given by ~um KkrmlmrUm with

Um Pm qmgz (mw for water or g for gas), S is the satura-

tion, P is the pressure, K kx

kykz

0@

1A is the absolute per-

meability of the formation, kr is the relative permeability and is as

. . . . . . . . . . . .

CopyrightVC 2013 Society of Petroleum Engineers

This paper (SPE 153255) was accepted for presentation at the SPE Middle EastUnconventional Gas Conference and Exhibition, Abu Dhabi, UAE, 2325 January 2012, andrevised for publication. Original manuscript received for review 30 November 2011. Revisedmanuscript received for review 7 January 2013. Paper peer approved 23 January 2013.

246 August 2013 SPE Production & Operations

a function of Sw, / is the porosity, q is the density, l is the viscos-ity, g is the gravity factor, and Q is the injection or productionrate. In this modeling, only diagonal permeability tensor is con-sidered. The gridblocks are aligned with the fracture in the exam-ples of this paper.

The pressures in the water and gas phases are related throughthe relation of the capillary pressure:

PcSw Pg Pw: 2This is represented as a function of water saturation Sw. This sys-tem is closed by the saturation relationship

Sw Sg 1: 3The water-based fracturing fluid is composed of water and

polymer. In the modeling, the polymer is considered as a compo-nent in the water phase and is governed by a polymer transportequation (Lecourtier et al. 1992). In our modeling, the mole con-servation (instead of mass conservation) is considered for thepolymer component

@

@t

/Swnwc

pw 1 /pF

divnwcpw~upw Qp 0; 4

where nw is the water-phase mole density, cpw is the mole fraction

of polymer in the water phase, pF is the mole number of polymeradsorbed on an unit volume of rock, Qp is the polymer injectionrate, and~upw is the Darcys velocity of the polymer, given by

~upw KkrwlwRm

rUw; 5

where Rm is the mobility reduction factor caused by the presenceof polymer. In a macroscopic scale, the mobility reduction factordepends mainly on the polymer concentration, the salinity, andthe shear rate, which are measured from the laboratory. The fluxdispersion/diffusion is neglected in the modeling.

The well production rates in a gridblock i are calculated usinga numerical productivity index (PI) by the following formulae:

Qg;i krglgPIiPg;i Pf ;i; 6a

Qw;i krwlwPIiPw;i Pf ;i 6b

and

Qp;i krwlwRmPIiPw;i Pf ;i; 6c

where Pm,i is the pressure of the phase m (mw or g) at the well-block I; Pf,i is the bottomhole well flowing pressure in the well-bore; and PIi is the numerical PI, which depends on the gridblocksizes, the block permeability, and the skin value. The concept ofnumerical PI was first introduced by Peaceman (1983) and thenimproved by Ding and Jeannin (2001). In the case where a fine-grid system is used to discretize the fracture for a fractured verti-cal well, the flow is linear inside the wellblock. The numerical PIis calculated by

PIi KfrachwD=2

; 7

where Kfrac is the fracture permeability, w is the wellblock width(fracture width), h is the wellblock height, and D is the wellblocklength (for well at the block interface). If a coarse-grid system isused or if the fracture is discretized for a fractured horizontalwell, the flow is radial or pseudoradial inside the wellblock.In that case, the numerical PI is given by

PIi Kilwlnr0=rw ; 8

where Ki is the average block permeability, lw is the well lengthinside the gridblock, rw is the wellbore radius, and r0 is the equiv-alent wellblock radius that depends on the gridblock sizes. Thereis a direct relation between the numerical PI and the skin S. In thecase of the presence of a skin S such as the choke skin for thecoarse-grid simulation, the numerical PI is calculated by

PIi Kilwlnr0=rw S : 9

Various numerical methods (Aziz and Settari 1979; Mattaxand Dalton 1990) can be used to solve these equations. Here, thesystem is solved by using the finite-difference approach with aCartesian grid. The Euler method is applied for the time discreti-zation. The pressure and the saturation, considered as primary var-iables, are obtained implicitly with Newton-Raphson iteration,while the polymer concentration is solved explicitly after obtain-ing gridblock pressures and saturations. Upstream mobility isused for both the water/gas and the polymer transport equations.

In general, the gas relative permeability is reduced in theinvaded zone because of polymer adsorption/retention, wettabilitychange, and water blocking. The reduction of the gas permeabilitycan be quantified from laboratory experiments (Bennion et al.2000; Bazin et al. 2010). In the modeling, the effect of the poly-mer on the gas relative permeability is simulated with imbibitioncurves for the fracturing-fluid invasion and drainage curves forthe back production. Although the fracturing-fluid viscosity isgenerally very high, the experiments (Bazin et al. 2010) show thatviscosity of fracturing fluid in the tight gas reservoir is very closeto that of water, because most of the polymer molecules areretained outside the formation.

In this work, we consider only the hydraulic modeling of fractur-ing-fluid invasion without considering the geomechanical aspectsfor the generation of the fracture. We assume that the fractures werealready created and the half-length, the width, and the fracture per-meability (or conductivity) are known. The fracture propagation isnot explicitly considered. The consideration of a fracture propaga-tion (Behr et al. 2006) as well as the coupled approach (Mirandaet al. 2010) could be a future work. The leakoff during the fracturingis represented by injecting an appropriate volume of fluid in the for-mations. The presence of a hydraulic fracture is taken into accounteither by using very fine gridblocks for the fracture discretization orwith an equivalent skin factor for the coarse-grid simulation. In thissection, we show some simulation results with our in-house near-well simulator, which uses very fine gridblocks around the fracture.The damage inside the fracture is taken into account through thefracture conductivity, and the mechanical damage is considered bymodifying the reservoir absolute permeability close to the fracture.This model can simulate, with a good precision, the fracturing-fluidinvasion and the cleanup behavior.

Numerical Examples. Example 1Hydraulically FracturedVertical Well. We consider a tight gas reservoir with a horizontalpermeability of 0.02 md and a vertical to horizontal permeabilityratio of 0.5. A hydraulic fracture is initiated from a fully pene-trated vertical well. This fracture is extended to the whole reser-voir thickness. The fracture half length is 50 m and its width is 2cm. A quarter of the geometry is usually used to simulate thehydraulically fractured well (Freeman et al. 2009). The size of thedomain is 550 m in the x-direction, 800 m in the y-direction, and56 m in the z-direction (Fig. 1). This zone is discretized by14345 gridblocks and the sizes of blocks are given in Table 1.This fracture is discretized by 5 gridblocks along its length withDx 10m and Dy 0:01m (a quarter of the geometry). Thebold numbers in Table 1 are the fractured gridblocks. The dimen-sionless conductivity C is given by

C KfracKres

w

L; 10

where Kfrac is the fracture permeability, Kres is the reservoir per-meability, L is the fracture half length, and w is the fracture width

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

August 2013 SPE Production & Operations 247

(the fracture width is 2 cm; Fig. 1 and Table 1 show only a quarterof the geometry). It is assumed that the fracture permeability is2 D, which corresponds to a dimensionless fracture conductivityof 40.

The considered reservoir is water-undersaturated, where theinitial reservoir water saturation of 0.2 is smaller than the irreduc-ible water saturation of 0.28. The relative permeability and capil-lary pressure curves are shown in Fig. 2. Because of waterblocking and polymer adsorption/retention, the gas relative per-meability is reduced from 0.59 to 0.37 in the damaged zone (frac-turing-fluid-invaded area). A volume of 316 m3 of fracturing fluidis injected into the fractured well (79 m3 for the quarter of the ge-ometry) during 1 day. The production starts on the fourth day.

The mechanical damage is first investigated by reducing theabsolute permeability in a given depth from the fracture face. Likethe studies in the literature (Holditch 1979; Gdanski et al. 2005;Ghahfarokhi et al. 2008), the results show that it has a significantimpact only when the absolute permeability is reduced by morethan 99% in a depth of several to several tens of centimeters, whichseems improbable if the fracturing fluid is correctly selected.

Numerical simulations show that the hydraulic damage is gen-erally small for this fractured vertical well. This conclusion is alsoobserved by other authors (Friedel 2004; Ghahfarokhi et al.2008). However, the hydraulic damage can be severe in twocases: (a) a low conductivity fracture and (b) the presence of apermeability jail. Therefore, we present only some results relatedto fracture conductiviies.

Fig. 3 presents the area of fracturing-fluid invasion around thefracture for the case of the conductivity C 40. Figs. 4 and 5present the gas-flow rate and the cumulative production respec-tively for dimensionless fracture conductivities of 40, 4, and 0.4with and without hydraulic damage. These simulations show that(1) the fracture conductivity has much more important impact onthe gas production than the hydraulic damage, and (2) the hydrau-lic damage is more severe for a low-conductivity fracture. Thecleanup period is short. It is confirmed that the hydraulic damageis generally not very great for a fractured vertical well. In the caseof low fracture conductivity (Cf 0.4), the hydraulic damage canreduce the cumulative gas production by 6% at 800 days. How-ever, the hydraulic damage is much more severe for the fracturedhorizontal well, which is shown hereafter.

Example 2Multifractured Horizontal Well. Consider thesame reservoir. Now, three transverse fractures are initiated froma horizontal well with a distance of 250 m between them. A vol-ume of 316 m3 of fracturing fluid, the same as the case of the frac-tured vertical well, is injected in each fracture. A quarter of thegeometry is presented in Fig. 6. It is assumed that no gas flowsdirectly into the horizontal well and all gases are produced fromthe fracture. The flow regimes inside the fracture are different fora hydraulically fractured horizontal well and in a fractured verti-cal well. The flow is linear in the fracture plane around a verticalwell, if the fracture is also vertical and the well is perforatedacross the entire fractured interval, while it is radial around a hori-zontal well (Fig. 7). The pressure drop with a radial flow is higherthan that with a linear flow. Therefore, for the same fracture con-figuration (same length and same fracture conductivity), a fractureinitiated with a horizontal well produces less than a fracture initi-ated with a vertical well. We present some numerical-simulationresults with the near-well model and compare the formation dam-age between the fractured horizontal and vertical wells.

Fig. 8 presents the gas-flow rate for this multifractured hori-zontal well with different fracture conductivities (40, 4, and 0.4)with and without hydraulic damage, and Fig. 9 presents the corre-sponding cumulative gas productions. We observed that theimpact of the fracture conductivity on the fractured horizontalwell is much greater than that on the fractured vertical well. Itreduces the gas production by a factor of 10 on the horizontal wellwhen the fracture conductivity is decreased from 40 to 0.4, whileit reduces only the production by a factor of 1.7 on the fracturedvertical well for the same conductivity variation (see also Figs. 4and 5). Moreover, the hydraulic damage in a fractured horizontalwell is also much greater than that in a fractured vertical well,especially for cases with low conductivities. The hydraulic dam-age decreases 22.3% of the cumulative gas production on 800days for the fractured horizontal well with C 0.4 instead of5.3% for the fractured vertical well with the same conductivity.Another observation is that the production from one single frac-ture with the horizontal well is much lower than that with the ver-tical well, especially in low fracture conductivity cases. Ofcourse, multifractures can be initiated with a horizontal well tocompensate for this shortcoming.

In the fracture plane, a horizontal well is represented by apoint source or a small wellbore, while a vertical well is repre-sented by a line source through the whole fracture height (see Fig.7). This fracture plane is limited by its size, and changing the con-ductivity (or permeability) in the fracture has much more impacton the radial flow for a horizontal well than on the linear flow for

Fracture (50 M)Well

800

m

550 m

Fig. 1Grid system for the simulation of the fractured verticalwell in xy plane (a quarter of the geometry).

TABLE 1GRID SYSTEM FOR THE SIMULATION OF THE FRACTURED VERTICAL WELL*

Gridblock Size (m)

Dx 10 10 10 10 10 10 20 30 40 60 70 80 90 100Dy 0.01 0.01 0.01 0.02 0.03 0.04 0.05 0.06 0.08 0.1 0.15 0.2 0.3 0.44

0.7 0.8 1 1.5 2 3.5 6 8 10 15 20 30 50 50 100 100 100 100 100 100

Dz 11.2 11.2 11.2 11.2 11.2

* Bold numbers correspond to the discretization of the fracture.


a vertical well. Low conductivity inside the fracture makes thecleanup of the invaded water more difficult for a radial flow to-ward a horizontal well. Therefore, the conductivity has a muchstronger influence on the fractured horizontal well. If the damageinside the fracture is great, the horizontal well production mightbe far from what we expect. The conductivity in the fracture is akey point for the success of horizontal well fracturing.

The near-well model can simulate details of the fracturing-fluid invasion and the impacts of different types of formationdamage on the well production. But this kind of model needs veryfine gridblocks around the well and the fractures, and is limited bya near-well domain around the fracture.

Simulation of Fracturing-Induced FormationDamageWith a Coarse-Grid Reservoir Model

Although a fine-grid near-well model can be used to simulate theformation damage on fractured wells, it is still necessary to studythe simulation of the formation damage with a coarse-grid reser-voir model for the following two reasons: (1) a fine-grid near-wellmodel cannot take into account full reservoir information and pro-duction scenarios, and (2) reservoir studies are usually performedwith a coarse-grid full-field model, and it is necessary to integrateformation damage information for the coarse-grid simulation offractured wells. The necessary full-field information for thehydraulically fractured well simulation has been considered in theliterature (Ehrl and Schueler 2000; Sadrpanah et al. 2006; Gataul-lin 2008; Fazelipour 2011). Here, we address particularly the sim-ulation of fractured wells with a coarse-grid reservoir simulator.

C = 40 hydraulic damage


C = 0.4 hydraulic damage

C = 40 no hydraulic damage


C = 0.4 no hydraulic damage

1000

10000

100000

1000000

1000100101

Gas

rate

(m3 /d

ay)

Time (day)

C = 40 hydraulic damageC = 4 hydraulic damageC = 0.4 hydraulic damageC = 40 no hydraulic damageC = 4 no hydraulic damageC = 0.4 no hydraulic damage

Fig. 4Hydraulic damage of the fractured vertical well with different conductivities (gas flow rate).

0

0.2

0.4

0.6

0 0.2 0.4 0.6 0.8 1Sw(a)

0 0.2 0.4 0.6 0.8 1Sw(b)

Rel

ative

per

meabi

lity

krwkrgkrg in the damaged zone

0

5

10

15

20

25

Capi

llary

pre

ssur

e (ba

r)

0.6krwkrgkrg in the damaged zone

krwkrgkrg in the damaged zone

Fig. 2Relative permeability and capillary pressure. (a) Hyster-esis of gas relative permeability; (b) capillary pressure.

Polymer concentration Pressure distribution

1.06

m

Fracture (50 m) Fracture (50 m)

1.06

m

Polymerconcentration

(ppm)Pressure

(bar)1500135012001050900750600450

425423421419417415413411409407405

3001500

Fig. 3Area of the fracturing-fluid invasion.


For the coarse-grid simulation, an equivalent wellbore radiusor skin factor is usually used for the fractured wells. However,there is not a standard approach to provide these equivalent pa-rameters, especially for finite-conductivity-fractured horizontalwells. For example, the analytical choke skin formula (Mukherjeeand Economides 1991; Economides et al. 2010), which is pro-posed for accounting for the radial flow around a horizontal wellin the fracture plane, is not always suitable for numerical simula-tions in complex cases, as shown in the examples hereafter. Gdan-ski et al. (2006) proposed to use a face skin factor, which is afunction of the saturation and the relative permeability, to takeinto account the fracturing fluid-induced formation damage andcleanup effect. That approach was developed to simulate transientcleanup behavior with a fine-grid model. The obtained face skin

can be used for coarse-grid simulations for a fractured verticalwell in a homogeneous media. Here, we present an inversionapproach to determine the skin or the numerical PI, which is alsosuitable for a multifractured horizontal well and in a heterogene-ous media.

Determination of Skins Through Inversion. A coarse-gridmodel cannot correctly simulate the transient behavior during thecleanup period because of the large sizes of the wellblocks (and/or the fracture block). However, an equivalent skin or numericalPI value used for long-term production simulation can be deter-mined through an inversion procedure (Ding and Renard 2005).

First, we perform a simulation with a fine-grid near-wellmodel, as presented in the previous part, around a near-well do-main. Then, we perform a coarse-grid simulation in the same do-main with a standard reservoir simulator without considering thehydraulic damage effectthat is, without simulating the fractur-ing-fluid invasion and the water production. The damage effectsare indirectly considered using skin factors in the standard reser-voir simulator. We match the long-term gas production (after thecleanup period) between a coarse-grid model and a fine-grid for-mation-damage model in a same near-well domain by inversion.We optimize the skin factors for the following problem:W

ell

Fracture (50 M) 550 m

800

m

Fracture (50 M)

Fig. 6Discretization for the multifractured well simulation (aquarter of the geometry).

vertical well

horizontal wellhorizontal wellhorizontal well

vertical well

horizontal wellhorizontal wellhorizontal well

vertical wellVertical well

horizontal wellhorizontal wellhorizontal wellhorizontal wellhorizontal wellhorizontal wellHorizontal well

(a)

(b)

Fig. 7Flow regimes inside the fracture. Flow around (a) a frac-tured vertical well and (b) a fractured horizontal well.












C = 0.4 no hydraulic damage0.01

0.1

1

10

1000100101Time (day)







Cum

ulat

ive g

as p

rodu

ctio

n (1

06 m

3 )

Fig. 5Hydraulic damage of the fractured vertical well with different conductivities (cumulative gas production).


JS1;; SL 12

1

N

XNn1

Qn qnS1;; SL2; 11

where Sl is the skin factor on the wellblock l (l 1, , L) in thestandard reservoir simulator, q is the well flow rate calculated bythe reservoir simulator without considering the physics of formationdamage, Q is the well flow rate calculated by the near-well model,and N represents the sampling points. We search for the optimalskin values so that the objective function (Eq. 8) is minimal. It issometimes more convenient to search for the optimal numerical PIsinstead of skins to minimize the objective function. It has to bemen-tioned that the presence of a hydraulic fracture can generate a nega-tive numerical PI with Peacemans well model, which cannot beused by a standard reservoir simulator. Here, we use the well modelproposed by Ding and Chaput (1999), which modifies transmissibil-ities around the fracture, for the coarse-grid simulation.

Numerical Examples. Example 3Coarse-Grid Simulation fora Fractured Vertical Well. Consider a reservoir of 1000100050 m. The reservoir is homogeneous, with horizontal permeability0.02 md, vertical permeability 0.01 md, and porosity 0.1. A uni-form Cartesian grid with 20 blocks in the x-direction, 20 blocks inthe y-direction, and five blocks in the z-direction, is used for thefull-field simulation, with a standard two-phase flow reservoirsimulator. The gridblock size is Dx 50 m, Dy 50 m, andDz 10 m.

A fractured vertical well, with a fracture half-length of 50 mand a fracture width of 1 cm, is considered. The fracture perme-ability is 2 D, which corresponds to a dimensionless fracture con-ductivity of 20 (the fracture width is 1 cm). This vertical well isfully penetrated and located at the block (15, 15) in the xy-plane.The fracture is oriented in the x-direction, and is opened throughthe whole thickness of the reservoir. A volume of 328 m3 of frac-tured fluid is injected into the reservoir to create the fracture. Theproduction starts at the fourth day. The relative permeability andcapillary pressure curves are the same as shown in Fig. 2.

In the coarse-grid simulation, a source/sink is considered inthe wellblocks (Fig. 10a). The formation damage caused by thefracturing-fluid invasion cannot be considered with this coarse-grid simulation. To get a reference solution, the grid is locallyrefined around the fracture as shown in Fig. 10b and Table 2, andthe near-well model approach is used to simulate fracturing-induced formation damage. For this particular case, the use of ananalytical equivalent wellbore radius (or analytical skin) is con-venient, because the fracture conductivity is high (C 20) andthe hydraulic damage is small for a fractured vertical well. Fig. 11shows a comparison between the coarse-grid simulation with theequivalent wellbore radius and the reference solution for the gasflow rate. It is found that the long-term production is very wellsimulated with the coarse-grid model, but it cannot give correctresults for the short time period (approximately 30 to 40 days).This inaccurate simulation in the short-term period is related totwo main factors:

. . . . . .



1000

10000

100000

1000000C = 40 hydraulic damageC = 4 hydraulic damageC = 0.4 hydraulic damageC = 40 no hydraulic damageC = 4 no hydraulic damageC = 0.4 no hydraulic damage

Gas

flow

rate

(m3 /d

ay)

1000100101Time (day)

Fig. 8Hydraulic damage of a fractured horizontal well with different conductivities (gas flow rate).

0.001

0.01

0.1

1

10

100 C = 40 hydraulic damageC = 4 hydraulic damageC = 0.4 hydraulic damageC = 40 no hydraulic damageC = 4 no hydrualic damageC = 0.4 no hydraulic damage

Cum

ula

tive ga

s pr

oduc

tion

(106

m

3 )

1000100101Time (day)

Fig. 9Hydraulic damage of a fractured horizontal well with different conductivities (cumulative gas production).


- The hydraulic formation damage associated with watercleanup.

- The gridblock storage effect caused by the large wellblocksize.

For this high conductivity fracture initiated from a verticalwell, using the skin obtained from the inversion (without usingthe equivalent wellbore radius) gives similar numerical PIs andgas-production profiles. The results are not presented here.

Example 4Coarse-Grid Simulation for a MultifracturedHorizontal Well. Considering the same reservoir geometry, pet-rophysical properties and the same coarse grid discretization as inExample 3, a horizontal well with three transverse fractures with

distances of 100 m between them is implemented, as shown inFig. 12. The horizontal well is drilled in the middle layer of thereservoir, and the fractures are created through the whole reser-voir thickness. It is assumed that all productions come from thefractures and the well does not have direct contribution to the gasproduction. Therefore, the three wellblocks [(15,13,3); (15,15,3)and (15,17,3)] are located only in the middle layer of the coarse-grid system. The half-length of the fracture is 50 m and its widthis 1 cm. The fracture conductivity is 2, lower than that in Example3. A local grid refinement is also given in Fig. 12b for the simula-tion of the reference solution, which takes into account thephysics of the fracturing-fluid invasion and its back production.

Fracturedwell Well

Fracture

(a) (b)

Fig. 10Grid systems for the fractured well in a full-field simulation. (a) Coarse-grid simulation; (b) local grid refinement for the ref-erence solution simulation.

TABLE 2GRIDBLOCK SIZES AROUND THE FRACTURE IN THE LOCALLY REFINED ZONE

FOR THE REFERENCE MODEL

Block Size in x-Direction Block Size in y-Direction

25 15 15 10 5 2.5 1.2 25 15 10 8 6 3.5 2 1.5 1 0.8 0.7

0.6 0.3 0.2 0.1 0.1 0.44 0.3 0.2 0.15 0.1 0.085 0.06 0.05 0.04

0.03 0.02 0.01 0.010.1 0.1 0.2 0.3 0.6 1.2

0.012.5 5 9 9 9 9 8 9 9 9 9 5 2.5

0.01 0.01 0.02 0.03 0.04 0.051.2 0.6 0.3 0.2 0.1 0.1

0.06 0.085 0.1 0.15 0.2 0.3 0.44 0.7 0.8 1

1.5 2 3.5 6 8 10 15 25

0.1 0.1 0.2 0.3 0.6

1.2 2.5 5 10 15 15 25

* Bold numbers correspond to the fracture.

10000

100000

1000000

Reference

Coarse grid without coupled modeling

Gas

flow

rate

(m3 /d

ay)

1000100101Time (day)

Fig. 11Gas flow rate with the coarse-grid simulation using the equivalent wellbore radius.


We perform first a coarse-grid simulation with the choke skinproposed by Mukherjee and Economides (1991). This skin is ini-tially proposed for the analytical modeling of well performancesfor fractured horizontal wells. Fig. 13 presents the coarse-gridsimulation results with the analytical choke skin and with the skinobtained from the inversion Eq. 11. To calculate the skin from theinversion, fracturing-fluid-induced formation damage is simulatedwith a fine-grid near-well model in a small domain around thefracture, and the inversion procedure is applied to match the gasproduction from 200 to 500 days by modifying the numerical PIvalues (or skin factors) on a local coarse-grid system in the samenear-well domain. The obtained numerical PIs (or skins) are usedfor the full-field coarse-grid simulation. It is found that the analyt-ical choke skin is not suitable for the numerical simulation, andthe errors are large in both the cleanup period and long-term pro-duction. Using the numerical PI (or skin) from the inversion givesmuch better results for the coarse-grid simulation. It gives accu-rate long-term production calculation, but we have always inaccu-rate results during a long transient cleanup period, which has asignificant impact on the cumulative gas production in this case.

In general, if the transient cleanup period is short, using nu-merical PIs (or skins) determined from the inversion can be con-sidered suitable for the coarse-grid simulation. If the cleanupperiod is long, the production during this period cannot beneglected. In this case, we propose to use the coupled modelingtechnique. This technique provides time-dependent numerical PIsto improve the coarse-grid simulation accuracy during the cleanupperiod.

Coupled Modeling for Fractured Wells

Coupled Modeling Technique. The coupled modeling techniquewas presented by Ding (2010, 2011) for the coupled simulationbetween a near-wellbore model and a reservoir model. Here, wepresent its application to fractured wells. The algorithm of thecoupled modeling is summarized by the following steps (Fig. 14):

1. Run the full-field reservoir model (RM) to the time T0, thebeginning of the coupled simulation.

2. Initialize the near-well model (NW) for pressure and satura-tion using data from the reservoir model with appropriate down-scaling techniques.

3a. Run the full-field RM from time T0 to T1.3b. Run the NW model from T0 to T1.4a. Update numerical PIs for the full-field RM.4b. Update boundary conditions for the NW model using the

full-field simulation results.5. Repeat Steps 3 and 4 with a new time interval (from T1 to

T2, , from Tn1 to Tn).6. Stop coupled modeling and continue the full-field simula-

tion (RM) from Tn.Data exchanges between the reservoir model and the near-well

model are performed through updating numerical PIs for the res-ervoir model and boundary conditions for the near-well model.The updated numerical PIs correct inaccuracies in the coarse-gridsimulation.

The coupled approach is generally not CPU-time-consuming,because the full-field model is sequentially simulated. Moreover,this method allows the implementation of a local timestepping

WellWell

Frac

ture

s

(a) (b)

Fig. 12Grid systems for the multifractured horizontal well simulation. (a) Coarse grid (wellblocks are in the middle layer); (b) localgrid refinement for the reference solution simulation.

10000

100000

Gas

pro

duct

ion

(m3 /d

ay)

Reference solution

Coarse grid simulation with the analytical choke skin

Coarse grid simulation with the skin from inversion

1000100101Time (day)

Fig. 13Gas flow rate with the coarse-grid simulations.


strategy (the NW grid, adapted to complex physics around thewellbore and the fracture, needs smaller timesteps compared withthe timesteps on the RM model). The near-well model is used as apredictor of the numerical PI on the full-field reservoir grid. Thisstrategy improves considerably the modeling of fractured wells ina full-field reservoir simulation.

Numerical Examples. Example 5Coupled Modeling for aHydraulically Fractured Vertical Well. Consider again the frac-tured vertical well with the coarse-grid model in Example 3.Now, we perform a coupled modeling by constructing a fine-gridnear-well model in a small domain around the well and the frac-ture, as shown in Fig. 15. Time-dependent numerical PIs areupdated for the coarse-grid model during the coupled simulation.

First, a coupled modeling of 50 days is performed, whichincludes 1 day of hydraulic fracturing (fracturing-fluid invasion),2 days of well closure, and 47 days of production, with timesteps

for data exchange every 0.1 day. Fig. 16 shows the results of thecoupled modeling with both the near-well fine-grid and the full-field coarse-grid simulations. The near-well model simulation isended at the 50th day, while the coarse-grid simulation continueswith the final updated numerical PIs. Both the near-well modeland the coarse-grid model give results very close to the referencesolution in the coupling period. After the coupling period, thecoarse-grid simulation can still give satisfactory results, becausethe final updated numerical PI is suitable for the long-term pro-duction simulation. It shows that a coupled modeling of 47 daysduring the gas production is sufficient. The areas of the fractur-ing-fluid invasion around the fracture are shown in Fig. 17 forboth the reference solution and the solution from the near-well-bore model. The zones of the fracturing fluid invasion are thesame.

It has to be mentioned that the reservoir is in capillary pressurenonequilibrium initial state. The initial reservoir water saturationis 0.2 and the irreducible water saturation is 0.28. Because the

Reservoir model (RM)

Near-well model (NW)





Tn: end of thecoupled modeling

T

Update numerical PIs (skins)

Initialize the near-well model



Reservoirmodel (RM)

Near-wellmodel (NW)

T0: start of thecoupled modeling

Update boundary conditions



RM (T0)

RM (T1)

RM (T2)

RM (Tn)

NW (T0)

NW (T1)

NW (T2)

NW (Tn)

Fig. 14Coupled modeling algorithm.

Well Well

(a) (b)

Fig. 15Grid systems for the coupled simulation. (a) Full-field coarse-grid model; (b) near-well fine-grid model.


coarse-grid wellblock is very large, almost all injected fracturingfluid is blocked in the coarse wellblock and cannot be reproduced.The water (fracturing fluid) production cannot be correctly simu-lated with the coarse-grid system. However, the prediction ofwater production is not always required if we are particularlyinterested in the gas production with a full-field model.

Example 6Coupled Modeling for a MultifracturedHorizontal Well. Now, let us consider the coupled modeling fora multifractured horizontal well. Consider the same case asdescribed in Example 4. The grid systems for the coupled model-ing are given in Fig. 18, where the coarse grid is identical to thatin Example 4 and a very fine grid is used for the near-well model

100001 10

Time (day)100

100000

1000000

Gas

pro

duct

ion

(m3 /d

ay)

ReferenceCoarse grid with coupled modelingNear-well modelCoarse grid with a constant skin

Fig. 16Gas flow rate from the coupled modeling.

4.4

m

4.4

m

Sw

(a) (b)

Sw

Near-well model Reference Solution 10.90.80.70.60.50.40.30.20.10

10.90.80.70.60.50.40.30.20.10

Fig. 17Area of fracturing-fluid invasion. (a) Near-well model; (b) reference solution.

Well

Well

(a) (b)

Fig. 18Grid systems for the coupled modeling of the multifractured horizontal well. (a) Full-field coarse-grid model; (b) near-wellfine-grid model.


simulation around the fracture. Both homogeneous and heteroge-neous media are considered.

The cleanup period is very long for this multifractured hori-zontal well, as shown in Example 4. Therefore, a long duration isrequired for the coupled modeling. Fig. 19 presents the results ofthe coupled simulation for the gas flow rate in the homogeneouscase with a coupled duration of 300 days. The results of the coupledmodeling are very close to the reference solution. The coarse-gridsimulation shows a very high gas rate at the first step; then, the nu-

merical PI is corrected to get a reasonable value. Fig. 20 shows thegas flow rate for a coupled modeling of 100 days. In spite of a rela-tively long duration of the coupled modeling, the results are notgood enough and the coarse-grid simulation starts to diverge at 100days because of the long cleanup period required for this low-con-ductivity multifractured well.

For the heterogeneous case, the permeability distribution isgenerated with a geostatistical model in a stratigraphic fine gridwith block sizes of 10 m in the x-direction and 10 m in the y-direction. The average horizontal permeability is 0.02 md and thevertical and horizontal permeability ratio is 0.5. An upscaling pro-cedure is applied to get the equivalent coarse-grid permeabilityfor the coarse-grid reservoir model (Fig. 21a). The near-wellmodel permeabilities, which are obtained by using a downscaling(if a near-well gridblock is smaller than the geostatistical grid-block) and an upscaling (if a near-well gridblock is larger than thegeostatistical gridblock) technique, are shown in Fig. 21b. To getthe reference solution, a local grid refinement with the same per-meability as in the near-well model is used around the fracture.Fig. 22 presents the simulation results for a coupled modeling of300 days in this heterogeneous medium, and Fig. 23 presents theresults for a coupled modeling of 100 days. The coarse-grid simu-lation gives very satisfactory results in the heterogeneous mediumfor both coupled modeling of 100 days and 300 days.

The required period for the coupled modeling is generallyunknown, because we dont know a priori the cleanup durationfor a real application. However, an analysis of numerical PI varia-tions during the coupled modeling can provide information on the

10000

100000G

as ra

te (m

3 /day

)Reference Coarse grid with coupled modelingNear-well model

1000100101Time (day)

Fig. 19Gas flow rate for a coupled modeling of 300 days forthe multifractured well in the homogeneous medium.

10000

100000

Gas

rate

(m3 /d

ay)

Reference Coarse grid with coupled modelingNear-well model

1000100101Time (day)

Fig. 20Gas flow rate for a coupled modeling of 100 days forthe multifractured well in the homogeneous medium.

1000 m(a) (b)

1000

m

350 m

450

m

K (mD)K (mD)0.070.063

0.0560.0490.0420.0350.0280.0210.0140.007

0.070.0630.0560.0490.0420.0350.0280.0210.0140.0070

Fig. 21Permeability distribution for the coupled modeling in the heterogeneous medium. (a) Coarse-grid permeability (middlelayer); (b) permeability in the near-well model (middle layer).

10000

100000

Gas

pro

duct

ion

(m3 /d

ay) Reference

Coarse grid with coupled modelingNear-well model

1000100101Time (day)

Fig. 22Gas flow rate for a coupled modeling of 300 days inthe heterogeneous medium.


necessary duration for a coupled simulation. For example, it isreasonable to stop a coupled modeling when the numerical PI var-iation is small. The analysis of the required duration for a coupledmodeling is essential for the success of a coupled simulation infield applications and is an ongoing effort.

Conclusions

The fracturing-fluid-induced formation damage on a fracturedwell in tight gas reservoirs has been studied using a near-wellmodel. The hydraulic damage can be severe particularly in low-conductivity fracture cases or with specific relative permeabilitycurves. Moreover, numerical models have shown that the damagein a fractured horizontal well can be much greater than that in afractured vertical well. The fracture conductivity is the key issuefor the gas production with fractured horizontal wells in very low-permeability reservoirs.

We also examined fractured wells on coarse-grid full-fieldsimulations in tight reservoirs. An analytical skin cannot, in gen-eral, correctly model well performances with a coarse-grid simu-lation. However, an inversion procedure can be used to determinea numerical skin, which is suitable to simulate long-term well pro-ductions. But using a constant skin cannot correctly simulate thetransient behavior during the long cleanup period and predict cu-mulative gas productions.

To simulate the whole production behavior of fractured wells,especially the transient behavior during the long cleanup period,with a coarse-grid model, the coupled modeling technique can beused. A sector model for determining skin during transient flow iscoupled with a full-field reservoir simulator to make appropriateadjustments to the well skin factors so that flow behavior in thefull-field model can be modeled correctly using variable skin fac-tors over the whole life of the project. The coupling algorithm isvalidated on an example of multifractured wells in a heterogene-ous media.

Nomenclature

cpw mole fraction of polymer in waterC conductivityD wellblock lengthg gravityh wellblock heightkr relative permeabilityK absolute permeability tensorL fracture half lengthPI productivity indexq well flow rate obtained from the near-well modelQ well flow raterw wellbore radiusr0 equivalent wellblock radiusRm mobility reduction factorS skin

Sm saturation of the phase m

t timeu velocityw fracture width

x,y,z coordinatesDx,Dy,Dz gridblock sizes

l viscositypF polymer absorbed on the rockn mole densityq density/ porosityU potential

Subscripts

frac fractureo oilp polymer

res reservoirw water

Acknowledgments

The authors would like to thank GDFSUEZ and IFPEN for sup-porting the publication of this work.

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Didier-Yu Ding is a Principal Research Engineer at IFP in RueilMalmaison, France. His research interests include numericalmodeling, reservoir simulation and characterization, complexwells, and near-well flow. He holds a BS degree in mathemat-ics from Peking University and MS and PhD degrees in appliedmathematics from the Universite de Paris.

Hoel Langouet is a Research Engineer at EDF R&D in the fieldof quality measurements and uncertainties. He holds an MScdegree in applied mathematics from the Paris VI Universityand a PhD degree, also in applied mathematics, from IFPEnergies nouvelles and University of Nice Sophia Antipolis.

Laurent Jeannin joined GDFSUEZ E&P International in 2008 asSenior Reservoir Engineer. He worked from 19982008 as aResearch Geoscientist at IFPEN in the Transfer in Porous Mediaand Mechanics Departments. He holds a Masters degree fromEcole desMines de Saint-Etienne and a PhD degree in physics.


Documents

SPE-153255-PA (Simulation of Fracturing-Induced Formation Damage and Gas Production From Fractured Wells in Tight Gas Reservoirs)