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Abstract Ensuring quantitative prediction of eroded sand volume is a major challenge for companies, which seek to conduct effective sand management. This is particularly a key point for Cold Heavy Oil Production With Sand.

IFP has been studying the geomechanical aspects of heavy oil cold production for several years from both the experimental and theoretical points of view [Deruyter & al., 1998], [Nauroy J.-F., 1999]. While experimental studies of sand erosion are mostly based on linear flow through cylindrical cells [Tremblay & al., 1995], IFP has designed a special oedometric cell to simulate a radial flow around a well drilled in an unconsolidated sand reservoir.

The current device allowed to observe two types of erosion figure under CT-scan, defined as "cavity" or "spread erosion". Two main key parameters governing erosion have been identified.

Dimensional analysis shows that CHOPS in situ conditions should lead to a "cavity" type erosion. Various theoretical models describing sand erosion and mixed sand/fluids flow have been investigated. An algorithm allowing to predict the formation of a cavity has notably been defined and already validated for a 1D numerical modeling. A 2D numerical modeling is in progress.

Introduction Cold Heavy Oil Production With Sand (CHOPS) is one of the most effective production method for heavy oils located in unconsolidated reservoirs, e. g. in Athabasca. In some cases of conventional oil production from poorly consolidated reservoirs, Sand Management appears to be more profitable than total Sand Control. The challenge is now to predict, for a given well, the ratio of eroded sand to produced oil as a function of reservoir and production parameters.

IFP has been studying the geomechanical aspects of heavy oil cold production for several years from both the experimental and theoretical point of view [Deruyter & al., 1998], [Nauroy J.-F., 1999]. IFP has notably designed a special oedometric cell to simulate a radial flow around a well drilled in an unconsolidated sand reservoir (Fig. 1).

At the center of the cell, a metallic tube perforated by several holes and going through the sand bed represents the well and its perforations. A hydraulically loaded piston applies an axial stress to the sand bed, while its radial strain is zero. The fluid is injected at the periphery of the cell to ensure a radial flow. The drawdown pressure (pressure difference between the periphery and the center of the cell) is controlled and can be increased to enhance sand production. While sand is being produced, the sand bed can be observed under CT-scan.

We will first present a rapid review of the various experimental results obtained on sand erosion. We will then focus on IFP radial flow cell and the two types of erosion figure ("cavity" and "spread erosion") observed under CT-scan according to two main key parameters.

As dimensional analysis shows that CHOPS in situ conditions should lead to a "cavity" type erosion, modeling efforts have been devoted to the formation of a cavity. We will point out the main encountered difficulties and describe the retained solutions.

State of the art in experimental study of sand erosion When considering the experimental results that have been obtained in the past years on sand erosion, several types of experimental device have to be distinguished: cylindrical cells with axial flow, plane cells with radial flow and plane cells with plane strains.

Cylindrical cell with axial flow

The Alberta Research Council has conducted various tests, which consist in setting an axial flow through a cylindrical cell, first with one perforation and an imposed flow or pressure gradient [Tremblay B. & al., 1996, 1998], and then with two perforations [Tremblay B. & al., 2002].

These experiments have lead to the development in the sand bed of one or two "wormholes" according to the number of perforations. But the shape of these "wormholes" appears to be strongly dependent on the geometry and dimensions of the cell. Indeed, the diameter of the "wormholes" observed with the two first cells was around 4 cm. While, in the third cell,

SPE 86949

Sand Erosion in Cold Heavy-Oil Production Yalamas T., Nauroy J.-F., Bemer E., Institut Français du Pétrole and Dormieux L., Garnier D., Laboratoire des Matériaux et des Structures du Génie Civil

2 SPE 86949

which was larger, one "wormhole" reached a 17-cm diameter. Consequently, these tests do not allow to conclude on the geometry of the flow paths ensuring the rapid communications observed in situ between the wells. Plane Cell with radial flow

During his Ph-D, P. Cerasi has realised tests with a Hele-Shaw cell [Cerasi, 1996]. This cylindrical cell of small thickness (around 1 cm) has a hole at its center, which allows to produce the fluid. The confining pressure is not controlled. While imposing an increasing flow rate, Cerasi has observed three flow types: laminar filtration of the porous medium, erosion instability (some canals free of grain appear), and porous medium liquefaction. The erosion instability features could be linked with the "wormhole" assumption.

Plane Cell with plane strains

The sand is disposed in a parallelepipedic cell (height: 600 mm, length: 900 mm, thickness: 20 mm) and saturated with water. A metallic pipe, placed at the center of the cell with two diametrically opposed holes, represents a casing and its perforations. This experimental device has been developed at IFP, as part of a feasibility study of erosion experimental modeling, to represent a reservoir with a well exploited in cold production and constitute. A confining pressure was first applied followed by a hydraulic gradient, which yielded a flow of water through the sand bed. Some tests have lead to sand flow whose characteristics give information on the phenomena taking place inside the sand bed.

Initial tests with Fontainebleau Sand have lead to an immediate coming of sand after the drawdown. A model sand with a less regular grain shape ensuring more concavo-convex contacts has then been chosen. Sand arrivals interrupted by periods of free of sand water flow have notably been observed. This could result from the development of stable archs.

The beginning of sand erosion appears to depend on hydraulic gradient and confining pressure. Cylindrical cell with radial flow

Taking into account the interesting results obtained with the feasibility study cell, IFP has designed a new experimental device (Fig.1). At the center of the cell, a metallic tube perforated by several holes and going through the sand bed represents the well and its perforations. A hydraulically loaded piston applies an axial stress to the sand bed, while its radial strain is zero. The fluid is injected at the periphery of the cell to ensure a radial flow. The drawdown pressure (pressure difference between the periphery and the center of the cell) is controlled and can be increased to enhance sand production. While sand is being produced, the sand bed can be observed under CT-scan. Very significant improvement have been made:

the fluid flow through the sand bed is radial, the confining pressure on the sand bed is

well controlled, the cell is designed to be opered under CT-scan in

order to get pictures of the sand bed during tests, one of the key points being that the geometry of this

cell does not favour any erosion geometry.

This device has been operated since the end of 2001 and more than 30 tests have been realised.

Principal features of the experimental device

The cell geometry is an oedometric one: internal diameter of the cell: 30 cm height of the cell: 20 cm height of the sand bed: 6.5 cm

The metallic tube representing the well has a 1-cm diameter. In this tube, one or several holes, which are 3 to 5 mm in diameter, represent the perforations. These holes could be kept closed or opened.

Three independent porous sectors, located at the periphery of the cell, allow to inject the interstitial fluid. For the moment, only water has been used. When both the sectors and the center holes are open, a radial flow is created in the sand bed.

A piston is placed at the top of the sand bed in order to applied a uniform axial stress (confining pressure) on the sand bed.

A GDS pump is used to control the confining pressure imposed on the piston.

One buffer cell is used to maintain a steady upstream pressure.

To collect the sand at the exit of the main cell and to control the downstream pressure, a receptive cell with a pressure-regulating valve is used.

A LVDT transducer is placed between the piston and the cap of the cell to record the sand bed axial strain.

Test process

Setting and consolidation The sand is disposed in the cell in successive layers up to a

height of 6.5 cm and the obtained sand bed is slightly confined. The sand is then satured with the pore fluid. Only water has yet been used. The desired confining and pore pressures are finally applied.

After the sand bed consolidation, CT-scan pictures of the sand bed every 3-mm are taken and defined as the initial state of the sand bed.

The perforations, which have been kept closed during the consolidation phase, are now opened, the downstream and upstream pressures being equal.

Sand bed

Axial stress

Reservoir pressure

Well

Fig. 1: Sand production cell

SPE 86949 3

Production phase The downstream pressure is then progressively decreased

to a given value and a radial flow appears between the injection sectors and the perforations. Depending on the hydraulic gradient, confining pressure and relative density, we do or do not observe sand comings.

When sand comings are observed, we stop the hydraulic flow by closing the perforations and take new CT-scan pictures of the sand bed.

We repeat this production phase several times for each test. Preliminary tests

Sand nature influence In Canadian reservoirs (e.g. Elk Point), the sand is both

very fine (d50<300 µm) and tangled. Dusseault and Van Domselaar (1982) give a porosity of 30 to 32% for Cold Lake field and 28 to 34% for Athabasca field. They point out the high number of concavo-convex contacts, which result of sand dissolution and recrystallization phenomena [Dusseault & al., 1978].

From a granulometric point of view, this sand is very close to Fontainebleau sand. We thus first used this sand, which led to immediate and massive sand coming. We then chose a rougher model sand showing more concavo-convex contacts and thus an apparent cohesion.

Perforation diameter Three different perforation diameters have successively

been tested: 3-mm, 4-mm, and 5-mm, leading to different size ratio between the sand grains and perforations. With the smaller perforations, no coming of sand could be observed denoting a scale effect. The 5-mm diameter perforation is about 8 times larger than the biggest grains. This value has to be compared to the in situ size ratio of 1 to 100 between the sand grains and the perforations, which could not be reproduced with the cell. Tests results

All the tests presented here have been realized with our model sand and a 5-mm diameter perforation.

Erosion schemes Two erosion schemes have been observed (Fig. 3 & 4): development of a cavity, spread erosion (sand coming massively with a drop of

density in one area of the sand bed). The main governing parameters appear to be the effective

consolidation pressure and the initial relative density of the sand bed before consolidation (fig 2).

We can notice that the initial relative density varies from 65 to 85 % depending essentially of the setting of the sand bed (which is done by hand).

Spread erosion During tests 8, 11, 12, 20, 27 and 28, massive sand coming

has been observed since the first production phase. When the cell was opened, at the end of the test, we noticed a weak area of lesser density in the sand bed, which also appears clearly on CT-scan pictures (Fig. 3).

The exact geometry of the concerned area is difficult to define accurately and is not exactly the same for all the tests. But it always starts at the perforation and spreads toward the periphery.

Knowing the final mass of produced sand, we tried to estimate the density of the weak area.

In the case of test 27 (Fig. 3), we obtained a relative density in the weak area less by 40% than the relative density after consolidation.

Development of a cavity Cavity close to the well For a higher density or a more important confining

pressure, the erosion process is very different. Prior to induce sand coming under an increasing drawdown, we generally had to reduce the effective confining pressure.

The sand is no more coming massively. We observe alternatively sand bursts (around 300 mm3 of weak sand) and "grain to grain" comings, while CT-Scan pictures show the formation of a cavity in front of the perforation. The cavity is first very localized in front of the perforation, but its height and its diameter increase as water and sand are produced (Fig. 4). The final mass of produced sand is small compared to the massive sand production associated to spread erosion. As long as we product water, we keep on producing sand and so enlarging the cavity. But, if the water flow is stopped, the cavity is mechanically stable.

0

100

200

300

400

500

600

700

60 65 70 75 80 85 90 95 100

Initial Relative Density (%)

Pcef

f (kP

a)

20 28

12 11

8

27

13 21

15

17

23

22 30 31

32

Spread erosion

Cavity

Fig. 2: Prediction of erosion figures

Test n° 27

After the first production phase. After the second production phase.

Weak density area Cavity close to the periphery

Fig. 3: Erosion localization (test n° 27)

4 SPE 86949

Fig. 4: Cavity close to the well (test n°17)

Cavity within the sand bed Tests 30 & 31 have finally led to the formation of a cavity,

but have shown a massive sand production at the start. For these tests, the cavities have not been initiated close to the well but within the sand bed. In the case of test 30, several production phases have been conducted and led to a gradual increase of the cavity (Fig. 5).

These results show the effect of local heterogeneities in the sand bed density.

Conclusion

The conducted tests have clarified the link between erosion schemes, confining pressure and initial relative density. According to our results, reservoir conditions would lead to the development of a "cavity", whose geometry will depend on the reservoir heterogeneity.

All the tests have been made with water. It would then be interesting to study the influence of the fluid viscosity on the erosion schemes.

Another key parameter could be the granulometry of the sand.

Numerical modeling The mechanisms involved in the erosion of weakly consolidated sandstone are very complex. They notably depend on the geomechanical properties of the sand, on the flow properties of the fluids (oil, water and gas) and on the nature of the sand/fluid and fluid/fluid interactions. The modeling aim is to predict sand production rate and its effect on the oil production rate and the oil recovery ratio.

Three different approaches can be found in the literature: the development of a cylindrical zone of enhanced permeability around the well [Dusseault & al., 1994], the development of wormholes (enhanced permeability channels) from the well [Tremblay & al., 1999], [Dusseault & al., 1997], or a homogenized approach considering the development of an heterogeneous area damaged by sand erosion [Shao & al., 2002], [Wang & al., 2000].

We chose to distinguish two zones: a zone of intact reservoir, which has a poroelastic behavior, and a zone of slurry (mixture of oil and sand), which follows the behavior of a Poiseuille fluid. No assumption on the geometry of the boundary between these two zones is made. We then defined an algorithm, which allows to predict the evolution of the moving boundary between the two zones. This algorithm has been successfully programmed with SCILAB for a 1D modeling.

Modeling assumption

The object is first to develop a tool able to predict the flows of sand and oil during a test in IFP cell. In a second time, this tool will be transposed to real cases.

This paper deals with a 1D modeling. If we consider an experimental production phase where sand is coming, the sand bed could be represented by an external zone of intact sand, which has a poroelastic behavior, and an internal zone of slurry (mixture of oil and sand), which follows the behavior of a Poiseuille fluid (Fig. 6).

We then have to solve an "academic" hydromechanics calculation on the porous medium (intact part of the reservoir) [Dormieux L., Bourgeois E., 2002], with two main difficulties:

the boundary between the slurry and the porous medium evolves as more sand is produced, so the problem to solve has a geometry varying with time,

the boundary conditions (pressure and displacement) at the interface are a priori unknown.

First prodution phase Last prodution phase

Fig. 6: Representation of the sand bed

Initial state

Final state Water produced: 17,5 L

State 1 Water produced: 5 L

State 2 Water produced: 11 L

Fig. 5: Cavity within the sand bed (test n°30)

"Slurry"

V(t)

P2

L(t)

"Intact" sand

x

P1

O

P0

SPE 86949 5

Relation between V, vs and Q V : slurry velocity V=ks(P0-P1)/L(t) [m/s]

sv : skeleton velocity in porous medium [m/s] Q : filtrationvector in porous medium )( sf vvQ −= ϕ [m/s]

Mass conservation at the slurry/porous medium

interface gives:

:yieldswhich

sandfor ))(1())(1(

oilfor )()(

)()(

)(

)(

VvQ

LVcLv

LVcLv

sLL

sL

fL

=+

⎪⎩

⎪⎨⎧

−−=−−

−=−

&&

&&

ϕ

ϕ

Hydromechanical study of the porous medium Initial conditions

⎩⎨⎧

==

=0

0At t 10

LPP

x=L(t) x=H Concerned

equation Hydraulics VvQ s

LL =+ )()( p=P2 Diffusion

Mechanics 0Pxx −=σ 0=ξ Mechanical

balance

Constitutive equations

Mechanical balance: 0)( =+∂∂

xxx fxσ

The volumetric force, )(xkf fx ξ−= has to be introduced due to the 1D modeling to represent the friction stresses at the porous medium contour ([kf]=[Pa.m-2]). It will not appear in the 2D modeling.

Diffusion equation: 2

2

xPk p ∂

∂=Φ&

where Φ is the volumetric flow of fluid mass and kp is the hydraulic conductivity of the porous medium.

Sand behavior: The intact sand is represented by a brittle poroelastic

medium.

⎪⎩

⎪⎨⎧

+=

−+=

xx

xxxx

bMdPd

bdPdd

εφ

εµλσ )2( 0

with Cxx ′≤σ where:

µλ and 0 are Lame coefficients b is Biot coefficient (b=1) M is Biot modulus

Resolution algorithm

We consider an initial state defined by a cavity of length L(t0)=L with no slurry flow V(t0)=0 and a uniform pressure in the porous medium P1(t0)=P2(t0)=P0(t0)=1.

The stress states of pressure and stress in the porous

medium are then the following:

⎪⎩

⎪⎨

⎧

=+==

−=

0)()()(1)(

1)(

xPxxxP

x

xxeff

xx

σσ

σ

We then drop P1 to zero, while P0 and P2 are kept

unchanged in a first time. The pressure gradient between P0 and P1 induces a displacement velocity in the slurry:

xs eVtL

tPtPktV −=

−= V with

)()()(

)( 10 .

We then run a calculation in the porous medium with these boundary conditions. It is important to note that the fluid pressure in the porous medium at the interface slurry/porous medium is not imposed. This pressure is a result of the poroelastic calculation in the porous medium and is not a priori equal to P0. However, at equilibrium, these two pressures have to be identical. This is ensured through an iterative calculation, which yields the correct P0(t) value.

The calculation conducted with new boundary conditions gives new pressure and stress distributions in the porous medium. Several cases are possible:

The effective stress is in every point lower than the sand strength. The sand bed is then mechanically steady and we can skip to the next time step.

There is an area in the porous medium where the effective stress is higher than the sand strength. The sand bed is then eroded up to the first encountered point of this area called xrup. Staying in the same time step, we run a new calculation with updated boundary conditions: interface position: Lnew(t)=L(t)+xrup slurry pressure at the interface: P0(t)=-σ(xrup)

slurry velocity: )(

)()( 10

tLPtP

ktVnew

s−

=

Fig. 7: Initial boundary conditions on the porous medium

P0(t0)=P2

H

L(t)

ξ=0P2

Porous medium

φ, Q, vs V=0 Slurry

6 SPE 86949

Main results The numerical results presented here do not pretend to be

quantitative. The object is only to present a qualitative behavior.

Steady state The 1D modeling allows to analytically determine an

asymptotic steady state where pressure and stress no more depend on time. This steady state is physically admissible if the maximum effective stress in the sand bed is lower than the sand strength, that is if:

µλ 2 ; ; ;

:

1)]1(tanh[])1(1[

1

0 +=

∆′

===

≤−−+

fHcL

s

pk

LHLkHc

kHA

PCA

HLA

kk

A

where

AAAAAA

Using the above equation to determine material

characteristics and pressure boundary conditions theoretically leading to a steady state after an erosion of half the length of the sand bed (AL=1/2), we verified that, fed with those parameters, our numerical model actually tended towards a steady state (Fig. 8).

Production curves

The model gives at each time step the length of the cavity

and the velocity of the slurry, which allows to determine: the cumulated oil volume produced at the well, the cumulated

sand volume eroded at the slurry/porous medium interface and the concentration of oil (resp. sand) in the slurry (Fig. 9). Taking into account the velocity of the slurry and its concentration in sand, we can also deduce the volume of sand effectively produced at the well.

Conclusions The first results obtained with our sand erosion algorithm are very encouraging. Indeed, when this algorithm will be introduced in a 3D finite elements program, we will be able to predict the flows of sand and oil from only a few classical fluid and sand characteristics. Note particularly that no assumption on the geometry of the cavity is required.

The calculations could be improved through more accurate constitutive laws for the sand, the slurry and the oil, especially in the case of heavy oil.

A 2D modeling is in progress and its results will be compared with the tests conducted in IFP cell.

Even if the study has initially been initiated for CHOPS, the results can be adapted to conduct sand management for conventional oils. Acknowledgments We would like to thank Total, and especially Philippe Marchina, for their support on the experimental work and INRIA, ENPC and the SCILAB Consortium for the development of this free scientific software. References 1. Deruyter C., Moulu J.-C., Nauroy J.-F., Renard G., Sarda J.-P.

Bibliographie sur la "Production froide des huiles visqueuses", ARTEP, 1998.

2. Nauroy, J.F., 1999, "Mécanismes de production massive de sable dans les huiles lourdes", Rapport IFP n°45577.

3. Tremblay, B., Sedgwick, G., and Forshner, K., 1995, "Imaging of sand production in a horizontal pack by X-ray computed tomography", SPE 30248.

4. Tremblay B., Sedgwick G. and Forshner K., "Simulation of Cold Production in Heavy Oil Reservoirs: Wormhole Dynamics", SPE 35387, 1996.

5. Tremblay B., Sedgwick G. and Don Vu, "CT Imaging of Wormhole Growth under Solution-gas Drive", SPE 39638, 1998.

6. Tremblay B., Oldakowski K., "Wormhole Growth and interaction in a large sand pack", SPE 39638, 2002.

7. Cerasi P., "Etude de la croissance d’une instabilité d’érosion dans un milieu poreux non consolidé. Application à l’angiogénèse", Thèse de l’université Paris 7-Denis Diderot, 1996.

8. Dusseault M. and Van Domselaar H. "Unconsolidated sand sampling in canadian and venezuelan oil sands", Heavy Crude and Tar Sands, 1982.

9. Dusseault M. and Morgerstern N., "Shear strength of Athabasca oil sands", Canadian Geotechnical Journal 15, 2, 1978.

10. Dusseault M., Dulien F. and Geilikman M., "Sand production as a viscoplastic granular flow", SPE 27343, 1994.

11. Tremblay B., Yuan J. Y. and Babchin A., "A wormhole network model of cold production in heavy oil", SPE 54097, 1999.

12. Dusseault M. and Geilikman M., "Dynamics of wormholes and enhancement of fluid production", 48th An. Tech. Meeting of the Petroleum Society, 1997.

13. Shao J.F. and Marchina P., "A damage mechanics approach for the modelling of sand production in heavy oil reservoirs", SPE/ISRM 78167, 2002.

Fig. 8: Effective stress in the sand bed

Cumulated Oil Volume

Cumulated Eroded Sand Volume at the interface (*10)

Cumulated Produced Sand Volume at the well (*10) Oil Concentration

in the slurry

Time

Fig. 9: Produced volume in function of time

Traction Compression

Theoretical curve obtained for steady state

Curve obtained with numerical program (after 4000 time steps)

Stress (MPa)

Slurry Intact sand bed

SPE 86949 7

14. Wan R.G. and Wang J., "Modelling sand production within a continuum mechanics framework", CIPC 2000, Calgary, Alberta.

15. Dormieux L., Bourgeois E., "Introduction à la mécanique des milieux poreux", Presses des Ponts et Chaussées, 2002.

Notations c : oil concentration in the slurry φ : porous medium porosity Q : filtration vector in porous medium (Q= φ(vf- vs)) [m/s]

fv : fluid velocity in porous medium [m/s] sv : skeleton velocity in porous medium [m/s]

V : slurry velocity V=ks(P0-P1)/L(t) [m/s] ks : hydraulic conductivity in the slurry [m2Pa-1s-1] kp : hydraulic conductivity in the porous medium [m2Pa-1s-1] P1 : well pressure [Pa] P2 : reservoir pressure [Pa] P0 : slurry pressure at slurry/sand interface [Pa] ξ : axial strain σxx : total axial stress [Pa] σeff : effective axial stress [Pa] C ′ : sand strength [Pa]