SPE 75158AN ALTERNATIVE MODEL

FOR FILTER CAKE FORMATION IN FRACTURES

Randy Seright New Mexico Petroleum

Recovery Research Center

TOPICS COVERED IN SPE 75158 1. New model for filter cake formation in

fractures.2. Effects of temperature and gel composition

on extrusion for Cr(III)-acetate-HPAM gels. 3. Extrusion behavior for a guar-borate gel. 4. Effects of gel composition, fracture width,

and addition of particulates on washout of gels from fractures (during brine injection).

WHAT ARE GEL PROPERTIES DURING EXTRUSION THROUGH FRACTURES?

GEL USED: Cr(III)-acetate-HPAM

0.5% Ciba Alcoflood 935 HPAM,0.0417% Cr(III)-acetate,1% NaCl, 0.1% CaCl2, pH=6. Gelation time ~ 5 hrs at 41°C.Aged 24 hours at 41°C before use.Injected into brine-saturated fracturedcores, 41°C.

PROPERTIES OF Cr(III)-ACETATE-HPAM GEL DURING EXTRUSION THROUGH FRACTURES

• A minimum pressure gradient must be met

before a formed gel will extrude through a fracture.

• Once the minimum pressure gradient is met, the pressure gradient during gel extrusion is not sensitive to injection rate.

• Once the fracture is filled with gel, pressure gradients are stable (no progressive plugging).

• The pressure gradient for gel extrusion varies inversely with the square of fracture width.

PROPERTIES OF Cr(III)-ACETATE-HPAM GEL DURING EXTRUSION THROUGH FRACTURES

• Gels dehydrate, thus retarding the rate of movement of the gel front.

• Although water leaks off through the fracture faces, crosslinked polymer cannot.

• Dehydrated (concentrated) gel is immobile.

• Mobile gel is the same as the injected gel.

• Mobile gel wormholes through immobile gel.

0.01

0.1

1

10

0.0001 0.001 0.01 0.1 1 10

Time, days

Le

ak

off

ra

te,

ft/d

129 ft/d (12x12-in. fracture)413 ft/d (6x1.5-in. fracture)413 ft/d (12x12-in. fracture)413 ft/d (48x1.5-in. fracture)1,030 ft/d (48x1.5-in. fracture)4,130 ft/d (48x1.5-in. fracture)33,100 ft/d (48x1.5-in fracture)

ul = 0.05 t -0.5Average Injection Flux

Leakoff rate = total matrix production ratetotal fracture area

wf = 0.04 in.

WHY DOES ul = 0.05 t -0.5 ? Analogy with leakoff from hydraulic fracturing:ul = C1 t -0.5 from SPE Monograph Volume 2 (1970), p. 33.Basis: Assume formation of a filter cake of uniform thickness, L, and permeability, k, with pressure drop, p.

ul = p k / ( L) and L = C2 ul dt

Solution: ul = C1 t -0.5 C1 = [pk/(C2)]0.5

porous rock

fracture face

filter cake, k L

fluid flow in fracture

water leakoffp

WHY DOES ul = 0.05 t -0.5 ?

Our problem is slightly different:• The filter cake is

not areally uniform. • Fresh gel

wormholes through concentrated gel.

0

0.2

0.4

0.6

0.8

1

0.0001 0.001 0.01 0.1 1 10Time, days

Fra

ctio

n

Fraction of fracture area

covered by immobile

concentrated gel

1 minute

30 minutes

Fraction of fracture area

covered by mobile

wormhole gel

BASIS OF NEW MODEL (Model details are in SPE 75158): On first contact, fracture area is covered with mobile gel.With time, more and more concentrated gel accumulates.Area contacted by mobile gel decreases with time.Mobile gel forms wormholes through immobile gel.Dominant leakoff is from mobile (wormhole) gel.

CONVENTIONAL FILTRATION MODELVERSUS THE NEW MODEL (SPE 75158)

CONVENTIONAL MODEL ASSUMES:• Areally uniform coverage with filter cake.• Leakoff rate decreases with time because the

filter cake becomes thicker with time.

NEW MODEL ASSUMES:• Two types of areal coverage• Mobile gel—the dominant water source.• Immobile gel—minor water source.

• Leakoff rate decreases with time because the area covered by mobile gel decreases with time.

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0.1

1

10

0.0001 0.001 0.01 0.1 1 10Time, days

Le

ak

off

ra

te, ft

/d

0.02

0.04

0.08

0.16

ul = 0.05 t -0.5

wf,inches

Gel: 0.5% HPAM, 0.0417% Cr(III)-acetate, 41°C.

Flux: 129 to 66,200 ft/d,Lf : 0.5 to 32 ft,hf : 1.5 to 12 inches,wf : 0.02 to 0.16 inches.

Summary of all tests to date at 41°C.

New modelul = um / [1 + ul dt /wf ]

Conventionalfilter cake model New model

Vertical viewsintersecting the fractures

Porous rock

Filter cake orconcentrated gel

Active flow path

Fra

ctu

re h

eig

ht

{ {

Fracture width

Pressure gradients required to extrude a Cr(III)-acetate-HPAM gel through fractures

0.1

1

10

100

1000

0.001 0.01 0.1 1

Fracture width, inches

Pre

ssur

e gr

adie

nt, p

si/ft

650-mD sandstone50-mD sandstone1.5-mD limestone

dp/dl=0.02/wf2

Conventionalfilter cake model New model

Vertical viewsintersecting the fractures

Porous rock

Filter cake orconcentrated gel

Active flow path

Fra

ctu

re h

eig

ht

{ {

Fracture width

1

10

100

0 10 20 30 40 50 60 70 80 90 100Fracture volumes of gel injected

Pre

ssu

re g

rad

ien

t, p

si/f

t

Pressure Behavior in the Fracture During

Gel Injection

Gel injection rate = 200 cm3/hr or 413 ft/d,Lf x hf x wf = 48x1.5x0.04-in.

After 1st gel contact, the conventional model predicts that flow channel width should decrease and pressure gradient should increase with gel throughput. The new model predicts that they should remain about the same.

CONCLUSIONS For extrusion of Cr(III)-acetate-HPAM gels through

fractures in water shutoff applications, a new filter cake model was developed that:

1. is based on fracture area in contact with immobile concentrated gel increasing with time rather than filter cake thickness increasing with time.

2. predicts leakoff rates similar to those for the conventional filter cake model.

3. correctly predicts that pressure gradients during gel extrusion do not increase with throughput.

4. may be of interest in other areas (i.e., hydraulic fracturing, produced water re-injection).

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0.0001 0.001 0.01 0.1 1 10Time, days

Av

era

ge

le

ak

off

ra

te,

ft/d

New model for Cr(III)-acetate-HPAM

0.36% guar, 0.018% NaBO2,0.24% tallow soap, 0.1% surfactant, aged 1 day at 40°C,Lf x hf x wf = 6x1.5x0.04 in., Injection flux = 4,130 ft/d.

LEAKOFF RATES: Guar-borate vs. Cr(III)-acetate-HPAM

Average dp/dl = 21.7 psi/ft,Breakthrough at 9.2 fracture volumes

0.36% guar, 0.018% NaBO2, 0.24% tallow soap, 0.1% surfactant, aged 1 day at 40°C, Lf x hf x wf = 12x12x0.04 in.

Flo

w d

irection

Compared to the conventional filter cake model, if dp/dl and the total filter cake volume are fixed, the new leakoff model predicts:

•similar leakoff rate behavior,•higher average fluid velocities,•higher shear rates at the fracture wall,•higher shear stresses at the fracture wall.

 

wc = flow opening for conventional filter cake model

ww = wormhole width ww/ wc > 1 -1 n 0

w uave w dp/dl

Constant pressure gradient

(ww /wc)1/(n+1) (ww /wc)

(n+2)/(n+1) ww /wc 1

Constant injection

ratewc /ww 1 (wc /ww)(n+1) (wc /ww)(n+2)

PROPERTY COMPARISONS FOR A POWER-LAW FLUID: New Model Prediction Divided by Conventional Model Prediction