Immiscible Displacement

8/6/2019 Immiscible Displacement

1/30

Immiscible DisplacementImmiscible Displacementy After primary recovery, a substantial amount of oil remains unrecoverable.

Various methods of improving oil recovery have been developed.

Either water or gas.

y In addition to supplement energy to reservoir as well as push the oiltowards the producing well.

y Immiscible gas injection:-

Inefficient due to:-

1. Non-wetting phase.

2. High mobile due to less viscous,results in excessive bypassing of oil.

3. High relative gas permeability.

However, crestal gas injection is much preferred than pattern gas injection.


2/30

y Immiscible water injection:-

1. More wetting than gas, thus enters larger number of pores in reservoir.

2. High viscous than gas.

3. Good for water wet reservoir than oil wet reservoir.

However, wettability also plays important role on the ultimate oil recovery.

During immiscible displacement process the free energy of the system willchange as the displacement progresses. Our objective is to determinewhether the displacement will lead to a decrease or an increase in the free

energy of the system.

A system in equilibrium always seeks to minimize its free energy.Therefore, a displacement that leads to a decrease in the free energy of

the system is favored.

We wish to examine the direction of energy change during an immiscible

displacement at the pore scale.

Characterization of Microscopic Pore Level immiscible Displacements


3/30

Displacement of aDisplacement of a NonwettingNonwetting Phase by a Wetting PhasePhase by a Wetting Phase

Consider the displacement of a nonwetting phase by a wetting phase, such aswater displacing oil in a water wet medium. The interfacial forces and

interfacial areas at an instant are also shown.

Free energy of the system is also function of the interfacial areas.


4/30

Displacement of a Nonwetting Phase by a Wetting PhaseDisplacement of a Nonwetting Phase by a Wetting Phase

Consider the displacement of a nonwetting phase by a wetting phase, such aswater displacing oil in a water wet medium. The interfacial forces and

interfacial areas at an instant are also shown.

Free energy of the system is also function of the interfacial areas.


5/30

Let the interface move to the right by a small distance dx. The change in the

free energy of the system as the interfacial areas change is given by:-

Suppose the wettingnonwetting phase interface maintains the same shape

during the displacement. Then


6/30

Also, = and =

Finally the change in free energy:-

We also know from the figure:-

Right side of above equation is positive. So left hand side will be more than thepositive number.

we see that the change in the free energy during the displacement is negative.

This means that the free energy will decrease as the nonwetting phase is

displaced by the wetting phase.This is a favored displacement.


7/30

Displacement of a Wetting Phase by aDisplacement of a Wetting Phase by a NonwettingNonwetting PhasePhase

Consider the displacement of a wetting phase by a nonwetting phase, such as

water displacing oil in an oil wet medium.Let the interface move to the right by a small distance dx.

Because the nonwetting phase never contacts the solid,


8/30

Hence free energy of the system:-

This shows that the free energy of the system increases during the

displacement.This is not a favored displacement.

To minimize the increase in free energy of the system during thedisplacement, r* will be as small as possible. Thus, the injected nonwettingphase will channel or finger through the wetting phase leaving behind asignificant wetting phase film and residual wetting phase saturation.

This means that the waterflood efficiency of an oil wet medium will beless than the waterflood efficiency of a water wet medium. Thisobservation is in agreement with the microscopic picture of thedisplacements shown in above figures.


9/30

CapillaryCapillary pressurepressure relationshiprelationship forfor aa porousporous mediummedium

consistingconsisting ofof immiscibleimmiscible phasesphases

When two immiscible fluids are in contact, there is a pressure discontinuity

between the two fluids which depends upon the curvature of the interfaceseparating the two fluids. This pressure difference or excess pressure is knownas the capillary pressure.

The pressure on the concave side of the interface is higher than that on theconvex side of the interface.


10/30

Figure shows a curve interface between two immiscible fluids. One pressureis greater than other.The capillary pressure is given by the following equation

r1 and r2 are referred to as the principal radii of curvature of the Interface.

A mean radius of curvature, rm, may be defined as

For a spherical liquid drop, r1 = r2 = r, the radius of the drop. The capillarypressure or the excess pressure of the drop is given by


11/30

For a flat interface, r1 = r2 = . In this case, the capillary pressure is zero.

Type of phases saturations:-

a. Funicular :complete covering by wetting phase

b. Pendular: partially cover soild surface


12/30

Pc vs R vs Sw relationship:-

As Pc is inversely proportional to R and R is directly proportional to Sw as

shown in figure.

If the wetting fluid saturation in the pendular ring is reduced, r1 and r2 will

be reduced. However, r1 will be reduced more than r2 as the wetting phaserecedes into the corners of the contact of the grains. As a result, the capillary

pressure will increase. If the wetting fluid saturation is increased, r1 and r2will increase and the capillary pressure will decrease. Therefore, an inverserelationship exists between the capillary pressure and the wetting phasesaturation for a porous medium.

Note:- Low wetting phase saturation corresponds to high capillarypressure and high wetting phase saturation corresponds to low capillary

pressure.


13/30

DRAINAGE CAPILLARY PRESSURE CURVEDRAINAGE CAPILLARY PRESSURE CURVE

A process in which the wetting phase saturation decreases is known asdrainage whereas the converse process in which the wetting phase saturation

increases is known as imbibition.

The capillary pressure curve would look like the one shown in Figure. This

figure shows a typical drainage capillary pressure curve obtained by displacingthe wetting phase from a porous medium with a non-wetting phase.


14/30

The drainage capillary pressure curve has several characteristicfeatures. The curve shows that a minimum positive pressure (Pd)must be applied to the non-wetting phase in order to initiatethe drainage. This minimum pressure, which is known as the

displacement pressure, the threshold pressure or the entrypressure.

If the rock does not have a strong wettability preference for theinitially saturating fluid, then the displacement pressure will bezero. If the rock has a strong preference for the displacing fluid,

then no pressure is required to initiate the displacementbecause it will occur spontaneously.

As the pressure of the non-wetting phase is increased, smallerand smaller pores are invaded by the non-wetting fluid.Eventually, the wetting phase becomes discontinuous and can nolonger be displaced from the medium by increasing the capillarypressure. Therefore, an irreducible wetting phase saturation isachieved for the porous medium at a high capillary pressure.

At the irreducible wetting phase saturation, the capillary

pressure curve becomes nearly vertical.


15/30

y The irreducible wetting phase saturation is a function of the grain size (poresize), the wettability of the medium and the interfacial tension between the

wetting and non-wetting Fluids.

What information does the capillary pressurecurve for a reservoir rock provide about therock?

Figure 7.13 shows the drainage capillary

pressure curves for four rocks:-

A,B,C and D.


16/30

1. Rock A has the least displacement pressure. Therefore, it has the largestpores connected to the surface. Its capillary pressure curve remainsessentially flat as the wetting phase saturation is decreased from 100% to60%. This means that many of the pores are invaded by the nonwetting

fluid at essentially the same capillary pressure.

This indicates that A has uniform pores or is well sorted.

Rock A also has the least irreducible wetting phase saturation, indicating that

it has relatively larger grains and pores than the other rocks.

2. RockB has a higher displacement pressure than A. Therefore, it has smallerpores than A. RockB has a higher irreducible wetting phase saturation than A,

which is consistent with its finer grains and pores.

3. RockC is even more fine grained than B because of its higher displacement

pressure.This means that C has awider pore size distribution than A and B.Therefore, C is poorly sorted. It has a higher irreducible water saturation thanB, which is consistent with its finer grains and pores.


17/30

4. Rock D is extremely fine grained, extremely poorly sorted and would be avery poor reservoir rock. This observation is based on its very high

displacement pressure, very steep capillary pressure curve and very highirreducible wetting phase saturation. Without being told, one can easily infer

that this rock is essentially made of clay.

Conclusion:- Since permeability is proportional to the square of the mean grain

Size (pore size), it is easy to see that Rock A has the highest permeability,followed by B,C and D in that order.

From this discussion, we conclude that the rock with the higher capillarypressure curve is a less desirable reservoir rock than the one with the lower

capillary pressure curve.


18/30

DETERMINATIONDETERMINATION OFOF THETHE RESERVOIRRESERVOIR FLUIDFLUID

SATURATIONSSATURATIONS BYBY USEUSE OFOF DRAINAGEDRAINAGE CAPILLARYCAPILLARY

PRESSUREPRESSURE CURVECURVE

Initially, the petroleum reservoir was saturated with water before oilmigrated into the reservoir and displaced the water. The displacementof a wetting phase by a non-wetting phase is simulated in the

laboratory measurement of the drainage capillary pressure curve.

The final fluid distribution in the reservoir is determined by the

equilibrium between capillary and gravitational forces.Consider the static equilibrium for the water and oil. From hydrostatics, for the

water,


19/30

On integrating,

On subtracting,

We select as datum the free water level at which the capillarypressure is zero.

where is the density of water minus the density of oil.


20/30

Figure shows

(1) a typical static fluid

distribution in a

homogeneous reservoir,(2) the oil-water contact,

(3) the free water level and

(4) the oil and water

pressure profiles.

Note the transition zoneabove the oil water

contact in which the watersaturation decreases from

100% to the irreduciblewater saturation.


21/30

It should be noted that the capillary pressure in the reservoir is highest atthe top of the reservoir. In order to prevent escape of the hydrocarbon

from the reservoir, the cap rock must have a displacement pressure that is

higher than the maximum capillary pressure labeled Pcap in the figure.

Shales typically form the cap rock in many reservoirs. Shales are finegrained and have very high displacement pressures. The shale, which is

saturated with water, will prevent the oil from penetrating it because its

displacement pressure is higher than the maximum capillary pressure inthe reservoir.

Of course, some may think that the oil does not penetrate the shalebecause it has a low permeability. However, the correct analysis is that the

shale prevents the oil from penetrating it because its displacementpressure is much higher than the pressure in the oil phase.

This is a capillary phenomenon not a Darcy law phenomenon.


22/30

CAPILLARY PRESSURE HYSTERESISCAPILLARY PRESSURE HYSTERESIS

Capillary pressure curves show a marked hysteresis depending on

whether the curve is determined under a drainage process or animbibition process.

Figure shows typical drainage and spontaneous imbibition capillary

pressure curves for the same porous medium. At any wetting phasesaturation, the drainage capillary pressure is higher than the imbibition

capillary pressure.


23/30

At a capillary pressure of zero, the spontaneous imbibition curveterminates at a wetting phase saturation that may or may not

correspond to the true residual non-wetting phase saturation

depending on the wettability of the rock. If the rock has a strongpreference for the wetting phase, then the wetting phase saturationat which the imbibition curve terminates will be close to the true

residual non-wetting phase saturation, Sor, which is equal to (1-Swro).This is the case shown in previous figure.

If the rock does not have a strong preference for the wetting phase,then the wetting phase saturation at zero capillary pressure on the

imbibition curve will not correspond to the true residual non-wetting phase saturation. This means that (1-Swro) will be larger

than Sor.

The branch of the imbibition curve labeled 3 on the figure is the

forced imbition capillary pressure curve of the rock. Note that this

branch constitutes a negative capillary pressure. Note also that thetrue residual nonwetting saturation (Sor) in this case can only by

determined by forced displacement not by spontaneous imbibition.


24/30


25/30

CapillaryCapillary pressurepressure hysteresishysteresis cancan bebe explainedexplained inin aavarietyvariety ofof waysways..


26/30

The pore structure also plays a role in the capillary pressure hysteresis.

Consider the capillary pressure versus wetting phase saturation

relationship for the idealized pore shown in Figureduring drainage and

imbibition.


27/30

During drainage, the pore is initially full of the wetting fluid. Next, the capillarypressure is increased to a higher value to drain some of the wetting fluid. Thehigher capillary pressure versus the wetting phase saturation is a point on thedrainage capillary pressure curve.

Next, we consider the imbibition process as shown. At c, the capillarypressure is high at a wetting phase saturation of nearly zero.

After the wetting fluid has been imbibed to the equilibrium level shown inFigure. The imbibition capillary pressure will be approximately the same as thedrainage capillary pressure of Figure b.

Because the mean curvature of the interfaces at c and d are about the same.However, the wetting phase saturation at d is considerably lower than at b.Thus, at the same capillary pressure, the wetting phase saturation forimbibition is less than for drainage.This is hysteresis.

Capillary pressure hysteresis presents no problem in reservoir

engineering analysis as it is usually clear which curve should be used for aparticular analysis. The drainage curve should be used for estimating theinitial fluid saturation distribution in the reservoir whereas the imbibitioncurve should be used for analyzing a waterflood performance in a water-wet reservoir.


28/30

CAPILLARY IMBIBITIONCAPILLARY IMBIBITIONConsider a reservoir consisting of two layers with different

permeabilities and capillary pressure curves as shown in Figure (a) and(b). Initially, both layers are in capillary equilibrium at their respective

irreducible water saturations.

Let this equilibrium be disturbed by waterflooding the two layers. Theinjected water will advance further into the more permeable layer

(Figure (c)). The oil and water pressures are continuous across theboundary between the two layers.

Thus, at the boundary,

Thus, at equilibrium, the capillary pressures in the two porous mediawill be equal at their boundary.


29/30

In Figure c, sections A and D and C and F are in capillary equilibrium, so nofluid exchanges will occur between these sections. Sections B and E are

not in capillary equilibrium, so fluid exchanges will occur in an effort toachieve capillary equilibrium. Section E will loose water to section B and

gain oil from B while section B will gain water from E and loose oil to Euntil a new capillary equilibrium is achieved.


30/30

Thus, water will be imbibed into the less permeable layer from the more

permeable layer and oil will be expelled from the less permeable layerinto the more permeable layer for subsequent displacement. This fluid

exchange is beneficial to the oil recovery process.However, the imbibitionprocess is very slow.

Therefore, the water injection rate must be sufficiently slow for imbibitionto assist in waterflooding the low permeability layer.

Similarly, Naturally fractured reservoirs (fissured reservoirs) presentanother example of capillary imbibition. The fractures have zero capillarypressure whereas the matrix blocks have normal capillary pressurecurves. When the fractures become 100% saturated with water whichcomes in contact with the oil saturated matrix blocks, the capillary

equilibrium will be disturbed.

Water will be imbibed into the matrix blocks, expelling oil from the matrixblocks into the fractures. Ultimately, the oil saturation in the matrix willbe reduced to the residual oil saturation over time.

Immiscible Displacement

Documents

Transcript of Immiscible Displacement