EOR 19 Mayo 2015

Apuntes de Recuperacin Mejorada de Petrleo (EOR)

Jos Cndor, Ph.D., P.Eng.

19 mayo 2015

Fuerzas Capilares Fuerzas viscosas

Desplazamiento macroscpico

Desplazamiento Microscpico Presin Capilar

Modelo de tubo capilar Sistema aire/agua

La altura del agua en un tubo capilar es funcin de: Tensin de adhesin entre el aire y el agua Radio del tubo Diferencia de densidades entre los fluidos

Esta relacin puede derivarse del balance entre las fuerzas verticales hacia arriba debido a la tensin de adhesin y a fuerzas verticales hacia abajo debido al peso del fluido. La fase mojante ser mayor en capilares pequeos h: altura del agua en un tubo capilar aw: TIF entre aire y agua : angulo de contacto aire/agua. Se mide en la fase mas densa r: radio del capilar g: aceleracion de la gravedad aw: diferencia de densidades entre agua y aire

aw

aw

grh

cos2


Altura vs radio del capilar

Agua

Petrleo

1 2 3 4

AT = wo cos() Tension de adhesion Pc = Po Pw = h = (w o) g h


Presin capilar Sistema petrleo/agua

Donde Pc: presin capilar entre el petrleo y el agua ow: TIF entre petrleo y agua : ngulo de contacto petrleo/agua r: radio del capilar

rP owc

cos2


Presin capilar Medicin en laboratorios

Se puede determinar Pc con los mtodos: Diafragma poroso Inyeccin de mercurio Centrifuga Dinmica

Cap

illar

y p

ress

ure

, psi

a

Wetting phase saturation, %

Measured data points

Irreducible Wetting Phase Saturation

Displacement pressure

0 100


Leverett Funcin J

La funcin J se usa para promediar los datos de presiones capilares de una roca dada de un reservorio dado

La funcin J a veces puede extenderse a diferentes reservorios que tengan similares litologas

La funcin J generalmente no correlaciona con precisin para diferentes litologas

Si las funciones J no son exitosas en reducir la dispersin en una serie de datos, entonces probablemente estemos en un caso de variacin de tipos de roca

Desplazamiento Microscpico Permeabilidad relativa

Permeabilidad absoluta

La permeabilidad absoluta es la permeabilidad de un medio poroso saturado con un solo fluido (ejemplo Sw=1)

La permeabilidad absoluta puede calcularse desde la ecuacin de Darcy

L

pAkq


Flujo multifasico en reservorios

Los reservorios comnmente tienen 2 o 3 fluidos Sistemas agua-petrleo Sistemas petrleo-gas Sistemas agua-gas Sistemas de tres fases (agua, petrleo, y gas)

Para evaluar sistemas multifasicos se debe considerar las permeabilidades efectiva y relativa


Permeabilidad efectiva

La permeabilidad efectiva es una medida de la conductancia de un medio poroso para un fluido cuando el medio esta saturado con mas de un fluido. El medio poroso puede tener una conductancia distinta y medible para cada fase presente en el medio

Oil

Water

Gas

L

Akq

o

ooo

L

Akq

w

www

L

Akq

g

gg

g

Usando Steady state y para 1D:

qn = volumetric flow rate for a specific phase, n

A = flow area

n = flow potential drop for phase, n (including pressure, gravity and capillary pressure terms)

n = fluid viscosity for phase n

L = flow length


Permeabilidad relativa

La permeabilidad relativa es la relacin de la permeabilidad efectiva de un fluido a una saturacin dada a una permeabilidad base dada

La permeabilidad base es tpicamente definida como: Permeabilidad absoluta, k Permeabilidad del aire, kaire Permeabilidad efectiva de la fase no-mojante a saturacin

irreductible Porque la definicin de permeabilidad base varia, la definicin

de permeabilidad relativa siempre debera incluir sus porcentajes de saturacion


Permeabilidad relativa

Oil

Water

Gas

k

kk

o

ro

)3.0,5.0(

)3.0,5.0(

k

kk

w

rw

)3.0,5.0(

)3.0,5.0(

k

kk

g

rg

)3.0,5.0(

)3.0,5.0(

So =0.5

Sw =0.3 Sg = 0.2


Funciones de la permeabilidad relativa

0.40

0

0.20

0.40 0 1.00 0.60 0.20 0.80

Water Saturation (fraction)

Rel

ativ

e Pe

rmea

bili

ty (

frac

tio

n)

1.00

0.60

0.80

Water

krw @ Sor

Oil

Two-Phase Flow Region

kro @ Swi Wettability and direction of saturation change must be considered

drainage imbibition

Base used to normalize this relative permeability curve is kro @ Swi

As Sw increases, kro decreases and krw increases until reaching residual oil saturation

Imbibition Relative Permeability (Water Wet Case)


Efecto de la mojabilidad cuando Sw aumenta

0.4

0

0.2

40 0 100 60 20 80 Water Saturation (% PV)

Rel

ativ

e Pe

rmea

bili

ty, F

ract

ion

1.0

0.6

0.8

Water

Oil

Strongly Water-Wet Rock

0.4

0

0.2

40 0 100 60 20 80 Water Saturation (% PV)

Rel

ativ

e Pe

rmea

bili

ty, F

ract

ion

1.0

0.6

0.8

Water Oil

Strongly Oil-Wet Rock

Water flows more freely Higher residual oil saturation

Fluid saturations

Geometry of the pore spaces and pore size distribution

Wettability

Fluid saturation history (i.e., imbibition or drainage)

Factors Affecting Relative Permeabilities

Characteristics of Relative Permeability Functions

Relative permeability is unique for

different rocks and fluids

Relative permeability affects the flow

characteristics of reservoir fluids.

Relative permeability affects the

recovery efficiency of oil and/or gas.

Applications of Relative Permeability Functions

Reservoir simulation

Flow calculations that involve multi-

phase flow in reservoirs

Estimation of residual oil (and/or

gas) saturation

Desplazamiento Microscpico Fuerzas Capilares

c) Permeabilidad Relativa 3 phases

Ternary Diagrams

Because So+Sw+Sg=1, we can use a ternary diagram to represent three phase saturations, and plot values of relative permeability as the independent variable.

Two of the three saturations are independent

We can plot in 2-D space using two independent (not same direction) coordinates

Ternary Diagrams

Plot Point for:

Sw=0.30

So=0.25

Sg=0.45

0.00 So 1.00

Viscous Force

Viscose forces in a porous medium are reflected in the magnetude of the pressure drop that occurs as a result of fluid

flow through porous medium.

One of the simplest approximations used to calculate the viscous force is to consider a porous medium as a bundle of

parallel capillary tubes.

With this assumption, the pressure drop for laminar flow through a single tube is given by Poiseuilles law.

Viscous Force

Capillary Number

Water floods typically operates at conditions where Nca < 10-6, and Nca values on the order

of 10-7 are probably most common.

ow

wcaN

All sweep efficiencies can be increased by decreasing the

mobility ratio by either:

rwOil kor i.e. steam flooding

rowater kor

Oil recovery would still be limited by the residual or trapped

oil saturation. Methods that target to reduce this saturation

include solvent flooding.

Increasing i.e. polymer flooding

Lowering

Displacement Sweep Efficiency

Desplazamiento Macroscpico de fluidos

Efficiency of a Displacement Process

Trapped Oil

ME

= (Microscopic Efficiency) (Volumetric Efficiency)

Production

Injection

EME VE


Macroscopic Displacement

E

DV EEE Where;

= Overall displacement efficiency

VE = Macroscopic displacement efficiency

= Microscopic displacement efficiency

DE

However,

LE

LAV EEE

= Areal Sweep efficiency

= Lateral Sweep efficiency

AE


Therefore, using all these definitions, the oil recovery equation is

To use this equation we must have methods to evaluate the different

efficiencies.

Estimates are available from:

Correlations

Scaled laboratory experiments

Numerical simulation

)(***O

PoiLADP

B

VSEEEN

Oil Recovery Equation


RE

placeinnhydrocarboofVolume

displacednhydrocarboofVolumeER

and is the volumetric sweep efficiency defined as

typical values of the overall recovery efficiency are:

Steam injection 30%-50%

Polymer injection 30%-55%

CO2 injection 30%-65%

Solvent injection 35%-63%

RE

RE

RE

RE

Action on Sweep

Efficiency at the

Macroscopic Scale

By increasing water

viscosity

Polymer

flooding

By decreasing the oil

viscosity

Steam drive

In-situ combustion

Carbon dioxide drive

Action on Displacement

Efficiency at the Pore

Scale

Miscible hydrocarbon

gas flooding

Surfactant flooding

By using a miscible

displacing fluid

By reducing the

interfacial tension

By action on the

rock wettability

Alkaline flooding

Action on Sweep & Displacement Efficiency

This figure illustrates the concept of the vertical and

areal sweep efficiency

The following figure illustrate the definition

of areal sweep efficiency

areaTotal

agentdisplacingbycontractedArealEA

These correlations are for piston like displacements in

homogeneous, confined patterns. When the well patterns are

unconfined, the total area can be much lager and smaller .

Areal Sweep Efficiency

The most common source of areal sweep efficiency data is from

displacements in scaled physical models. Several correlations exist

in the literature. Craig (1980) in his SPE monograph the reservoir

engineering aspects of waterflooding discusses several of these

methods.

AE


AREAL SWEEP EFFICIENCY

When oil is produced from patterns of injectors and producers, the flow is

such that only part of the area is swept at breakthrough. the expansion of

the water bank is initially radial from the injector but eventually is focused

at the producer.

The pattern is illustrated for a direct line drive at a mobility ratio of unity.At breakthrough a considerable area of the reservoir is unswept.

Parameters Affecting

The following definitions are needed to describe the effects of reservoir and fluid properties upon the efficiencies:

Mobility Ratio

Dimensionless Time

Viscous Fingering

Injection/Production well pattern

Reservoir permeability heterogeneity

Vertical Sweep Efficiency

Gravity Effect

Gravity/ Viscous Force Ratio

AE

Mobility Definition

The mechanics of displacement of one fluid with another are controlled by differences in the ratio

of effective permeability and viscosity

The specific discharge (flow per unit cross sectional area) for each fluid phase depends on

This is called the fluid mobility( ):

k

k

Mobility Control

d

W

WW

k

O

O

O

k

Mobility controls the relative ease with which fluids can flow

through a porous medium.

= mobility of the displacing fluid phase

= mobility of the displaced fluid phase

dM D /

D

Mobility ratio

The mobility ratio is an extremly important parameter in any displacement process. It affects both areal and vertical sweep,

with sweep decreasing as M increases for a given volume of

fluid injected.

M 1 then unfavorable displacement

Viscous Fingering

The mechanics of displacing one fluid with another are relatively simple if the displaced fluid (oil) has a tendency to

flow faster than the displacing fluid (water).

Under these circumstances, there is no tendency for the displaced fluid to be overtaken by the displacing fluid and the

fluid fluid (oil-water) interface is stable.

EOR-Chapter 2

Viscous Fingering

If the displacing fluid has a tendency to move faster than the displaced fluid, the fluid-fluid interface is unstable.

tongues of displacing fluid propagate at the interface.

This process is called viscous fingering.

EOR-Chapter 2

Viscous Fingering

- Decreases when the mobility ratio increases because the displacement front

becomes unstable. This phenomena, known as viscous fingering results in an

early breakthrough for the displacing fluid, or into a prolonged injection to

achieve sweep-out. The next figure illustrates this phenomena, which is

commonly observed in solvent flooding.

AE

EOR-Chapter 2

Flooding Patterns

Permeability Heterogeneity

It is often has a marked effect on areal sweep. This effect may be quite different from

reservoir to reservoir, however, and thus it is

difficult to develop generalized correlations.

Anisotropy in permeability has great effect on the efficiency.

Effect of Mobility Ratio

The following figures show fluid fronts at different points in a flood for different mobility ratios. These

results are based on photographs taken during

displacements of one colored liquid by second,

miscible colored liquid in a scaled model.

Correlations Based on Miscible Fluids, Five-Spot Pattern.

Figure 1 shows fluid fronts at different points in a flood for

different mobility Ratios. The Viscosity Ratio varied in different

floods and, because only one phase was present, M is given by

Equation.

D

dM

Correlations Based on .

Figure-1: Miscible displacement in a quarter of

a five-spot pattern at mobility ratios

M=2.40

PV

BT BT

M=4.58

0.3

0.2

0.1 0.06

0.2

0.3

0.1

PV

PRODUCING WELL PV=PORE VOLUME INJECTED

X INJECTION WELL BT=BREAKTHROUGH

Figure 2: Miscible displacement in a quarter of a five-spot pattern at mobility

ratios>1.0,viscous fingering (from Habermann)

M=17.3 M=71.5

BT BT

0.15 0.05

PRODUCING WELL PV=PORE VOLUME INJECTED

X INJECTION WELL BT=BREAKTHROUGH

Figure-3: Miscible displacement in a quarter of a five-spot pattern at mobility

ratios>1.0,viscous fingering (from Habermann)

Vertical sweep ( displacement) efficiency, pore space invaded by the

injected fluid divided by the pore space enclosed in all layers behind the

location of the leading edge (leading areal location) of the front.

Areal sweep efficiency, must be combined in an appropriate manner with

vertical sweep to determine overall volumetric displacement efficiency. It is

useful, however, to examine the factors that affect vertical sweep in the

absence of areal displacement factors.

Vertical Displacement Efficiency

EOR-Chapter 2



Vertical Displacement Efficiency is controlled primarily by four factors:

Heterogeneity

Gravity effect Gravity segregation caused by differences in density

Mobility ratio

Vertical to horizontal permeability variation

Capillary forces

EOR-Chapter 2 53

Observation of thre figure indicates a stratified reservoir with layers of different

permeability. The displacement of the fluid is an idealized piston-flow type. Due to

the permeability contrast the displacing fluid will break through earlier in the first

layer, while the entire cross-section will achieve sweep-out at a later time, when layer

#4 breaks through.

Heterogeneity

Heterogeneity:Location of the water front at different Location

Heterogeneity:Dykstra-Persons model

Gravity Segregation in Horizontal Bed

Water tongue

Water

Gas umbrella

Gas

Apuntes de Recuperacin Mejorada de Petrleo (EOR)

Jos Cndor, Ph.D., P.Eng.

19 mayo 2015

Fuerzas Capilares Fuerzas viscosas

Desplazamiento macroscpico

Documents

EOR 19 Mayo 2015