Efficiency of a Displacement Process

1
Chapter 4

• Efficiency of a Displacement Process

2
Efficiency of a Displacement Process

• Introduction
• Microscopic Displacement of Fluid in a Reservoir
• Macroscopic Displacement of Fluids in a Reservoir

3
Efficiency of a Displacement Process
Production

• Trapped Oil

Injection
(Microscopic Efficiency)
(Volumetric Efficiency)
4
Overall Displacement Efficiency
Where E overall hydrocarbon displacement
efficiency ,the volume of hydrocarbon displaced
divided by the volume of hydrocarbon in place at
the start of the process measured at the same
conditions of pressure and temperature
Macroscopic (Volumetric) displacement efficiency
Microscopic (Volumetric) hydrocarbon
displacement efficiency.
5
Microscopic Macroscopic sweep efficiencies
6
Efficiency of a Displacement Process

• Macroscopic Displacement

Where Overall
displacement efficiency
Macroscopic displacement efficiency
Microscopic displacement efficiency
7
Efficiency of a Displacement Process

• However,

Areal Sweep efficiency Lateral Sweep
efficiency
8
Oil Recovery Equation
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
9
Oil Recovery Equation
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
10
Action on Sweep Displacement Efficiency
By increasing water viscosity
Polymer flooding
Action on Sweep Efficiency at the Macroscopic
Scale
Steam drive
In-situ combustion
By decreasing the oil viscosity
Carbon dioxide drive
By using a miscible displacing fluid
Miscible hydrocarbon gas flooding
Action on Displacement Efficiency at the Pore
Scale
Surfactant flooding
By reducing the interfacial tension
Alkaline flooding
By action on the rock wettability
11
Microscopic efficiency largely determines the
success or failure of any EOR process. For crude
oil it is reflected in the magnitude of Sor (
i.e., the residual oil saturation remaining in
the reservoir rock at the end of the process).
Microscopic Displacement of Fluids
12
Displacement Sweep Efficiency
This efficiency is measured directly from a
coreflood (since 1). It can also be
evaluated from the Buckley-Leveret (or fractional
flow theory). For an immiscible displacement
is bounded by a residual phase saturation of
the displaced phase Sor. Miscible displacements
eliminate - in principle -
13
Example

• Initial oil saturation, Soi, is 0.60 and Sor in
  the swept region for a typical water flood is
  0.30
• ED (Soi Sor) / Soi
• ED ( 0.60 0.30 ) / 0.60
• ED0.50
• A typical waterflood sweep efficiency, Ev, at the
  economic limit is 0.70. Therefore,
• E EDEV 0.50 X 0.70 0.35

14
Important factors relating to microscopic
displacement behavior

• Capillary Forces
• Surface Tension and IFT
• Solid Wettability
• Capillary Pressure
• Viscous Forces

15
Important factors relating to microscopic
displacement behavior

• Capillary forces have a detrimental effect, being
  responsible for the trapping of oil within the
  pore.
• Trapping is a function of the ratio of Viscous to
  Capillary forces.
• The residual oil saturation decreases as the
  ratio (Viscous force/ Capillary force)
  increases.

16
Capillary Forces Surface Tension and IFT

• Whenever immiscible phases coexist in a porous as
  in essentially all processes of interest, surface
  energy related to the fluid interfaces influences
  the saturations, distributions and displacement
  of the phases.

Oil
Connate Water
Sand Grain
Close up of oil water between grains of rock
17
Capillary Forces Surface Tension and IFT

• The surface force, which is a tensile force, is
  quantified in terms of surface tension

Air or Vapor
L
Liquid

• The force per unit length required to create
  additional surface area is the surface tension,
  usually expressed in dynes/cm.

18
Capillary Forces Surface Tension and IFT

• The term surface tension usually is reserved
  for the specific case in which the surface is
  between a liquid and its vapor or air. If the
  surface is between two different liquids, or
  between liquid and solid, the term interfacial
  tension is used.
• The surface tension of water in contact with its
  vapor at room temperature is about 73 dynes/cm.
• IFTs between water and pure hydrocarbons are
  about 30 to 50 dynes/cm at room temperature.

19
Capillary Forces Surface Tension and IFT

• One of the simplest ways to measure the surface
  tension of liquid is to use a capillary tube.
• At the static condition the force owing to
  surface tension will be balanced by the force of
  gravity acting on the column of fluid.

20
Capillary Forces- Solid Wettability

• Fluid distribution in porous media are affected
  not only by the forces at fluid/fluid interfaces,
  but also by force of fluid/solid interfaces.
• Wettability is the tendency of one fluid to
  spread on or adhere to a solid surface in the
  presence of a second fluid.
• When two immiscible phases are placed in contact
  with a solid surface, one phase is usually
  attracted to the solid more strongly than the
  other phases. The more strongly attracted phase
  is called the wetting phase.

21
Capillary Forces- Solid Wettability

• Rock wettability affects the nature of fluid
  saturations and the general relative permeability
  characteristics of a fluid/rock system.
• The following figure shows residual oil
  saturations in a strongly water-wet and a
  strongly oil-wet rock.

Water-wet System
Oil-wet System
22
Capillary Forces- Solid Wettability

• Wettability can be quantitatively treated by
  examining the interfacial forces that exist when
  two immiscible fluid phases are in contact with a
  solid.

Water
23
Wettability

• Where , , IFTs between water
  and oil, oil and solid, and water and solid
  respectively, dynes/cm.
• , contact angle, measured through the water

24
Capillary Forces- Capillary Pressure

• A pressure difference exists across the
  interface. This pressure, called Capillary
  pressure can be illustrated by fluid rise in
  capillary tube.
• The figure shows rise in a glass capillary. The
  fluid above the water is an oil, and because the
  water preferentially wets the glass of the
  capillary, there is a capillary rise.

25
Capillary Pressure Equation

• The difference pressure between oil water at the
  oil/water interface

26
Capillary Forces- Capillary Pressure

• Capillary pressure is related to
• the fluid/ fluid IFT
• Relative permeability of fluids (through )
• Size of capillary (through r)
• The phase with the lower pressure will always be
  the phase that preferentially wets the capillary.
• Pc varies inversely as a function of the
  capillary radius and increases as the affinity of
  the wetting phase for the rock surface increases.

27
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.

28
Viscous Force

• Capillary Number
• Water floods typically operates at conditions
  where Nca lt 10-6, and Nca values on the order of
  10-7 are probably most common.

29
Displacement Sweep Efficiency is a function of

• Mobility ratios
• Throughput or Transmissibility
• Wettability
• Dip angle
• Capillary number

30
Displacement Sweep Efficiency
All sweep efficiencies can be increased
by decreasing the mobility ratio by either
Lowering
?i.e. steam flooding
Increasing
i.e. polymer flooding
Oil recovery would still be limited by the
residual or trapped oil saturation. Methods that
target to reduce this saturation include solvent
flooding.
31
Trapped Oil Saturation
Experimental evidence suggests that under most
conditions the residual oil saturation (usually a
non-wetting phase) can be as large as the wetting
phase saturation. The relationship between
trapping wetting or non-wetting phase and a local
capillary number indicates experimental evidence
of trapping in a permeable media.
This relationship is called the capillary
desaturation curve. The local capillary number is
Where
displacing fluid viscosity
interfacial tension between displacing and
displaced fuid u displacing superficial
velocity
32
Trapped Oil Saturation
Typical capillary desaturation curve
33
Trapped Oil Saturation
Note that it is required a substantial increase
in the capillary number to reduce the residual
oil saturation. The capillary number can be
increased by either. Lowering interfacial
tension miscible/solvent
methods Increasing viscosity of displacing fluid
polymer flooding. There are physical,
technical and economic limits of how much can the
displacing fluid viscosity and velocity be
increased, thus solvent methods are the natural
choice to increase the capillary number and
therefore lower the residual oil saturation
Capillary desaturation curves are also affected
by wettability, and pore size distribution.
34
Viscous Force

• Viscous forces in a porous medium can be
  expressed in terms of Darcys law

35
Calculation of pressure gradient for viscous oil
flow in a rock
36
Example Calculation of pressure gradient for
viscous oil flow in a rock

• Calculate the pressure gradient for flow of an
  oil with 10 cp viscosity at an interstitial flow
  rate of 1 ft/D. the rock permeability is 250 md
  and the porosity is 0.2.
• Solution

37
Example pressure required to force an oil trap
through a pore throat

• Calculate the threshold pressure necessary to
  force an oil trap through a pore throat that has
  a forward radius of 6.2 micro meter and radius of
  15 micro meter. Assume that the wetting contact
  angle is zero and IFT is 25 dynes/sec.
• PB-PA225(1/0.00062-1/0.0015) - 47300 dynes/cm2
• -473001.43810-5 - 0.68 psi

38
Macroscopic Displacement of Fluids in Reservoir

• Volumetric Displacement Efficiency Material
  Balance
• Volumetric Displacement Efficiency Expression
• Definition Discussion of Mobility Ratio
• Areal Displacement Efficiency
• Correlations
• Vertical Displacement Efficiency
• Volumetric Displacement Efficiency

39
Macroscopic Displacement of Fluids In a Reservoir

• IntroductionOil recovery in any displacement
  process depends on the volume of reservoir
  contacted by the injected fluid. A quantitative
  measure of this contact is the volumetric
  displacement (sweep) efficiency defined as the
  fraction of reservoir (or project )PV that has
  been contacted or affected by the injected fluid.
  Clearly, is a function of time in a
  displacement process.Overall displacement
  efficiency in a process can be viewed
  conceptually as a product of the volumetric
  sweep, ,and the microscopic efficiency,

40
Volumetric Displacement Efficiency and Material
Balance

• Volumetric displacement ,or sweep efficiency, is
  often used to estimate oil recovery by use of
  material-balance concepts. for example, consider
  a displacement process that reduces the initial
  oil saturation to a residual saturation in the
  region contacted by the displacing fluid. If the
  process is assumed to be piston-like, the oil
  displaced is given by

Where oil displaced
, oil saturation at the beginning of
the displacement process, residual oil
saturation at the end of the process in the
volume of reservoir contacted by the displacing
fluid, FVF at initial conditions,
FVF at the end of the process, and
reservoir PV
41
Volumetric Displacement Efficiency and Material
Balance
Where OOIP at the beginning of
the displacement process. if displacement
performance data are available, above Eq. also
can be used to estimate volumetric sweep. For
example, if waterflood recovery data are
available, the equation can be rearranged to
solve for
42
Volumetric Displacement Efficiency and Material
Balance

• Where oil produced in the waterflood.

43
Volumetric Displacement Efficiency

• Volumetric Displacement Efficiency Expressed as
  the product of Areal and Vertical Displacement
  EfficienciesVolumetric sweep efficiency can be
  considered conceptually as the product of the
  areal and vertical sweep efficiencies. Consider a
  reservoir that has uniform porosity,thickness,and
  hydrocarbon saturation, but that consists of
  several layers. For a displacement process
  conducted in the reservoir, can be
  expressed as

44
Volumetric Displacement Efficiency
Where All efficiencies are expressed
as fractions. is the volumetric sweep
efficiency of the region confined by the largest
areal sweep efficiency in the system.For a real
reservoir, in which porosity,thickness,and
hydrocarbon saturation vary areally, is
replaced by a pattern sweep efficiency ,
45
Where pattern sweep
(displacment)efficiency,hydrocarbon pore space
enclosed behind the injected-fluid front divided
by total hydrocarbon pore space in the pattern or
reservoir a real reservoir.In essence, is
an ideal sweep efficiency that has been corrected
for variations in thickness,porosity,and
saturation. In either case, overall hydrocarbon
recovery efficiency in a displacement process may
be expressed as
Volumetric Displacement Efficiency
46
This figure illustrates the concept of the
vertical and areal sweep efficiency
47
The following figure illustrate the definition
of areal sweep efficiency
48
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 .
Oil Recovery Equation
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.
49
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.
50
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

51
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( )

52
Mobility Control
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
53
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 lt1 then favorable displacement
• M gt1 then unfavorable displacement

54
Dimensionless Time
This variable is used to scale-up between the
laboratory and the field . The dimensionless time
is defined as the
There are various definitions for the reference
pore volume according to the application.
55
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.

56
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.

57
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.
58
Flooding Patterns
59
Flooding Patterns
60
Flooding Patterns
61
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.

62
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.

63
Correlations Based on .
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.
64
Producing well
Breakthrough
Breakthrough
Pore Volumes Injected
Pore Volumes Injected
M0.151
M1.0
Injection well
Figure-1 Miscible displacement in a quarter of
a five-spot pattern at mobility ratioslt1.0
65
BT
BT
PV
PV
0.3
0.3
0.2
0.2
0.1
0.1
0.06
M4.58
M2.40

• PRODUCING WELL PVPORE
  VOLUME INJECTED
• X INJECTION WELL
  BTBREAKTHROUGH

Figure 2 Miscible displacement in a quarter of a
five-spot pattern at mobility ratiosgt1.0,viscous
fingering (from Habermann)
66
BT
BT
0.15
0.05
M71.5
M17.3

• PRODUCING WELL PVPORE
  VOLUME INJECTED
• X INJECTION WELL
  BTBREAKTHROUGH

Figure-3 Miscible displacement in a quarter of a
five-spot pattern at mobility ratiosgt1.0,viscous
fingering (from Habermann)
67
Habermann presented values of EA as a function
of dimensionless PVs injected,Vi/Vp,after
breakthrough, as shown in Figure 4 Results are
given for M0.216 (favorable) to 71.5
(unfavorable).
Correlations Based on .
Correlations Based on Miscible Fluids, Other
Patterns Numerous modeling studies for patterns
other than a five-spot have been reported. Craig
gives a summery listing of references. As an
example of such studies, Figure 5 shows one
reported result of areal sweep as a function of
mobility ratio for one-eighth of a nine-spot
pattern.
68
Areal Sweep Efficiency, EA
Pore Volume Injected, Vi/ Vp
Figure-4 Areal sweep efficiency after
breakthrough as a function of mobility ratio and
PVs injected
69
Correlation Based on Miscible Fluids

• Numerous modeling studies for patterns other than
  a five-spot have been reported.
• One-eight of a nine-spot pattern is shown as an
  example.
• This study was conducted with miscible liquids
  and the X-ray shadowgraph method

70
Figure-5Areal sweep efficiency as a function
of mobility ratio
71
Correlations Based on Immiscible Fluids, Five
Spot Pattern

• Craig et al. conducted an experimental study of
  areal displacement efficiency for immiscible
  fluids consisting of oil, gas, and water.The
  study was conducted in consolidated sandstone
  cores, and fronts were monitored with the X-ray
  shadowgraph technique.
• Figure 6 compares areal sweep efficiency at
  breakthrough as a function of mobility ratio to
  the data of Dyes et al., which were obtained with
  miscible fluids.

72
Water-Gas
Gas-Oil
Miscible
Areal Sweep Efficiency at Breakthrough ,EAbt
Mobility Ratio,M
Figure-6 Areal sweep efficiency at breakthrough
as a function of mobility ratio( immiscible fluid
displacement)
73
Prediction of Areal Displacement Performance on
the Basis of Modeling Studies

• Prediction based on Piston-Like Displacement
• Caudle Witte correlation
• Claridge correlation (viscous fingering)
• Mahaffey et. Al model (dispersion )
• Parallel plate glass model
• Mathematical Modeling-Numerical

74
Prediction of Areal Displacement Performance on
the Basis of Modeling Studies

• Prediction Based on Piston Like Displacement.
• Caudle and Witte published results from
  laboratory models of a five-spot pattern in which
  displacements were conducted with miscible
  liquids.
• The performance calculations are restricted
  to those floods in which piston-like displacement
  is a reasonable assumption i.e., the displacing
  phase flows only in the swept region and the
  displaced phase flows in the upswept region. No
  production of displaced phase occurs from the
  region behind the front.

75
Figure 8 gives EA as a function of M for
different values of the fractional flow of the
displacing phase ,fD, at the producing well.
Prediction Based on Piston Like Displacement
Figure 7 through 9 show data from the
experiments. In Figure 7, EA is given as a
function of M for various values of injected
PVs. The ratio Vi/Vpd is a dimensionless
injection volume defined as injected volume
divided by displaceable PV, Vpd. For a
waterflood, Vpd is given by
76
Prediction Based on Piston Like Displacement

• Figure 9 presents the conductance ratio, ,
  as a function of M for various values of EA, but
  only for values of M between 0.1 and 10.
  Conductance is defined as injection rate divided
  by the pressure drop across the pattern,
  
• At any mobility ratio other than
  M1.0,conductance will change as the displacement
  process proceeds. For a favorable mobility ratio,
  conductance will decrease as the area swept, EA,
  increases. The opposite will occur for
  unfavorable M values.
• The conductance ratio, shown in Figure 9 is the
  conductance at any point of progress in the flood
  divided by the conductance at that same point for
  a displacement in which the mobility ratio is
  unity (referenced to the displaced phase).

77
Prediction Based on Piston Like Displacement

• By combining Figures 7 through 9 , performance
  calculations can be performed. Areal sweep, as a
  function of volume injected, is available from
  Figure 7.
• Fractional production of either phase can be
  determined with Figure 8.
• Rate of injection may be determined as a function
  of EA from Figure 9.
• To apply Figure 9, however , it is also necessary
  to use the appropriate expression for initial
  injection rate. This is given by Craig for a
  five-spot pattern using parameters for the
  displaced phase

78
Where iinjection rate at start of a displacement
process, B/D kabsolute rock permeability
,mdKrdrelative permeability of displaced phase,
hreservoir thickness ,ft pressure
drop, psi viscosity of displaced phase,
cpddistance measured between injection and
production wells ,ft and rw wellbore radius, ft.
Prediction Based on Piston Like Displacement
At any point in the flood, the flow rate is
given by
79
Areal Sweep Efficiency,EA
Figure-7 Areal Sweep efficiency as a function of
mobility ratio and injected volume.
80
Areal Sweep Efficiency,EA
Mobility Ratio,M
Figure-8Areal sweep efficiency as a function of
mobility ratio and fractional flow at displacing
phase
81
Conductance Ratio,
Mobility Ratio,M
Figure-9Conductance ratio as a function of
mobility ratio and areal sweep.
82
Example Performance Calculations Based on
Physical Modeling Results

• A waterflood is conducted in a five-spot pattern
  in which the pattern area is 20 acres. Reservoir
  properties are

83
Required

• Use the method of Caudle and Witte to calculate
  
• (1) the barrels of oil recovered at the point in
  time
• at which the producing WOR20 ,
• (2) the volume of water injected at the same
  point
• (3) the rate of water injection at the same
  point in time
• (4) the initial rate of water injection at the
  start of waterflood

84
Solution

• Apply the correlations in Figs 7 through 9
• 1. Calculate oil recovered
• M2.9, fD20/21.95 From Fig 8, EA.94
• Np321000 STB
• 2. Calculate total water injected. From Fig 7,
  Vi/Vpd2.5 (at EA.94)
• Vpd Vp (Soi Sor) 341300 bbl
• Vi Vpd x 2.5 853300 bbl
• 3. Calculate water injection rate at the same
  point in time. From
• i63.4 B/D
• From Fig. 9, ?2.7, from 63.4x2.7
  171 B/D
• 4. Calculate initial water injection rate
• i63.4 B/D

85
Calculation of EA with Mathematical Modeling

• Models are based on Numerical analysis methods
  and digital computers
• Douglas et al-2D immiscible displacement. This
  method is based on the numerical solution of the
  PDEs that describe the flow of two immiscible
  phases in two dimensions
• Higgins and Leighton mathematical model is based
  on frontal advance theory

86
Comparison of calculated and experimental
results, 5 spot pattern (Douglas et al.)
87
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
88
Vertical Displacement Efficiency
89
Vertical Displacement Efficiency

• 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

90
Heterogeneity
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.
91
HeterogeneityLocation of the water front at
different Location
92
HeterogeneityDykstra-Persons model
93
Gravity Segregation in Horizontal Bed

• Water tongue

Water

• Gas umbrella

Gas
94
Gravity Effect
Gravity is a factor that affects the vertical
efficiency not only in heterogeneous reservoirs
but in homogenous as well. Gravity effects will
be important when (1) vertical communication is
good. This is satisfied when is large.


(2) When gravity forces are strong compared to
viscous forces. This is satisfied when the
gravity number Ng is large.
95
Gravity Effect
Where
relative mobility of displacing fluid
density difference (displaced -
displacing) u superficial velocity Both
numbers are dimensionless. The following figures
indicate gravity effects for two different
situations 1- Density of displacing fluid lower
that density of displaced fluid The displacing
fluid will tend to flow to the top of the
reservoir and bypass the fluid in the lower
region (tongue over).
96
Gravity Effect
Tonguing will occur when M lt 1 as long as
and Ng are large. The effect of heterogeneity and
gravity can be mitigated by a favorable mobility
ratio. Gravity tonguing does not require a
dipping reservoir (although dipping can be used
as an advantage when gravity is important).
Gravity tonguing is important in steam flooding
applications.
Density of displacing fluid lower that
density of displaced fluid
97
Gravity Effect
Density of displacing fluid higher
than density of displaced fluid
98
Gravity segregation occurs when the injected
fluid is less dense than the displaced fluid,
Figure10a.Gravity override is observed in steam
displacement, in-situ combustion, CO2 flooding,
and solvent flooding processes. Gravity
segregation also occurs when the injected fluid
is more dense than the displaced fluid, as
Figure10b shows for a waterflood.Gravity
segregation leads to early breakthrough of the
injected fluid and reduced vertical sweep
efficiency.
Effect of Gravity Segregation and Mobility Ratio
on Vertical Displacement Efficiency
99
Gravity Segregation in displacement processes
Displacing Phase
Displaced Phase
Displacing Phase
Displaced Phase
Displacing Phase
Displaced Phase
Gravity Override (a)
Gravity Underride (b)
Figure-10 Gravity Segregation in
displacement processes.
100
Experimental Result

• Craig et al. studied vertical sweep efficiency by
  conducting a set of scaled experiments in linear
  systems and five-spot models. Both consolidated
  unconsolidated sands were used.
• The linear models used were from 10 to 66 in.
  long with length/height ratios ranging from 4.1
  to 66.
• Experiments were conducted with miscible and
  immiscible liquids having mobility ratios from
  0.057 to 200.
• Immiscible water floods were conducted at Mlt1.
• Vertical sweep was determined at breakthrough by
  material balance and visual observation of
  produced effluent

101
Craig et al. Results

• Results of the linear displacements are shown in
  the next Figure, where EI at breakthrough is
  given as a function of dimensionless group called
  a viscous/gravity ratio.

102
Vertical sweep efficiency at breakthrough as a
function of the ratios of viscous/gravity forces,
Linear system (from Craig et al.)
103
Example Relative Importance of Gravity
Segregation in a Displacement Process

• A miscible displacement process will be used to
  displace oil from a linear reservoir having the
  following properties

104
Solution
105
Mathematical Model

• Spivak used a 2D and 3D numerical model to study
  gravity effects during water flooding and gas
  flooding

106
Gravity Segregation in two-phase flow
107
The correlations of Craig et al. and Spivak on
gravity segregation
The correlations of Craig et al. and Spivak
indicate the following effects of various
parameters on gravity segregation, as summarized
by Spivak

• Gravity segregation increases with increasing
  horizontal and vertical permeability.
• Gravity segregation increases with increasing
  density difference between the displacing and
  displaced fluids.
• Gravity segregation increases with increasing
  mobility ratio
• Gravity segregation increases with increasing
  rate. This effect can be reduced by viscous
  fingering
• Gravity segregation decreases with increasing
  level of viscosity for a fixed viscosity ratio.

108
Flow Regions in Miscible Displacement at
Unfavorable Mobility Ratios
Flow experiments in a vertical cross section in
horizontal porous media have shown that four flow
regions, are possible when the mobility ratio is
unfavorable.
Region I occurs at very low values and
is characterized by a single gravity tongue, with
the displacing liquid either underriding or
overriding the displaced liquid. Vertical sweep
is a strong function of .At larger
values, in region II, a single gravity
tongue still exists, but vertical sweep is
relatively insensitive to the value of the
viscous/gravity ratio.
SOLVENT
Oil
(A) REGIONS I AND II
109
Flow Regions in Miscible Displacement at
Unfavorable Mobility Ratios
The transition to region III occurs at a
particular critical value. In region
III, viscous fingers are formed along the primary
gravity tongue and appear as secondary fingers
along the primary gravity tongue. Vertical sweep
is improved by the formation of the viscous
fingers in this region. In region IV ,flow is
dominated by the viscous forces and by viscous
fingering. A gravity tongue does not form because
of the strong viscous fingering. The vertical
sweep in this region is relatively insensitive to

SOLVENT
SOLVENT
Oil
Oil
(B) REGION III
(C) REGION IV
110
Flow Regimes in Miscible Displacement
111
Volumetric Efficiency

• Methods of estimating volumetric displacement
  efficiency in a 3D reservoir fall into two
  classifications.
• Direct application of 3D models
• Physical
• mathematical
• Layered reservoir model.
• The reservoir is divided into a number of no
  communicating layers.
• Displacement performance is calculated in each
  layer with correlations of 2D.
• Performance in individual layers are summed to
  obtain volumetric efficiency

112
Volumetric Displacement Efficiency
113
Calculation of volumetric sweep with Numerical
Simulators