Basra University for oil & gas
College of oil and gas Engineering
Oil & gas engineering department
Water flooding
Lecture 2
October, 2017
Water flooding
Outline
Well pattern
Fluid mobility
Mobility ratio
Ideal displacement
Non-piston displacement
Viscous fingering
Mechanism of waterflooding behaviour
Fractional flow equation
Factros affecting Fractional flow curve
Well pattern
Regular patterns of wells are used
to sweep the entire area of a
reservoir with a waterflood.
INVERTED NINE SPOT
INVERTED SEVEN SPOT
FOUR SPOT
FIVE SPOT
DIRECT LINE DRIVE
STAGGERED LINE DRIVE
SEVEN SPOT
NINE SPOT
Fluid mobility, λ
The mobility of a fluid is the effective permeability of that fluid
divided by its viscosity
Mobility controls the relative ease with which fluids can flow through
a porous medium
λw = kw /μw
λo = ko /μo
Mobility is a function of saturation as the relative permeabilities to
oil & water depend on the fluid saturations
Mobility ratio, M
the ratio of the mobility of the displacing fluid behind the flood
front to that of the displaced fluid ahead of the flood front
M = λw / λo
Ahead of the water flood, oil alone is flowing & behind it water
alone is flowing
Flood front
Injector Producer
1-Sor
Water Oil
Swi
Ideal displacement
In ideal displacement, there is a sharp transition from Sor to
maximum oil saturation (1 - Swi) at the flood front.
Ideal displacement is the most favourable condition for
production but only occurs if M≤ 1
Flood front
Injector Producer
1-Sor
Water Oil
Swi
Ideal displacement
When M≤ 1, oil can flow at a rate greater than or equal to that of water
and is pushed ahead by the water bank in a piston-like fashion
The moveable oil volume (MOV) is given by:
MOV = (1 - Soi - Swi) Vp
The volume of oil recovered is exactly equal to the volume of water
injected
Non-Ideal displacement
Water is found to be more mobile than oil
M> 1 in this case, water push oil in a leaky piston-like fashion
Tongues of water bypass the oil leading to much less favourable saturation
profiles
More common displacement in nature
Flood front or shock front
Injector Producer
1-Sor
Behind the shock
At the end of the
front there is a
transition zone,
transition zone Water Oil
water alone is
where both water
flowing
and oil flow.
Swi
Non-Ideal displacement
When the flood front reaches the production well there is a sharp increase
in water cut. This event is called breakthrough (BT).
In non-ideal displacement, only a fraction of the MOV has been recovered
at water breakthrough
Addition water injection is required to recover the moveable oil
Several (5 or 6) MOV’s of water may be needed to displace a single MOV of
oil.
Producer moveable oil that
remains between the
Injector 1-Sor injector and producer
at BT
Oil
Water
Water breakthrough
Swi
Ideal or non-ideal displacement
To address the behaviour of displacement ( Ideal or non-
Idela), the end point mobility ratio is considered.
k′𝑟𝑤 /𝜇𝑤 0.9
M= 0.8 End point Krw Kro
k′𝑟𝑜 /𝜇𝑜 0.7 Kro
0.6
Where; 0.5 End point
Kr
M= the end point mobility ratio Kro
0.4
k′rw & k′ro = End point relative permeabilities 0.3
0.2
If M ≤ 1 : Oil is capable of travelling with a velocity equal to, or 0.1
greater than, that of water, no tendency for the oil to be by-
passed which results in the sharp interface between the fluids. 0
If M > 1 : Water travelling with a velocity greater than, that of 0 0.5 1
oil, there is a tendency for the oil to be by-passed. Sw
Viscous fingering
In non-ideal displacement, the Water
has a tendency to move faster than oil
the water-oil interface is unstable.
Tongues of displacing fluid propagate at
the interface. This process is called
viscous fingering
Reservoir heterogeneity is a key reason
for fingering
Mechanism of waterflooding behavoiur
1- Fractional flow equation
2- Frontal advance equation
3- Water flood behaviour in Linear system
Buckely-Leverett theory
Weldge Procedure
4- Water flood behaviour in multi-layered reservoirs
Fractional flow equation
Darcy equation
Fractional flow equation
Capillary pressure
The fractional flow equation is very important ??:
1- It facilitates the determination of the relative flow rates of oil and water at any
point in the porous media,
2- It incorporates all factors affecting the displacement efficiency of a water flood
project
Fractional flow equation
Assumptions for using fractional flow equation for linear
system
One-Dimension
Oil-water system
Uniform thickness
Diffuse conditions means that
Homogenous reservoir fluid saturations at any point
Diffuse conditions in the reservoir in the linear displacement path
are uniformly distributed with
respect to thickness
Fractional flow equation
Derivation of the fractional flow equation for a one-dimensional oil-
water system
Consider displacement of oil by water in a system of dip angle
Start with Darcy´s equations
Replace the water pressure by Pw = Po - Pcow , Then:
Fractional flow equation
Derivation of the fractional flow equation for a one-dimensional oil-
water system
Rearranging the equations to be written as follow:
Subtracting the first equation from the second one
Substituting for And
Fractional flow equation
Derivation of the fractional flow equation for a one-dimensional oil-
water system
solving for the fraction of water flowing, we
obtain the following expression for the fraction
of water flowing
For the simplest case of horizontal flow, with
negligible capillary pressure, the expression
reduces to
Fractional flow equation
Fractional flow equation in fields unit
sin () = positive for updip flow
sin () = negative for downdip flow
qt = water injection rate
FFE can be written for relative
permeabilities where ke=Kr.K
Fractional flow equation
Typical plots of relative permeabilities and the corresponding fractional
flow curve ( S-Shape curve) are:
Factors affecting Fractional flow equation
Capillary
Gravity (direction
pressure
and dip angle)
Flow rate Viscosity
Wettability
Factors affecting Fractional flow equation
1- Wettability
Kw will be smaller in a water wet rock
than in an oil wet rock, then fw will be
smaller in water wet
Since it is desirable to minimize fw at a
particular saturation condition, then:
Water-wet reservoirs will yield a higher
displacement efficiency & higher oil
recovery than oil-wet reservoir
Factors affecting Fractional flow equation
2- Formation dip & direction of displacement
The effect of formation dip is dictated by
the gravity term, (ρw- ρo) sin
When water displaces oil up-dip:
sin () = + ve for updip flow
The effect of gravity will be to minimize fw, then
High displacement efficiency
When water displaces oil down-dip:
The effect of gravity is to decrease the disp.
efficiency
sin () = - ve for downdip flow
water should be injected dowh-dip to obtain maximum oil recovery
Factors affecting Fractional flow equation
3- Effect of capillary pressure
In water-wet system, as capillary pressure gradient increase, fw value
increases and the efficiency of the waterflood decreases
It would be desirable in a waterflood to decrease, or eliminate, the
capillary pressure gradient
This can be done by altering the wettability of the rock or by decreasing,
or eliminating, the interfacial tension between oil and water
Factors affecting Fractional flow equation
4- Effect of oil and water Mobilities
Improved oil recovery results from
decreasing the water mobility, or by
increasing the oil mobility
Kro & Krw are affected primarily by the
fluid saturations.
A displacement process can be
improved by increasing the water
viscosity or by decreasing the oil
viscosity
Water viscosity can be increased by the addition of
polymers
Factors affecting Fractional flow equation
4- Effect of injection Rate
The effect of rate varies depending upon whether
water is moving up-dip or down-dip.
A low value of rate is desirable if water is moving
up-dip (i.e., injection well is located downdip))
A large rate should be used for down-dip
displacement (i.e., injection well is located updip)
