Basra University for oil & gas
College of oil and gas Engineering
Oil & gas engineering department
Water flooding
Buckely-Leverett- Part 2
By Ali K. Al-Maliki, MSc
Novemeber, 2017
1
Water flooding
Outline
Application of BL & FFE
Average water saturation in swept area
Average water saturation at BT
Average water saturation after BT
Recovery factor calculations
Recovery calculations to BT
Recovery calculations after BT 2
Applications of BL & FFE
Main calculations for water flooding in homogenous reservoirs using BL
and S-shape curve:
1- Constructing water saturation profile
2- Breakthrough time
3- Cumulative water injection
4- Pore volume of water injected
5- Average water saturation in the Swept area
6- Recovery factor before, at and after Breakthrough
7- injection and production profile
8- Produced WOR and Wc
3
BL & FFE Application: Average SW calculation
The average water saturation in the swept
area is determined in both
1- Before and at Breakthrough
2- After Breakthrough
4
BL & FFE Application: Average SW at BT
Average Sw in the swept area at BT:
fwf
The tangent to the fractional flow curve
is extrapolated to fw = 1
The intercept with fw=1 is the average
water saturation, SwBT
The slope of the tangent can be
calculated as follow: Swf
5
BL & FFE Application: Average SW at BT
Average Sw in the swept area at BT:
Average Sw in the swept area
would remain constant with a 0.8
value of SwBT until BT occurs 0.7 1-Sor
0.6
At BT time, the flood front 0.5
saturation S reaches the Swf
Sw
wf
0.4
producing well and the water cut 0.3 Swf Swf=Swbt
increases suddenly from zero to 0.2
fwf 0.1
0 100 200 300
At BT, Swf= SwBT and fwf =fwBT Distance, ft 6
BL & FFE Application: Average SW at BT
Cumulative water injected at BT
7
BL & FFE Application: Average SW after BT
Average Sw in the swept area After BT:
After BT, the water saturation
0.8
& WC at the producing well Sw2, fw2
0.7
gradually increase due to
0.6
continuous injection of water
0.5
Swf
Sw
0.4
SW and water cut at the Swf
0.3 Swf=Swbt
producing well are denoted
0.2
as Sw2 and fw2
0.1
0 100 200 300
Distance, ft 8
BL & FFE Application: Average SW after BT
Welge graphical solution:
When the water saturation at the
producing well reaches any assumed
value S after BT, S-Shape curve is used to
w2
determine::
1- Producing water cut fw2
2- Average water saturation, Sw2
3- Cumulative water injected in pore volumes, Qi
9
BL & FFE Application: Average SW after BT
Welge graphical solution:
The saturation at which the tangent
intersects fw = 1 is the average water
saturation in the swept area, Sw2
The average water saturation can be
determined mathematically from:
10
BL & FFE Application: Average SW after BT
The cumulative pore volumes of water
injected, Qi at the time when the water
saturation reaches Sw2 at the
producing well
11
BL & FFE Application: Average SW after BT
The cumulative water injected when
the water saturation at the
producing well reaches Sw2
12
BL & FFE Application: Oil recovery calculations
A set of calculations are required to determine the water flooding
performance and to calculate the oil recovery versus time:
Oil production rate, Qo
Cumulative Water Injected, Winj
Water production rate, Qw
Surface water-oil ratio, WOR Water-injection rate, Iwj
Cumulative oil production, Np
Water-injection pressure, Pinj
Cumulative Water production, Wp
Recovery factor, RF
13
BL & FFE Application: Oil recovery calculations
Oil recovery calculations is divided into two parts: Assuming no
free gas in
the reservoir
1-Before breakthrough time calculations
2-After breakthrough time calculations
Oil recovery before and after breakthrough is calculated by:
Np = N x EA x EV x ED N = OIIP at the start of water injection, STB
Np = cumulative oil production, STB
EA = Areal sweep efficiency, fraction
Ev = Vertical sweep efficiency, fraction
ED = Displacement sweep efficiency, fraction
14
BL & FFE Application: Oil recovery calculations
Before Breakthrough: Assuming
no free gas
The cumulative oil production is simply equal to the in the
volume of water injected with no water production reservoir,
Sgi=0
Np = Winj
Wp = 0
Qw = 0
15
BL & FFE Application: Oil recovery calculations
At Breakthrough: Assuming
no free gas
ED can be calculated by determining the average water in the
saturation at breakthrough reservoir,
Sgi=0
Np at breakthrough is calculated from:
16
BL & FFE Application: Oil recovery calculations
After Breakthrough: Assuming
no free gas
in the
Oil recovery calculations after breakthrough are reservoir,
based on determining ED at various assumed Sgi=0
values of Sw at the producing well
17
BL & FFE Application: Oil recovery calculations
Procedure for recovery calculations before and after BT:
1- Construct the fractional flow curve
2- Select several values of water saturations between Swf and
(1 – Sor) and determine the slope (dfw/dSw) at each saturation
3- Perform recovery calculations to breakthrough
4- Perform recovery calculations after breakthrough
18
BL & FFE Application: Oil recovery calculations
Sw BT
Recovery calculations to breakthrough (S = 0, E , E = 100%)
gi A V
(Sgi = 0, EA, EV = 100%)
Plot fw vs. Sw
Tangent the curve from Swi, then
𝒅𝒇𝒘
determine Swf , fwf and
𝒅𝑺𝒘 𝑺𝒘
𝒇
Extrapolate the tangent at fw=1 and
determine the average water
saturation at the breakthrough, Sw BT
19
BL & FFE Application: Oil recovery calculations
Recovery calculations to breakthrough (Sgi = 0, EA, EV = 100%)
Calculate pore volumes of water
injected at BT
Calculate the cumulative water
injected at BT
20
BL & FFE Application: Oil recovery calculations
Recovery calculations to breakthrough (Sgi = 0, EA, EV = 100%)
Calculate the displacement efficiency at BT
Calculate cumulative oil production at BT
Np = N x EA x EV x ED
Calculate time to BT assuming iw=constant
21
BL & FFE Application: Oil recovery calculations
Recovery calculations to breakthrough (Sgi = 0, EA, EV = 100%)
Select several values of injection time less than the BT time (t < tBT)
and calculate the followings:
WORs, Qw and Wp are all
equals zero as no water
has arrived the producer
yet because the chosen
time is less than BT time
22
BL & FFE Application: Oil recovery calculations
Recovery calculations to breakthrough (Sgi = 0, EA, EV = 100%)
Calculate the surface water–oil ratio WORs at BT
Construct a table as follow:
t Winj Np Qo WOR Qw Wp
0 0 0 0 0 0 0
fwBt is the water cut
at BT ( fwBT = fwf)
t1 ---- ---- ---- 0 0 0
t2 ---- ---- ---- 0 0 0
t3 ---- ---- ---- 0 0 0
BT ---- ---- ---- --- ---- ---- 23
BL & FFE Application: Oil recovery calculations
Recovery calculations After breakthrough (Sgi = 0, EA, EV = 100%)
Choose several values of Sw2 between Sw Bt and (1-Sor)
Determine fw2 & dsw/dfw corresponding each Sw2
Calculate the average water saturation in the swept area for each sw2:
Find it from extrapolating the tangent to fw=1
Or use the following equation:
24
BL & FFE Application: Oil recovery calculations
Recovery calculations After breakthrough (Sgi = 0, EA, EV = 100%)
1
4- Find average Sw
0.98
1
0.9 0.96
0.8 0.94
fw
0.7
0.92
0.6
3- tangent
0.9 the curve, find dfw/dsw
0.5
fw
0.4 0.88
2- Find fw
0.3 0.86
0.2
0.84
0.1
0.82
0
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8
0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74 0.76 0.78 0.8
Sw
1- Select SW Sw
25
BL & FFE Application: Oil recovery calculations
Recovery calculations After breakthrough (Sgi = 0, EA, EV = 100%)
Calculate the displacement efficiency ED for each
selected value
Calculate cumulative oil production Np for each selected value of Sw2
Np = N x EA x EV x ED
Calculate pore volumes of water
injected, Qi, at each Sw2
26
BL & FFE Application: Oil recovery calculations
Recovery calculations After breakthrough (Sgi = 0, EA, EV = 100%)
Calculate cumulative water injected for each Sw2
Calculate the time to inject Winj barrels of water
27
BL & FFE Application: Oil recovery calculations
Recovery calculations After breakthrough (Sgi = 0, EA, EV = 100%)
Calculate cumulative water production WP at any time t
from the material balance equation
Calculate the surface water–oil ratio
WORs that corresponds to
each value of fw2
28
BL & FFE Application: Oil recovery calculations
Recovery calculations After breakthrough (Sgi = 0, EA, EV = 100%)
Calculate the oil and water flow rates
29
BL & FFE Application: Oil recovery calculations
Recovery calculations After breakthrough (Sgi = 0, EA, EV = 100%)
Construct a table as follow:
Sw2 fw2 dfw/dsw s-w2 Ed Np Qi Winj t Wp WORs Qo Qw
Swbt fwbt -- s-wbt Edbt Npbt Qibt Wibt tbt 0 -- -- --
-- -- -- -- -- -- -- -- -- -- -- -- --
-- -- -- -- -- -- -- -- -- -- -- -- --
-- -- -- -- -- -- -- -- -- -- -- -- --
-- -- -- -- -- -- -- -- -- -- -- -- --
1-Sor 1 -- -- -- -- -- -- -- -- -- 0 --
30
BL & FFE Application: Oil recovery calculations
Additional calculations:
𝑁𝑃
𝑅𝐹 =
𝑁
31
