design concepts in waterflood processes
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DESIGN CONCEPTS IN WATERFLOOD PROCESSE
SELECTION OF OPTIMUM FLOOD PATTERN
RESERVOIR FILL-UP
WATER INJECTIVITY
INJECTION ALLOCATION
RESERVOIR VOIDAGE
TYPE OF FLOOD PATERN
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Peripheral floods
Suitable for dipping, relatively homogeneous reservoirs
Require adequate lateral continuity and high transmissibility
Require careful control of withdrawal from up-structure wells and shutting-in of high
water cut wells Uniform flood patterns If well drilling cost is low, utilize smaller uniform patterns with equal distances
between injectors and producers such as four, five and seven spot
Choice between normal and inverted patterns should be based on observed
injectivity
Selected pattern should provide optimum injection and production capacity
Selected pattern type, pattern size and injection rate should be consistent with
available fluid lifting, rock fracturing pressure and well injectivity
Guidelines for Pattern Selection
Example
An oil reservoir is considered for waterflooding with a desirable flood life of 10 years and
total water injection of 2.5 pore volumes.
Given data: Porosity 28%
Net reservoir thickness 64 ft
Reservoir depth 2200 ft
Water injectivity 1.65 Bbl/day/psi
Maximum lifting capacilty 700 BFPD
Average reservoir pressure 900 psia
Expected operating days per year 350
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Fracturing pressure gradient 0.85 psi/ft
Water formation volume factor 1.02 RB/STB
Using a maximum bottomhole injection pressure of 90% of fracturing pressure, and
assuming zero voidage rate, determine the appropriate flood pattern for the proposed
waterflood.
Assume that pattern size = A acre
Pore volume per pattern = 7758xAx64x0.28 = 139A MBbl
Total volume of water injection = 2.5x139A = 348A MBbl
Desired Injection rate = 348Ax1000 / (10x350) = 99.4A BWPD/pattern
Fracturing pressure = 0.85x2200 = 1870 psia
Maximum injection rate = 1.65x(1870x0.9900) = 1292 BWPD
Hence; Pattern size A = 1292 / 99.4 = 13 acreRequired lifting per pattern = 1292x1.02 = 1318 BFPD
Number of producing wells required per pattern = 1318 / 700 = 1.9
Therefore;
An inverted seven spot (with size of 13 acre) is recommended since this type of pattern
provides a producer-to-injector ratio of 2.
Reservoir simulation models can help in selecting the flood pattern type and size to
achieve maximum oil recovery with minimum injected water.
Selected flood pattern should utilize as many as possible of the existing producing
wells.
Some existing producing wells can be converted to injectors. It should be
remembered that poor producers also make poor injectors. Hence; before deciding
on converting a poor producing well to an injector, some analysis is required to
determine the reasons for poor productivity.
If anisotropy or natural fractures exist, pattern alignment and utilization of elongated
patterns should be considered in order to avoid premature water breakthrough.
Reservoir simulation models can help in selecting optimum pattern variations. In flood patterns within dipping reservoirs, injectors should be located off center
closer to the up-dip side to delay the breakthrough time in down-dip producing
wells.
The shape and size of flood patterns located near fault planes or flow barriers
should be properly adjusted to in order avoid lack of communication between
injectors and producers in the same pattern
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Reservoir Fill-up
A fill-up period is required if free gas exists in the reservoir before waterflood
Oil production response in usually starts after fill-up period
During fill-up period, a significant amount of free gas goes back into solution
Waterflood design should allow for the fill-up period and its effect on production
performance and injectivity
Reservoir simulation models automatically account for fill-up effects
Reservoir engineering calculations can also be made using conceptual models to
provide approximate values for fill-up effects
Filled-Up Volume
If production occurs during fill-up:
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Wif= (Vp Sgi/ Bw) + (Npf Bo/ Bw) + Wpf
If no production occurs during fill-up:
Wif= Vp Sgi/ Bw
FILLED UP TIME
tif= Wif/ qinj = [(Vp Sgi/ Bw) + qo tif{(Bo/ Bw) + WOR}] / qinj
Solving for tifrequires an iterative procedure if qoand WOR are functions of time
Example
Calculate the volume of injected water required for fill-up, length of the fill-up period and
volumetric sweep efficiency for a waterflood pattern with the following characteristics:
Pattern size 20 acre
Gross reservoir thickness 72 ft
Net-to-gross ratio 0.86
Porosity 26%Initial free gas saturation 15%
Initial water saturation 31%
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Water saturation at breakthrough 63%
Oil production rate 158 BOPD
Water-oil ratio 0.7
Water injection rate 2500 BWPD
Oil formation volume factor 1.22 RB/STB
Water formation volume factor 1.03 RB/surface Bbl
Example, continued
Pore volume Vp= 7758x20x72x0.86x0.26 = 2498 MBbl
First iteration: Wif= 2498x0.15 / 1.03 = 364 MBbl
tif= 364000 / 2500 = 145.6 days
Second iteration:
Wif= (2498x0.15 / 1.03) + (158x145.6 / 1000)[(1.22 / 1.03) + 0.7] = 407.1 MBbl
tif= 407100 / 2500 = 162.8 days
Third iteration:
Wif= (2498x0.15 / 1.03) + (158x162.8 / 1000)[(1.22 / 1.03) + 0.7] = 412.3 MBbl
tif= 412300 / 2500 = 164.9 days
Fourth iteration:
Wif= (2498x0.15 / 1.03) + (158x164.9 / 1000)[(1.22 / 1.03) + 0.7] = 412.9 MBbl
tif= 412900 / 2500 = 165.2 days
Hence; Fill-up volume = 413 MBbl and Fill-up period = 165 days
Volumetric sweep efficiency at fill-up = 413x1.03 / [2498(0.630.31)] = 53.2%
Water Injectivity
Water injection rates play an important role in project design and economics Injection rates directly impact surface facilities and flood life
Water injection rate into a given well depends on:
-- Fluid viscosity and density
-- Fluid saturation distribution
-- Water quality
-- Reservoir depth
-- Injection tubing size and roughness
-- Bottomhole pressure in injection wells Pinj
-- Bottomhole flowing pressure in producing wells Pw-- Reservoir permeability
-- Flood pattern shape and size
-- Relative permeability characteristics
Water injectivity Jwis defined as:
Jw= qinj/ P
where P = PinjPw
Jwcan be estimated from Darcys Law and can be measured from well tests
Procedure to estimate Jwdepends on the flood stage:
-- From start till interference
-- From end of interference till fill-up
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-- From end of fill-up till breakthrough
-- From breakthrough till abandonment
Injectivity calculations:
First stage; Based on radial flow around injection wells
Third and fourth stages; Based on pattern shape, mobility ratio and areal sweepefficiency
Second stage; Use average between end of first and beginning of third stages
Note: First and second stages apply only for reservoirs with initial free gas
saturation Sgi
First Stage: From Start till Well Interference
where: k = absolute permeability, md
krw= water relative permeability at Swbt
kro= oil relative permeability at Swi
h = net reservoir thickness, ft
w= water viscosity, cp
o= oil viscosity, cp
Bw= water formation volume factor
S = skin factor
First stage applies as long as: rob< D /2
When oil banks from adjacent injectors meet: robmax= D / 2 and the second
stage starts
])(5.0)ln()ln([
00708.0
Skkr
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kr
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ro
o
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w
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w
wb
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ww
w
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First Stage: Example
Flood pattern 20-acre five-spot
Net reservoir thickness 54 ft
Porosity 24%
Permeability 174 md
Initial water saturation Swi 28%
Oil relative permeability at Swi 0.86
Average water saturation at breakthrough Swbt 62%
Water relative permeability at Swbt 0.15
Initial gas saturation 12%
Oil viscosity 1.3 cp
Water viscosity 0.5 cp
Water formation volume factor 1.02 RB/surf Bbl
Wellbore radius 0.4 ft
Bottomhole pressure in producer 600 psia
Bottomhole pressure in injector 1300 psia
Skin factor +0.9
Estimate:Time required to inject 30 MBbl of water per pattern at flood start Injected
volume and injection rate at start of well interference
First Stage: Example, continued
Oil bank outer radius rob= [1.787x30000 / (54x0.24x0.12)]0.5= 186 ft
Water bank outer radius rwb= 186x[0.12 / (0.62 0.28)]0.5= 111 ft
P = 1300 600 = 700 psi
Injection rate = = 2103 BWPD
gi
inj
ob
Sh
Wr
787.1
wi
bt
w
gi
obwb
SS
Srr
]9.0)86.03.1
15.05.0(5.0)
111186ln(
86.03.1)
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15.05.0[02.1
7005417400708.0
x
xxx
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Distance between adjacent injection wells D = (20x43560)0.5= 933 ft
Maximum value of rob: robmax= 933 / 2 = 466.5 ft
Corresponding value of rwb= 466.5x[0.12 / (0.62 0.28) ]0.5= 277 ft
Hence; at start of well interference:
Volume of injected water = 54x0.24x0.12x(466.5)
2
/ 1.787 = 189400 Bbl
Injection rate = = 1843 BWPD
Third and Fourth Stages: After Fill-up
M = 1 and Sgi= 0
Five spot pattern:
d = distance between injector and producer
Line drive with (d/a) 1:
d = distance between rows
a = distance between producers
Seven spot pattern:
d = distance between wells
Third and Fourth Stages: After Fill-upM = 1 and Sgi= 0
Nine spot pattern: d = half the length of pattern side
R = ratio of producing rate of corner to side wells
P is based on bottomhole flowing pressure of corner well
]9.0)86.0
3.1
15.0
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5.466ln(
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]619.0)/[ln(003541.0
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www
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003541.0
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and if P is based on bottomhole flowing pressure of side well
Third and Fourth Stages: After Fill-up
For unit mobility ratio M = 1; hence; kro/ o= krw/ w
Injectivity for this condition is designated as base (initial) injectivity Jw0
For example, for Five spot pattern:
For M = 1: As Eaincreases, Jwremains equal to Jw0
For M < 1: As Eaincreases, Jwdeclines
For M > 1: As Eaincreases, Jwincreases
Conductance ratio:
= Jw/ Jw0= qinj P
0/ qinj0 P
is a function of mobility ratio M and areal sweep efficiency Ea
can be used to estimate changes in injectivity with time
]2
693.0}272.0)/{ln(
2
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wow
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Third and Fourth Stages: Example
Estimate the water injection rate initially and after cumulative injection reaches 350
MBbls for a waterflood that has the following characteristics:
Flood pattern 20-acre five-spot
Net reservoir thickness 54 ft
Porosity 24%Permeability 174 md
Initial water saturation Swi 28%
Oil relative permeability at Swi 0.86
Average water saturation at breakthrough Swbt 62%
Water relative permeability at Swbt 0.15
Vertical sweep efficiency at breakthrough 80%
Initial gas saturation 0
Oil viscosity 1.3 cp
Water viscosity 0.5 cp
Water formation volume factor 1.02 RB/surf Bbl
Wellbore radius 0.4 ft
Bottomhole pressure in producer 600 psia
Bottomhole pressure in injector 1300 psia
Skin factor +0.9
Third and Fourth Stages: Example, continued
Distance between injector and producer:
d = (20x43560 / 2)0.5= 660 ft
Base injectivity:
Jw0
= 0.003541x0.86x174x54 / [1.02x1.3x(ln(660 / 0.4)0.619 + 0.9)]= 2.81 Bbl/day/psi
Initial injection rate = 2.81x(1300600) = 1967 BWPD
Mobility ratio M = (0.15x1.3) / (0.86x0.5) = 0.45
Pore volume per pattern = 7758x20x54x0.24 = 2011 MBbl
After injection of 350 MBbl:
Volumetric sweep efficiency Ev= 350 / [2011(0.620.28)] = 0.512
Areal sweep efficiency Ea = 0.512 / 0.8 = 0.64
From the correlation, Conductance ratio = 0.65
Hence; Water injection rate = 0.65x1967 = 1278 BWPD
Injection Allocation
Allocation of injected water is required in order to assure a uniform oil displacement
and optimum oil recovery
This is a key step in waterflood optimization and requires cooperative effort from
geologists and reservoir engineers
Injection allocation consists of two parts:
Balancing the injection rate and cumulative injection between various patterns
according to their pore volume
Achieving a uniform injection profile covering all reservoir flow units within
waterflood interval
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Continued monitoring is required to assure that allocated injection rates and
injection profiles are implemented
Balanced injection also:
Prevents fluid migration across pattern boundaries
Results in uniform fluid lifting requirements in producing wells
Minimizes premature water breakthrough
Injection rates for various patterns are calculated as follows:
Injection rate for pattern n qinjn= qinj
tVpn/ Vp
t
Where: qinjn= injection rate for pattern n
qinjt= total injection rate for the waterflood
Vpn= net pore volume for pattern n
Vpt= total net pore volume for waterflood area
Example
Total injection rate = 30000 BWPD
Total pore volume = 54750 MBbl
Pattern 1 2 3 4 5 6 7 8 9
Pore volume 5246 4246 6689 6027 7635 7988 3899 5866 7155
Injection rate 2875 2327 3665 3302 4183 4377 2137 3214 3920
Actual injected volumes can deviate from design values due to:
Unknown reservoir heterogeneity
Presence of natural fractures and thief zones
Formation damage in injection wells Non-uniform initial fluid saturation distribution in the reservoir
Non-uniform reservoir pressure distribution
Irregular pattern shapes
Monitoring and suitable remedial work should be conducted
Pattern voidage maps, Halls plots, production bubble maps and performance plots are
useful in this regard
Original injection allocation is usually revised based on actual performance and updated
reservoir studies
Maintaining uniform injection profile in all injection wells is a difficult task
Layer heterogeneity, shale breaks and thief zones affect injection profiles
Dual tubing strings with packers, twin injection wells and limited entry techniques
can help obtaining uniform injection profiles
Frequent spinner surveys, tracer surveys and use of observation wells are helpful
in determining actual injection profiles and water front movement
Cased-hole logging and 4-D seismic surveys also are done in some waterflood
projects to provide insight about fluid distribution and oil displacement
Note that these techniques are expensive, time consuming and require experience
and high technical capability
Relationship to Reservoir Pressure
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After reservoir fill-up, the next step is to raise average reservoir pressure to a
reasonable value
Selection of the pressure value is usually guided by fluid lifting conditions, available
water pumps, fracturing pressure and bubble point of reservoir oil
In general, a pressure value within 10 - 20% tolerance below the initial bubble point
is reasonable Raising average reservoir pressure is generally combined with fil-up period
Water injection and fluid withdrawal rates should be controlled in order to achieve a
negative reservoir voidage rate for a calculated period of time
After the desired reservoir pressure is reaches, waterflood is operated at zero
voidage rate to maintain the pressure
Voidage definition
Cumulative voidage =
NpBo+(GpNpRs)Bg+WpBwWinj-We
Voidage rate =
qo[Bo+(RpRs)Bg+WORBw]qinjBw-we
If voidage rate = 0 Reservoir pressure remains constant
If voidage rate > 0 Reservoir pressure will decline
If voidage rate < 0 Reservoir pressure will increase
Injection-Withdrawal Ratio
Defined as Injection rate / fluid withdrawal rate
IWR = qinjBw/ [qo{Bo+ (RpRs) Bg+ WOR Bw}]
IWR > 1 during reservoir fill-up period
IWR = 1 during pressure maintenance period
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Note that IWR does not take the water influx rate (we) into account due to the difficulty in
its estimation
If the water influx rate is known, the modified IWR is:
(IWR)m= (qinjBw+ we) / [qo{Bo+ (RpRs) Bg+ WOR Bw}]
Changes in reservoir pressureP = ( V / Vpct)
ct= cp+ Swcw + Soco+ Sgcg
Where: P = change in reservoir pressure, psi
V = cumulative reservoir voidage in RBbl
Vp= reservoir pore volume, Bbl
ct= total system compressibility, 1/psi
Sw, Soand Sgare water, oil and gas saturations
cw, coand cgare water, oil and gas compressibilities, 1/psi
cpis pore volume compressibility, 1/psi
After reservoir fill-up:
ct= cp+ Swcw+ Soco
ctafter fill-up
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Average producing WOR 1.8
Average producing GOR 405 SCF/STB
Oil formation volume factor 1.28 RB/STB
Gas formation volume factor 1.5 RB/MCF
Solution gas-oil ratio 368 SCF/STB
Expected water influx rate 8600 RB/day
Total compressibility ct= [6.8 + 0.38x3.2 + 0.62x14]x10-6= 16.7x10-6psi-1
Required change in reservoir pressure = 970635 = +335 psi
Required cumulative negative voidage = 187x106x335x16.7x10-6= 1046 MRBbl
Required voidage rate = 1046000 / (6x30) = 5812 RB/day
Current withdrawal rate = 14860[1.25+(674-315)x0.0022+0.87x1.03] = 43627 RB/day
Hence; Required water injection rate = 4362713500 + 5812 = 35939 BWPD
(IWR)m= (35939 + 13500) / 43627 = 1.13
Fluid withdrawal rate during pressure maintenance =
18500[1.28 + (405 - 368)x0.0015 + 1.8x1.03] = 59006 RB/day
Hence; Required water injection rate = 590068600 = 50406 BWPD
(IWR)m= (50406 + 8600) / 59006 = 1
Notes: -- Calculated injection rate during pressure maintenance period is quite sensitive to
the GOR and WOR values
-- It is recommended that reservoir engineers keep material balance to provide
reliable water influx estimates
Voidage Maps
Voidage analysis based on entire waterflood area is sometimes misleading Some waterfloods could have adequate voidage control as a whole but the
distribution for various parts may not be acceptable, i.e. some patterns may have
positive voidage while other patterns have negative voidage
Reservoir engineers should calculate voidage for individual patterns and prepare
appropriate voidage maps
Voidage maps (based on cumulative or current rate) provide visual illustration of
injection and withdrawal distribution
Voidage maps provide guidelines for making suitable changes to achieve optimum
oil displacement and recovery
Allocation factors
Calculating cumulative voidage or current voidage rate for a pattern requires the
application of well allocation factors:
Applied to injectors in normal Applied to producers in inverted patterns
Simple method:
Allocation factor = Angle of contribution / 360
Examples:
Corner well in nine-spot pattern = 90/360 = 0.25
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Side well in nine-spot pattern = 180/360 = 0.5
All wells in four-spot pattern = 60/360 = 0.167
All wells in five-spot = 90/360 = 0.25
All wells in seven-spot = 120/360
More accurate allocation factors are based on angle of contribution iand weighting
factors wirelated to reservoir characteristics
Appropriate weighting factors are usually estimated by engineers and geologists
familiar with the reservoir
Approximate weighting factors:
wi= (kh)ifor voidage rate
wi= (h)ifor cumulative voidage
Fi= wii / wi I
Allocation factors for peripheral wells are estimated based on their location and primary
production
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Allocation factors, Example
Allocation factors from the eight producing wells in this nine-spot pattern are:FA= 90 w5/ (90 w1+ 90 w2+ 90 w4+ 90 w5)
FB= 180 w5/ (180 w2+ 180 w5)
FC= 90 w5/ (90 w2+ 90 w3+ 90 w5+ 90 w6)
FD= 180 w5/ (180 w4+ 180 w5)
FE= 180 w5/ (180 w5+ 180 w6)
FF= 90 w5/ (90 w4+ 90 w5+ 90 w7+ 90 w8)
FG= 180 w5/ (180 w5+ 180 w8)
FH= 90 w5/ (90 w5+ 90 w6+)
Uses of voidage maps
Provide guidelines in making operational decisions to:
Increase or decrease water injection rates
Modify lifting capacities in certain wells
Drill additional infill wells
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Example of voidage maps
This voidage map indicates that:
1. Several patterns in the center of flood area need additional injection2. Need to decrease injection rate, modify fluid lifting or add infill producing wells in the
eastern part of flood area