All hydrocarbon reservoirs are surrounded by water-bearing rocks called aquifers which they effect on reservoir performance. it's a key role for production evaluation and therefore it should be managed.

1. Reservoir Management
Sadeq Rajabi

2. Introduction
 Nearly all hydrocarbon reservoirs are surrounded by
water-bearing rocks called aquifers.
 Aquifers may be substantially larger than the oil or gas reservoirs they adjoin as
to appear infinite in size
 Aquifers may be so small in size as to be negligible in their effect on reservoir
performance
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3.  As reservoir fluids are produced, a pressure differential develops
between the surrounding aquifer and the reservoir. The aquifer reacts
by encroaching across the original hydrocarbon-water contact.
 Many gas and oil reservoirs produced by a mechanism termed water
drive. (natural water drive)
 water drive is dependent on the size of aquifer and the pressure drop
from the aquifer to the reservoir.
 During production aquifer response comes in a form of water influx,
commonly called water encroachment
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4. Classification of AQUIFERS
 Degree of pressure maintenance
 Flow regimes
 Outer boundary conditions
 Flow geometries
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5. Degree of Pressure Maintenance
 Active water drive: The term active water drive refers to the
water encroachment mechanism in which the rate of water influx
equals the reservoir total production rate. during any long period,
the production rate and reservoir pressure remain reasonably
constant
 Partial water drive: a relatively small. aquifer can
guarantee only limited pressure maintenance
 Limited water drive: The term active water drive refers to
the water encroachment mechanism in which the rate of water
influx is less than the reservoir total production rate.
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6.  where
We = cumulative water influx, bbl
t = time, days
Np = cumulative oil production, STB
GOR = current gas-oil ratio, scf/STB
Rs = current gas solubility, scf/STB
Bg = gas formation volume factor, bbl/scf
Wp = cumulative water production, STB
dNp/dt = daily oil flow rate Qo, STB/day
dWp/dt = daily water flow rate Qw, STB/day
dWe/dt = daily water influx rate ew, bbl/day
(GOR − Rs)dNp/dt = daily free gas flow rate, scf/day
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7. OUTER BOUNDARY CONDITIONS
 Infinite system indicates that the effect of the pressure
changes at the oil/aquifer boundary can never be felt at the outer
boundary.
 Finite system indicates that the aquifer outer limit is affected by
the influx into the oil zone and that the pressure at this outer limit
changes with time.
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8. FLOW REGIMES & FLOW GEOMETRIES
 Steady-state
 Semisteady-state
 Unsteady-state
 Edge-water drive
 Bottom-water drive
 Linear-water drive
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9. WATER INFLUX MODELS
 Pot aquifer
 Schilthuis’ steady-state
 Hurst’s modified steady-state
 The van Everdingen-Hurst unsteady-state
Edge-water drive
Bottom-water drive
 The Carter-Tracy unsteady-state
 Fetkovich’s method unsteady-state
Radial aquifer
Linear aquifer
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10. Small or pot aquifer
 Where
We = cumulative water influx, bbl
cw = aquifer water compressibility, psi−1
cf = aquifer rock compressibility, psi−1
Wi = initial volume of water in the aquifer, bbl
 where
ra = radius of the aquifer, ft
re = radius of the reservoir, ft
h = thickness of the aquifer, ft
φ = porosity of the aquifer
 Where
f = fractional encroachment angle
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11. Schilthuis’ steady-state
 Where
ew = rate of water influx, bbl/day
k = permeability of the aquifer, md
h = thickness of the aquifer, ft
ra = radius of the aquifer, ft
re = radius of the reservoir
t = time, days
C = the water influx constant , bbl/day/psi
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12. Hurst’s modified steady-state
 dimensionless radius
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13.  Dimensionless diffusivity equation for the following two reservoir-aquifer
boundary conditions:
• Constant terminal rate
• Constant terminal pressure
 Constant terminal rate
• the rate of water influx =constant(for a given period)
• the pressure drop at the reservoir-aquifer boundary is calculated
 Constant terminal pressure
• a boundary pressure drop =constant (over some finite time period)
• water influx rate is determined
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The van Everdingen-Hurst (VEH) model

14. 14
(a) an edge-water drive
(b) a bottom-water drive

15. 15
Edge-Water Drive
The authors expressed their mathematical relationship for
calculating the water influx in a form of a dimensionless
parameter that is called dimensionless water influx WeD.
Dimensionless water influx as a function of the dimensionless
time tD and dimensionless radius rD.
 Where
t = time, days
k = permeability of the aquifer, md
φ = porosity of the aquifer
μw = viscosity of water in the aquifer, cp
ra = radius of the aquifer, ft
re = radius of the reservoir, ft
cw = compressibility of the water, psi−1
cf = compressibility of the aquifer formation, psi−1
ct = total compressibility coefficient, psi−

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17. 17
We = cumulative water influx, bbl
B = water influx constant, bbl/psi
Δp = pressure drop at the boundary, psi
WeD = dimensionless water influx

18. 18
 Pressure Drop in Boundary
principle of superposition
 where
(We)Δp1 = B Δp1 (WeD)t3
(We)Δp2 = B Δp2 (WeD)t3 − t1
(We)Δp3 = B Δp3 (WeD)t3 − t2

19. Bottom-Water Drive
Coats (1962)
WeD as a function of rD, tD, and zD
 where
kv = vertical permeability
kh = horizontal permeability
Allard and Chen (1988)
 Where
zD = dimensionless vertical distance
h = aquifer thickness, ft
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20. 20

21. The Carter-Tracy unsteady-state
 where
B = the van Everdingen-Hurst water influx
tD = the dimensionless time as defined by Equation 10-17
n = refers to the current time step
n − 1 = refers to the previous time step
Δpn = total pressure drop, pi − pn, psi
pD = dimensionless pressure
p′D = dimensionless pressure derivative
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22. The following approximation could also be used between tD > 100:
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23. Fetkovich’s method
 where
ew = water influx rate from aquifer, bbl/day
J = productivity index for the aquifer, bbl/day/psi
pa = average aquifer pressure, psi
pr = inner aquifer boundary pressure, psi
 where
Wi = initial volume of water in the aquifer, bbl
ct = total aquifer compressibility, cw + cf, psi−1
pi = initial pressure of the aquifer, psi
f = θ/360
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24.  Lee and Wattenbarger (1996)
 where
w = width of the linear aquifer
L = length of the linear aquifer
rD = dimensionless radius, ra/re
k = permeability of the aquifer, md
t = time, days
θ = encroachment angle
h = thickness of the aquifer
f = θ/360
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25. References
 Advanced Reservoir Engineering
by Paul McKinney, Tarek Ahmed
 Petrowiki
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26. THANK
YOU
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