HISTORY MATCHING
Definition:
History matching is the process of modifying some
of the reservoir model data until a reasonable
comparison (match) is obtained between the
observed history data and simulator results.
Objectives:
The primary objectives of history matching are to
improve and validate the simulation model so
that it can be used with confidence to predict the
future performance of the reservoir.
PARAMETERS THAT ARE
MATCHED
Average Reservoir Pressure
 Field Total Production Rates
 Well Production Rates
- Water rate
- Gas rate
 Average Well Pressure
 Well Flowing Bottom Hole Pressure

PARAMETERS THAT CAN BE
MODIFIED
Fluid properties
 Relative permeability
- Change end point values
- Change shape of curve
 Capillary pressure data

PARAMETERS THAT CAN BE
MODIFIED

Reservoir description data
- Permeability
- Porosity
- Thickness
PARAMETERS THAT CAN BE
MODIFIED

Well completion data
Productivity index

Initial fluid contacts
- Oil-water contact
- Gas-Oil contact
AVERAGE RESERVOIR
PRESSURE MATCH
1 dV Re ctotol
1 Qtotal ∆t
ceff = −
=
=
V dp
Vp ∆ p Vp ∆ p
( Q o Bo + Q w B w + Q g B g ) ∆ t
Qtotal ∆t
∆p=
=
c eff V p
( S o c o + S w c w + S g c g + c f )V p
Influencing parameters:
1. Fluid volumes: Porosity, thickness, oil-water and
gas-oil contacts
2. Total fluid withdrawal: Relative permeabilities and oilwater and gas-Oil contacts
3. Compressibilities (co , cw , cg , cf)
INDIVIDUAL WELLS
AVERAGE PRESSURE MATCH
After the average reservoir pressure match,
adjust the permeability locally (around the
wells) to obtain a match for the individual
wells average pressure.
- The simulator provides a pressure for
the cell where the well is located.
- A pressure buildup test provides a pressure
for the drainage area of the well.
PRESSURE BUILD-UP DATA
2600
Shut-in pressure
2400
2200
2000
1800
1600
1400
1
10
(tp+∆t)/∆t
100
AVERAGE WELL PRESSURE
CORRECTIONS
Adjustments of Observed Pressure Data
a) Build-up pressure data is available:
The shut-in pressure from build-up
should be taken at shut-in time, ∆ts
∆ts = (33.8 ϕ µ ct/k) (∆x2 + ∆y2)
The well block pressure is the same as
pws at ∆t = ∆ts
AVERAGE WELL PRESSURE
CORRECTIONS
b) Shut-in pressure is measured at one
shut-in time, ∆tm:
Correct pws by:
∆pws = [162.6 Qo Bo µo /kh] log(∆ts/∆tm)
pws at ∆tm should be on the straight line
of the Horner build-up plot
∆tm < 4.06x106 ϕ µ ct A/k
A = Drainage area of the well (acres)
PRODUCTION RATES MATCH
Match the water and gas production rates.
Parameters that can be adjusted:
1. Permeability, thickness, oil-water and
gas-oil contacts
2. Relative permeabilities (end points and
shape of the curves)
WELL MODEL
 Producer:
Q = Oil production rate
∆y
Pcell = Grid cell average pressure
pwf = Flowing bottom hole pressure
S = Skin factor
ro = 0.14 (∆x) 2 + (∆y ) 2
0.00708 k h
PI =
ln(ro / rw ) + S
∆x
PRODUCTION RATES MATCH
Qo = PIλ o ( p cell − p wf )
Q w = PIλ w ( p cell − p wf )
Q g = [ PIλ o ( p cell − p wf )]Rso + PIλ g ( p cell − p wf )
k
λ o = ro
µ o Bo
WOR =
k rw
λw =
µ w Bw
λg =
λ
Qw
= w
λo
Qo
Q w = WOR Qo
λ o Rso + λ g
λg
=
= Rso +
GOR =
λo
λo
Qo
Qg
Q g = GOR Qo
k rg
µ g Bg
FLOWING BOTTOM HOLE
PRESSURES
After the average wells pressure and production
rates match, adjust the individual wells productivity
index to obtain a flowing bottom hole pressure
match.
Qo = PIλo ( p cell − pwf )
pwf = pcell
k ro
λo =
µ o Bo
Qo
−
PIλo
INJECTION BOTTOM HOLE
PRESSURES
Gas Injector:
Qg = PI λT (Pinj – Pcell)
Pinj = Pcell + Qg / [PI λT]
Water Injector:
Qw = PI λT (Pinj – Pcell)
Pinj = Pcell + Qw / [PI λT]
λT = (kro/µoBo) + (krw/µwBw + (krg/µgBg)
History of Oil Production Rate
Oil Rate (STB/D)
700
600
500
400
300
200
100
0
1
2
3
Time (years)
4
History Matching
Parameters that were varied
 OWC
 Thickness
 Permeability
 Porosity
 Productivity
index
Effect of OWC on Average
Reservoir Pressure
2100
OWC = 6857
2000
OWC = 6852
1900
OWC = 6862
1800
1700
1600
1500
0
0.5
1
1.5
2
2.5
Time (years)
3
3.5
4
Effect of OWC on Water Rate
600
OWC = 6857
OWC = 6852
OWC = 6862
500
400
300
200
100
0
0
0.5
1
1.5
2
2.5
T ime (years)
3
3.5
4
Effect of Formation Thickness on
Average Reservoir Pressure
2100
Thickness = Base Case
2000
Thickness = 0.95* Base Case
Thickness = 1.05*Base Case
1900
1800
1700
1600
0
0.5
1
1.5
2
2.5
T ime (years)
3
3.5
4
Effect of Formation Thickness
on Water Rate
Water Rate (STB/D)
300
250
200
Thickness = Base Case
150
Thichness = 0.95*Base Case
Thichness = 1.05*Base Case
100
0
0.5
1
1.5
2
2.5
T ime (years)
3
3.5
4
Effect of Formation Permeability
on Average Reservoir Pressure
2100
Permeability = Base Case
Permeability = 0.8* Base Case
2000
Permeability = 1.2*Base Case
1900
1800
1700
1600
0
0.5
1
1.5
2
2.5
Time (years)
3
3.5
4
Effect of Formation Permeability
on Average Well Pressure
Pressure (psia)
2000
Permeability=Base Case
Permeability=0.8*Base Case
Permeability=1.2*Base Case
1900
1800
1700
1600
1500
1400
0
0.5
1
1.5
2
2.5
Time (years)
3
3.5
4
Effect of Formation Permeability
on Water Rate
300
250
200
Permeability = Base Case
Permeability = 0.8*Base Case
Permeability = 1.2*Base Case
150
0
0.5
1
1.5
2
2.5
T ime (years)
3
3.5
4
Effect of Formation Porosity on
Average Reservoir Pressure
2100
Porosity = Base Case
Poroslity = 0.9*Base Case
Poosiity = 1.1*Base Case
2000
1900
1800
1700
1600
0
0.5
1
1.5
2
2.5
Time (years)
3
3.5
4
Effect of Formation Porosity on
Water Rate
300
250
200
Porosity = Base Case
Porosity = 0.9*Base Case
Porosity = 1.1*Base Case
150
0
0.5
1
1.5
2
2.5
Time (years)
3
3.5
4
Pressure (psia)
Effect of Productivity Index on
Flowing Bottom Hole Pressure
1600
PI = 2.5
PI = 2.0
PI = 3.0
1400
1200
1000
800
600
0
0.5
1
1.5
2
2.5
Time (years)
3
3.5
4