Pete603 10
Pete603 10
Pete603 10
PVT
quantity
Pressure
V n 1
p p n 1
V 1 c f p p
n
i
n
i
Solutions:
take smaller timesteps
iterate on chord slope (IMPES)
30.7 Instability Error
Sw
Time
If a simulation run becomes unstable erroneous
saturations will occur.
30.8 Instability Error
Caused by taking timesteps which are
too large in an IMPES method.
Solution:
Take smaller timesteps
Use fully implicit method
30.9 Truncation Error
f(x + x) - f(x) x x 2
f (x) = - f (x) - f (x) + ....
x 2! 3!
f(x + x ) - f(x)
f (x) = - O x
x
800
DELT
10 days
600
5 days
1.25 days
400
0.15 days
200
0 20 40 60 80
TIME, days
Solution:
Use smaller gridblocks
Upstream relative permeabilities also help
minimize numerical dispersion.
Multipoint upstream sometimes used in tracer
studies
Use pseudorelative permeabilities
(pseudofunctions)
Choose timestep wisely in IMPES
(maximum stable timestep)
30.13 Numerical Dispersion
Do we want to remove numerical
dispersion altogether?
Buckley-Leverett flow does not apply for
many field cases.
Capillary pressure spreads out fluid front,
especially in low permeability reservoirs.
Permeability heterogeneity smears fluid
front (fingering).
Some numerical dispersion may be
acceptable.
30.14 Grid Orientation
Producer Producer
Injector
Producer Producer
30.19 Data Modification - 5 spot
ky
2
kx
2
30.21 Data Modification - 5 spot