Risk, Uncertainty and Priorities - Quantitative Models
437
The pattern of sub-salt pressure development and associated porosity retention must therefore be substantially different at location D compared to location
A. It is this difference which is of interest here. However, the actual speed of the
salt sheet is uncertain, as is the thickness, so that some degree of uncertainty
must also be present in the pressure buildup, in both magnitude and time at each
location.
Thus, both an estimate of average pressure buildup and of the range of uncertainty of the estimate are concern. These twin problems are addressed here.
4.1
Computer Model Manipulations
4.1.1
General Considerations
The dynamical control on the modeled development is that sedimentary thicknesses calculated forwards in time to the present day should agree with current
observations. This constraint is used to adjust parameters describing equations
of state behavior for each lithology until a minimum disagreement is reached
between calculations and observations (Lerche 1991).
For instance, for a fixed present day salt thickness, a range of salt speeds generates a set of overpressure build-up calculations at a given location. At each
time-step the overpressure with depth is recorded for each computer run, so that
the cumulative probability of obtaining less than a particular value of overpressure at each depth can be calculated. Thus, Fig. 9 shows cumulative iso-probability contours of excess fluid pressure with depth for location A at the present
day. As an example, from Fig. 9 we see that there is a 90% chance of an excess
pressure less than about 50 kgJ em at a depth of 2000 m, while there is only a 10%
chance of obtaining an excess pressure less than about 30 kgJcm- 2 at the same
depth. The median value (50% chance) for excess pressure at 2000 m depth is
about 40 kgJcm- 2 •
The same sort of diagram can be generated at each time-step at each location
across the section of figure 8, allowing for uncertainty in both the salt speed and
present -day salt thickness. Three measures provide indications of the influence
of moving salt sheets on lateral variations of excess pressure in formations below
the salt. First is a measure of the mean excess fluid pressure with depth at each
location and for each time step; we use the excess pressure (Pso) at 50% cumulative probability as this indicator. Second is the volatility, v, in the mean pressure
estimate Pso ' which provides a measure of the uncertainty in the 50% pressure
value; a definition of volatility is
v= (P90 - P lO)JPSO,
(1)
where P90(PlO) is the excess pressure value at 90% (10%) cumulative probability.
A low volatility, v< < 1, implies but little uncertainty in Pso so that there is not a
dramatic influence on excess pressure evolution due to the ranges of variation in
437
The pattern of sub-salt pressure development and associated porosity retention must therefore be substantially different at location D compared to location
A. It is this difference which is of interest here. However, the actual speed of the
salt sheet is uncertain, as is the thickness, so that some degree of uncertainty
must also be present in the pressure buildup, in both magnitude and time at each
location.
Thus, both an estimate of average pressure buildup and of the range of uncertainty of the estimate are concern. These twin problems are addressed here.
4.1
Computer Model Manipulations
4.1.1
General Considerations
The dynamical control on the modeled development is that sedimentary thicknesses calculated forwards in time to the present day should agree with current
observations. This constraint is used to adjust parameters describing equations
of state behavior for each lithology until a minimum disagreement is reached
between calculations and observations (Lerche 1991).
For instance, for a fixed present day salt thickness, a range of salt speeds generates a set of overpressure build-up calculations at a given location. At each
time-step the overpressure with depth is recorded for each computer run, so that
the cumulative probability of obtaining less than a particular value of overpressure at each depth can be calculated. Thus, Fig. 9 shows cumulative iso-probability contours of excess fluid pressure with depth for location A at the present
day. As an example, from Fig. 9 we see that there is a 90% chance of an excess
pressure less than about 50 kgJ em at a depth of 2000 m, while there is only a 10%
chance of obtaining an excess pressure less than about 30 kgJcm- 2 at the same
depth. The median value (50% chance) for excess pressure at 2000 m depth is
about 40 kgJcm- 2 •
The same sort of diagram can be generated at each time-step at each location
across the section of figure 8, allowing for uncertainty in both the salt speed and
present -day salt thickness. Three measures provide indications of the influence
of moving salt sheets on lateral variations of excess pressure in formations below
the salt. First is a measure of the mean excess fluid pressure with depth at each
location and for each time step; we use the excess pressure (Pso) at 50% cumulative probability as this indicator. Second is the volatility, v, in the mean pressure
estimate Pso ' which provides a measure of the uncertainty in the 50% pressure
value; a definition of volatility is
v= (P90 - P lO)JPSO,
(1)
where P90(PlO) is the excess pressure value at 90% (10%) cumulative probability.
A low volatility, v< < 1, implies but little uncertainty in Pso so that there is not a
dramatic influence on excess pressure evolution due to the ranges of variation in