A framework for history matching - StreamSim Technologies, Inc.

Questions & Answers
Technology
“How does Mepo check the quality of the
history match?”
The quality of the HM is simply quantified by the difference
between the measured and simulated values. All types of
measurement values such as pressures (BHP, RFT),
production rates, WCT and GOR, can be included. The
following definition of the objective function is used in Mepo:
Q denotes the quality, or objective function
i references an objective element, e.g. the oil rate at a
particular well
k references the time step at which an observed value exists
w is the weight of the objective element i at time step k
i,k
defines observed value of the objective element i at time step k
oi,k ci,k σi defines calculated value of the objective element i at time step k
is the standard deviation (the measurement error) of the
objective element i
n,m refers to all model parameters
x model parameter and mean value
C covariance matrix
“How does Mepo assess the uncertainty in
the production forecasts?”
Uncertainties are assessed by identifying several simulation
models that belong to different parts of the search space,
all having acceptable matches. In addition, experimental
design is used to assure a large initial variation of
parameter levels.
“Which optimisation methods are used in
Mepo?“
A pool of optimisation algorithms is implemented to assist
the engineer in the HM study. An evolution strategy is used
for global optimisation. Local search methods like a Simplex
algorithm and a gradient method are used for fine tuning
applications or small size problems. A Bayesian approach is
included to identify parameter sets with a good potential to
further improve the match.
An evolution strategy belongs to the class of evolutionary
algorithms, which use only the objective function value to
determine new search steps, and do not require any
gradient information from the optimisation problem.
They can therefore be used in cases where gradient information
is not available, and where traditional algorithms fail
because of significant non-linearities or discontinuities in the
search space. Evolutionary algorithms have proven to be
robust and easy to adopt to different engineering problems.
The nature of evolutionary algorithms is to use parallel
structures in generating parent-to-child sequences. This
principal feature can be easily transferred to parallel structures
of an optimisation program allowing parallel
computing to be used.
“Which parameters can be varied in the
history matching study?”
In principle, there are no limits to which parameters one
can alter, both discrete and continuous parameters can
be varied. Fault locations, relative permeability curves,
stochastic realisations, PVT data and grids are examples of
discrete parameters often used in an HM study. Uncertainties
in continuous parameters like permeability, porosity,
aquifer size and productivity index are also common. A
generalised pre-processing concept allows the inclusion of
basically every simulation parameter as a design or
optimisation parameter.