History Matching & Optimization
- In geosciences, it is rare that the physical model is accurate, generally
simplifications are made under certain assumptions. The input parameters of the
model are usually difficult to measure (porosity, permeability, saturation, etc..),
These measures are often incomplete or inaccurate, or simply impossible to achieve
(fracture length, etc..). These uncertainties will then affect the outcome of the
resolution of the direct problem. To reduce the uncertainties on the input parameters,
it is common to use easily measurable data (well tests, pressure, etc..) and simulated,
and to estimate the values of uncertain parameters for which simulations are to
better measured data: we speak of the inverse problem.
- The inverse problem aims to characterize the parameters of the model
to be consistent with the measured data. This procedure is called History Matching.
- The calibration of these dynamic tests is done using many direct flow
simulations on realistic geological models. This characterization step is particularly
costly in computation time and also mobilizes the expertise of reservoir engineers
to identify the most feasible solutions. To solve this problem it is necesary to
use optimization algorithms. However, the solutions are not unique and the algorithm
can be trapped in local minima.
- Innovative techniques resolve this kind of problem. Indeed, the global
optimization algorithm can get out of local minima to identify the best solutions
(those that best match the data). Also, to solve the problem of computation time
of reservoir simulations, it is conventional to use the proxy. Neural networks are
the best suited approach as they are very well adapted to represent nonlinear phenomena.
- As many fields around the world are reaching maturity, the need to
develop new tools that allows reservoir engineers to optimize reservoir performance
is becoming more demanding. One of the more challenging and influential problems
along these lines is the well placement optimization problem. In this problem, there
are many variables to consider: geological variables like reservoir architecture,
permeability and porosity distribution, and fluid contacts; production variables
such as well placement, well number, well type, and production rate; economic variables
like fluid prices and drilling costs. All these variables, together with reservoir
geological uncertainty, make the determination of a suitable development plan for
a given field difficult.
- To quantify the trust given to numerical results, it is important to
estimate the impact of data errors on the estimation of model parameters considered.
A typical approach is to perform a risk analysis a posteriori using Monte Carlo
simulations. This very simple approach to implement can be very costly in computation
time. Indeed, this method requires a large number of simulations to explore the
- The response surfaces are intended to represent schematically the response
of a model based on input parameters. A key issue of these methods is to achieve
a realistic representation of the response by limiting the cost calculation, i.e.
by performing a minimum of simulations (using experimental design), which can be
very long especially in the case of flow simulations. From these response surfaces,
a risk analysis is performed using Monte Carlo simulations.
- Learning methods, such as neural networks, are the best suited approach
as well they are very adapted to represent nonlinear phenomena.
Terra 3E offers different plug-ins for Petrel* answering these challengingly:
* Trademark of Schlumberger