Title
A Direct inverse model to determine permeability fields from pressure and flow rate measurements
Author
Brouwer, G.K.
Fokker, P.A.
Wilschut, F.
Zijl, W.
TNO Bouw en Ondergrond
Publication year
2008
Abstract
The determination of the permeability field from pressure and flow rate measurements in wells is a key problem in reservoir engineering. This paper presents a Double Constraint method for inverse modeling that is an example of direct inverse modeling. The method is used with a standard block-centered finite difference method. With an a priori grid block permeability field as input, two forward runs are made: the first is constrained with the measured pressures; the second is constrained with the measured flow rates. We calculate the pressures in the grid block centers from the first run, while from the second run we calculate the fluxes through the faces between the grid blocks. Substitution of these pressures and fluxes into Darcy's law then yields the transmissibilities at the faces and hence the permeabilities in the grid blocks. In this way the "hard" data (measured pressures and flow rates) are always honored while the "soft", geological data can be incorporated at the discretion of the geologist. Using a synthetic example, we demonstrate the method and compare the results with another method: Ensemble Kalman Filtering. The two methods agree within the scope of their applicability. The Double Constraint method focuses initially on determining spatial distributions of the permeability field for single-phase, steady state flow. For history matching an extension is required to non-steady state, two-phase flow conditions, which is already possible with EnKF. We are currently investigating the possibility of combining the two methods, whereby the strengths of the two methods could be fully exploited. © International Association for Mathematical Geology 2008.
Subject
Geosciences
Assimilation
Double constraint method
EnsembleKalman filter
History matching
Inversion
Permeability
Constraint theory
Finite difference method
Flow rate
Kalman filters
Mechanical permeability
Pressure measurement
Two phase flow
Darcy law
ensemble forecasting
finite difference method
flow measurement
inverse analysis
Kalman filter
numerical model
permeability
pressure
spatial distribution
two phase flow
To reference this document use:
http://resolver.tudelft.nl/uuid:195d982c-535a-4c16-9945-5bbb61ae9fc7
TNO identifier
240923
ISSN
1874-8961
Source
Mathematical Geosciences, 40 (8), 907-920
Document type
article