Data processing: measuring – calibrating – or testing – Measurement system in a specific environment – Earth science
Reexamination Certificate
2002-04-18
2003-12-09
Barlow, John (Department: 2862)
Data processing: measuring, calibrating, or testing
Measurement system in a specific environment
Earth science
C703S005000
Reexamination Certificate
active
06662109
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method of constraining by dynamic production data a fine geologic model representative of the distribution, in a heterogeneous reservoir, of a physical quantity characteristic of the subsoil structure, such as permeability or porosity.
2. Description of the Prior Art
The prior art to which reference is made hereafter is described in the following publications:
Wen, X.-H., et al.: “Upscaling hydraulic conductivities in heterogeneous media: An overview. Journal of Hydrology (183)”, ix-xxxii, 1996;
Renard, P.: “Modélisation des écoulements en milieux poreux hétérogénes: calcul des perméabilités équivalentes”. Thése, Ecole des Mines de Paris, Paris, 1999;
G. de Marsily: “De I'identification des systemes hydrologiques”. Thése, Université Paris 6, Paris, 1976;
Hu L.-Y. et al.: “Constraining a Reservoir Facies Model to Dynamic Data Using a Gradual Deformation Method”, VI European Conference on the Mathematics of Oil Recovery, Peebles, 1998;
Tarantola, A.: “Inverse Problem Theory: Method for Data Fitting and Model Parameter Estimation”. Elsevier, Amsterdam, 1987;
Anterion F. et al.: “Use of Parameter Gradients for Reservoir History Matching”, SPE 18433, Symposium on Reservoir Simulation of the Society of Petroleum Engineers, Houston, 1989;
Wen X.-H. et al.: “High Resolution Reservoir Models Integrating Multiple-Well Production Data”, SPE 38728, Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, San Antonio, 1997;
Chu L. et al. : “Computation of Sensitivity Coefficients With Application to the Integration of Static and Well Test Pressure Data”, Eclipse International Forum, Milan, 1994.
Numerical simulations of flow models are widely used in the petroleum industry to develop a reservoir and to predict its dynamic behavior according to various production scenarios. The geostatistical models used to represent the geologic structure of the reservoir (permeability, porosity, etc.) require an identification of a large number of grid cells that can reach about ten millions.
To be able to carry out numerical flow simulations within reasonable computing times, common practice consists in constructing a rough simulation model by grouping together grids with different properties into macrogrids and by assigning to the macrogrids an equivalent property calculated from the local properties. This operation is referred to as upscaling.
The aim of constrained reservoir characterization is to determine the parameters of the simulation model so that the latter can reproduce the production data of the reservoir to be modelled. This parameter estimation stage is also referred to as production data fitting. The flow simulation model is thus compatible with all of the available static and dynamic data.
In common practice, the parameters of the simulation model are estimated by means of a series of trials and errors using the flow simulator.
The problem of production data fitting can also be formulated as a problem of minimizing an objective function measuring the difference between the production data observed in the field and the predictions provided by the flow simulator. Minimizing is then carried out using optimization or optimum control techniques.
A method of predicting, by means of an inversion technique, the evolution of the production of an underground reservoir, notably of a reservoir containing hydrocarbons, is for example described in U.S. Pat. No. 5,764,515 filed by the assignee.
As soon as the parameters of the simulation model are adjusted, this model can be used to simulate the present and future behavior of the reservoir. An evaluation of the in-situ reserves is thus available and a development scheme optimizing the production can be determined.
Constrained reservoir characterization thus involves multiple techniques, from geostatistical modeling to optimization problems. The introduction of the main techniques used within the scope of the “inversion and upscaling” coupling methodology is dealt with in the section hereafter.
Geostatistical Modelling
Geostatistics, in its probabilistic presentation, implies that a spatial variable such as the permeability, for example, can be interpreted as a particular realization of a random function, defined by its probability law at any point in space. The increasingly common use of geostatistics by oil companies leads to the construction of fine models that can reach a large number of grid cells, In fact, geostatistics allows estimation of petrophysical properties in space from local measurements. Strictly speaking, realization of the geostatistical model has to be carried out on the scale of the measurement support, and the model thus obtained can then reach several million grid cells. Numerical flow simulation on the scale of the geostatistical model is not conceivable with the power of current computers. In order to reduce the number of grids, the grids have to be grouped together, which requires computation of the equivalent properties of the new grids as a function of the properties of the small-scale grids. This operation is referred to as upscaling.
Upscaling
Computation of the equivalent permeability of heterogeneous porous media has been widely studied by the community of geologists, reservoir engineers and more generally of porous media physicists.
From a mathematical point of view, the process of upscaling each directional permeability can be represented by the vectorial operator F defined by:
F
:R
m→R
M
k→K
(1)
k: the permeability on the scale of the geostatistical model (dimension R
m
); K:the permeability on the scale of the flow simulation model (dimension R
M
).
Wen et al. (1997) and Renard (1999), mentioned above, gave a review of the existing techniques from the prior art. Examples of known upscaling techniques are algebraic methods which involve simple analytical rules for plausible calculation of the equivalent permeabilities without solving a flow problem. The known method referred to as “power average” technique can be selected for example. The permeability K of block &OHgr; is equal to a power average, also called average of order
w
, whose exponent
w
ranges between −1 and +1:
K
(
w
)
=
(
1
mes
(
Ω
)
∫
Ω
k
w
ⅆ
Ω
)
1
/
w
(
2
)
The problem of the equivalent permeability calculation thus comes down to the estimation of the exponent w allowing minimization of the error induced by upscaling (defined according to a certain criterion). For media with an isotropic log-normal distribution and a low correlation length, it is well-known that:
w
=
1
-
2
α
(
3
)
&agr; being the dimension in space (&agr;=1, 2 or 3).
There are also known numerical upscaling techniques wherein calculation of the equivalent permeability involves solving the pressure p and velocity v fields of a local or global flow problem:
{
-
k
μ
∇
p
=
v
dans
Ω
div
(
v
)
=
0
dans
Ω
(
4
)
&mgr; denotes the viscosity of the flowing fluid.
Parameterization
The problem of geologic model updating by means of dynamic data is based on the solution of an inverse problem. This naturally poses the problem of the parameterization of the permeability field in order to allow minimization of the objective function which measures the difference (in the sense of the least squares) between the dynamic data observed in the field and the simulation results.
Parameterization of geostatistical models is a fundamental point which guarantees the success of the integration of the dynamic data into the geologic models. In fact, this integration is carried out according to an iterative procedure governed by the optimization process and disturbs an initial permeability field representative of the geostatistical model considered.
Ideally, the final permeability field must not only respect all the dynamic data take
Mezghani Mokhles
Roggero Frederic
Antonelli Terry Stout & Kraus LLP
Barlow John
Institut Francais du Pe'trole
Taylor Victor J.
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