Ensemble-based reservoir characterization method using multiple Kalman gains and dynamic data selection
The present disclosure relates to an ensemble-based reservoir characterization method using multiple Kalman gains and dynamic data selection. The method includes preparing available data; generating initial ensembles by using the prepared static data; clustering and separating the generated initial models on the basis of a distance-based method; selecting the dynamic data; dynamically simulating the selected dynamic data by using the generated ensembles; calculating multiple Kalman gains by using initial models clustered in the same group as the selected dynamic data; updating ensemble members by means of the selected dynamic data and the multiple Kalman gains; and predicting a movement of a reservoir by using the updated models, and evaluating uncertainty thereof. Therefore, multiple Kalman gains are calculated and a final model is obtained using the selected dynamic data, and a reliable uncertainty evaluation and a future movement prediction can be performed within a short time by using the final model.
1. An ensemble-based reservoir characterization method using multiple Kalman gains and dynamic data selection, the method comprising:
preparing available data including static and dynamic data;
generating initial ensembles by using the prepared static data;
clustering and separating the generated initial ensembles on the basis of a distance-based method;
selecting data among all the dynamic data;
dynamically simulating the selected dynamic data by using the generated initial ensembles;
calculating multiple Kalman gains by using initial models clustered in the same group as the selected dynamic data;
updating ensemble members by means of the selected dynamic data and the multiple Kalman gains; and
predicting a movement of a reservoir by using the updated ensemble members, and evaluating uncertainty thereof and wherein at the updating the ensemble members by using an ensemble smoother, the state vector v, representing the ensembles, is expressed by the following equation:
y
t
i
,
k
,
g
=
[
m
t
i
s
m
t
i
d
d
]
k
,
g
where, g represents a group a model belongs to and is selected from 1 to the number of clusters (N c ), k represents the model in the group g and is selected from 1 to the total number of models (N g ) in the group g, thus yti,k,g represents a state vector of k-th model in the group g at an initial time ti, m t i a and m t i d represent static and dynamic parameters at the initial time, ti, respectively, and d represents dynamic data prediction; and the state vector is assimilated by using the multiple Kalman gains and the dynamic data selection by the following equation:
y k,g a =y k,g p +K g ( d k,g −Hy k,g p )
where, superscripts a and p indicate an assimilated and a previous states, respectively, y k,g a and y k,g p mean an assimilated and a previous state vectors of the k-th model in the group g, respectively, H represents a measurement operator matrix, and dk,g represents the dynamic data predication of the k-th model in the group g.
2. The method of claim 1 , wherein at the calculating the multiple Kalman gains, the multiple Kalman gains are calculated by the following equation:
K g =C Y,g p H T ( HC Y,g p H T +C D ) −1
where, K g indicates a Kalman gain representing the group g among the multiple Kalman gains, C Y,g p− indicates a previous estimate error covariance of the group g, H represents a measurement operator matrix, and C D represents an observation error covariance, and H T means a transpose of the measurement operator matrix.
3. The method of claim 2 , wherein calculating the multiple Kalman gains includes calculating the multiple Kalman gains by group, after clustering the initial ensembles.
4. The method of claim 3 , wherein the distance-based method is obtained by:
obtaining a distance matrix;
converting the distance matrix into coordinate points in the metric space; and
classifying adjacent coordinate points into the same group.
5. The method of claim 4 , wherein the obtaining the distance matrix is performed by using a Minkowski equation, wherein definition of a distance is performed for the static data or the selected dynamic data;
the converting the distance matrix into the coordinate points in the metric space is performed by using multidimensional scaling; and
the classifying the adjacent coordinate points into the same group is performed by using K-means algorithm.
6. The method of claim 1 , wherein the selected dynamic data uses logically meaningful dynamic data only among all the available dynamic data, wherein the meaningful dynamic data have unique values different from the dynamic data.