Findings

Today, I read the paper again to understand the logic of the methodology in it and find some relationship between pseudo density log and pseudo NMR.

Since Density Log is often run over as a small portion of the well and log data of it is missed often, the methodology is constructed in pseudo-density log generation.

The methodology is concluded as following steps:

Data Preprocessing

1.     Normalization of well log data

2.     PCA for dimension reduction

Data Mining

3.     Electrofacies correlated with lithofacies are calculated by statistical analysis

4.     GMM transform well log data into Gaussian distribution so the mixture model becomes GMM

5.    EM can approximate  accurately after several iterations

6.     MBC do not define clusters of data, which improves GMM

7.     Sampling and discriminant analysis select sample points for well correlation

Data Postprocessing

8.     ANN extracts and recognizes the underlying dominant patterns and structural relationships among data

9.     Model is built up for pseudo density log data prediction and regeneration.

The figure of pseudo density log generation workflow is as follows:

Relationship between pseudo density log and pseudo NMR

Considering every step of the methodology, it is constructed for the compensation of Density Log weaknesses. Density Log is often run over as a small portion of the well and log data of it is missed often. Some parts of the methodology may be used in pseudo NMR.

Since real NMR is so expensive, we may also run over as a small portion of the well. We can construct a similar methodology step by step. The small portion of the data gotten by real NMR can be utilized to build up a model by ANN finally. As a result, the data of real NMR can be predicted and regenerated.

However, if we do not do any real NMR, the methodology may not be used into pseudo NMR. In addition, a small portion data of real NMR may just reflect the reservoir characterization in a portion part of the well, so the model built up by the methodology may not be able to predict the whole reservoir characterization accurately.

I will read more papers tomorrow, trying to find something more useful for pseudo NMR.

Following parts and conclusions

Well Log Data Ming

GMM assumes that one well log matrix is one mixture model, which is a probabilistic model. This method transforms well log data into Gaussian distribution, with the parameters . The objective function of EM algorithm is the likelihood of the GGM. The likelihood maximization is shown as follows:

EM can give a relatively accurate approximation after iterations.

The figure of GMM clustering results is as follows:

Well Correlation

It enables people to do well correlation by generating electrofacies after applying model-based clustering. Then the paper determines the size of the sample and select sample points with systematic sampling method.

Discriminant analysis (DA) it is a classification method where clusters from populations are known to be a priori, assuming that different classes generate data based on different Gaussian distributions.

To facilitate future improvement, we can use core analysis to calibrate well correlation results.

Well Log Data Postprocessing

Artificial neural network (ANN)

It is a dynamic computation system which is capable of extracting and recognizing the underlying dominant patterns among data, classifying new patterns and generalizing an output based on the learned data.

Feedforward back-propagation is a common scheme for training the network.

The figure of pairwise well prediction results is as follows:

Conclusions

The system consists of three components: data preprocessing, data mining and data postprocessing. The data are normalized, reduced in dimension, modeled and selected, then correlated, finally predicted and generated.

(Some of the equations cannot be shown in the Blogger. Tomorrow, I plan to read the paper again and find something useful for pseudo well log.)

Day2 on reading the paper

Well Log Data Preprocessing

Normalization: it's necessary because different types of well log data have different units. The equation is as follows:

x_(i,norm)=(x_i-μ_i)/(σ_i*‖x_i ‖_∞ )

In the equation, the most confusing part is ‖x_i ‖_∞, I find out that ‖x_i ‖_∞=sup|x_n |, it means that ‖x_i ‖_∞is the biggest among |x_n | if I am right.

PCA: it allows the reduction of the dimensionality (number of the columns) of the well log data but retains most of the variability of that data.The equation is as follows:

X_PCA=XV^T

Well Log Data Ming

Data mining is the computation process of discovering patterns in large data sets involving methods at the intersection of artificial intelligence, machine learning, statistics and database. The figure of data mining technologies is as follows:

In my opinion, although it may be an ideal tool in the automatic pseudo-density log generation system, it is challenging for people to combine so many kinds of complex methods together.

Lithofacies & Electrofacies

Electrofacies are calculated based on statistical analysis, having a correlation with lithofacies.

Gaussian Mixture Model

I am still trying to understand it. To be continued on next Monday.

Summary(the first three parts)

The main idea of this paper is to realize the Reservoir characterization.

It describes how one integrates a comprehensive methodology of data mining techniques and artificial neural network (ANN) in reservoir properties prediction and regeneration, especially in pseudo density log generation.

ANN is a machine-learning model to establish a model for analyzing experimental, industrial and field data.

Data mining technique is better than manual stratigraphic interpretation (labor intensive and time consuming).

The study obtains porosity by three steps:

1.     Preprocess the log data;

2.     Recognize pattern and interpret stratigraphic information;

3.     Choose a similar pattern as input to generate pseudo-density log using ANN.

Figure below is the workflow of pseudo density log generation. The results of three components will

predict actual density log.