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A comparative study of empirical, statistical, and soft computing methods coupled with feature ranking for the prediction of water saturation in a heterogeneous oil reservoir

  • Research Article - Applied Geophysics
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Abstract

The present research applies six empirical, three statistical, and two soft computing methods to predict water saturation of an oil reservoir. The employed empirical models are ‘Archie (Trans AIME 146(1):54–62, 1942),’ ‘DeWitte (Oil Gas J 49(16):120–134, 1950),’ ‘Poupon et al. (J Petrol Technol 6(6):27–34, 1954),’ ‘Simandoux (Revue deI’Institut Francais du.Petrol, 1963),’ ‘Poupon and Leveaux (1971),’ and ‘Schlumberger (Log interpretation principles/applications, p. 235, 7th printing. Houston, 1998)’; statistical methods are ‘multiple variable regression,’ ‘fine tree, medium tree, coarse tree-based regression tree,’ and ‘bagged tree, boosted tree-based tree ensembles’; and soft computing techniques are ‘support vector machine (SVM)’ and ‘Levenberg–Marquardt (LM), Bayesian regularization (BR), and scaled conjugate gradient (SCG)-based artificial neural network (ANN).’ In addition, log variables are ranked based on their significance in water saturation modeling. To achieve the goals, 521 data points are selected from three wells. Each data point has laboratory-derived core water saturation information and six well log features, such as gamma ray (GR), bulk density (RHOB), sonic travel time (DT), true resistivity (LLD), neutron porosity (φN), and Depth. Statistical indexes, namely regression coefficient, mean squared error, root mean squared error, average absolute percentage error, minimum absolute error percentage, and maximum absolute error percentage, are used to compare the prediction efficiency of study methods. Results show that the empirical models provide exceedingly poor prediction efficiency. Within the study models, fine tree, medium tree-based regression tree; bagged tree, boosted tree-based tree ensembles; fine Gaussian SVM; ANN with LM; and ANN with BR are very efficient predictive strategies. The log ranking reveals that GR and DT are the most important, whereas RHOB and φN are the least vital predictor variables in water saturation prediction.

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modified from Glover 2014; Shedid and Saad 2017)

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Abbreviations

AAPE:

Average absolute percentage error

ANN:

Artificial neural network

BR:

Bayesian regularization

LM:

Levenberg–Marquardt

MAPE:

Maximum absolute error percentage

MIPE:

Minimum absolute error percentage

MSE:

Mean squared error

MVR:

Multiple variable regression

NMR:

Nuclear magnetic resonance

RMSE:

Root mean squared error

RSS:

Residual sum of square

SCG:

Scaled conjugate gradient

SVM:

Support vector machine

SVR:

Support vector regression

LAM:

Laminated shale

STR:

Structural shale region

a :

Tortuosity factor

B:

Number of different bootstrapped training data sets

b j :

Bias related to neuron j

D :

Depth

DT:

Sonic travel time

e :

Residual error

\({\hat{f}}^{*b} (x)\) :

Bootstrap samples prediction

\({\hat{f}}_{{{{\rm bag}}}} (x)\) :

Final bagged samples prediction

GR:

Gamma ray

GRlog :

Gamma ray log response

GRmax :

Maximum gamma ray log response

GRmin :

Minimum gamma ray log response

I GR :

Shale index

LLD:

Deep resistivity log

m:

Cementation constant

n:

Saturation exponent

q :

Sonic response

R:

Regression coefficient

RHOB:

Bulk density

R sh :

Shale resistivity

R t :

True resistivity

R w :

Water resistivity

S w :

Water saturation

S wi :

Irreducible water saturation

V sh :

Shale volume

V BVM :

Bulk volume of movable fluid

V Lam :

Laminated shale volume

w :

Vector of network weight

W:

Weight vector

W :

Weighting matrix

W ij :

Linked weight between the neurons i and j

X :

Independent variable

y:

Label data

Y :

Dependent variable

\({\hat{y}}\) :

Predicted values

\({\hat{y}}_{{R_{j} }}\) :

Average response for the training observations within the Jth box

ε :

Constant error limits

ξ i :

Distance between the choice border and estimated values outside the border

ρ f :

Density of pore fluid

ρ ma :

Density of the matrix

φ :

Porosity (frac)

φ D :

Density porosity (frac)

φ Dc :

Corrected effective density porosity (frac)

φ e :

Effective porosity (frac)

φ N :

Neutron porosity (frac)

φ in :

Inter-matrix porosity

φ Nc :

Corrected effective neutron porosity (frac)

φ S :

Sonic porosity (frac)

φ Sc :

Corrected effective sonic porosity (frac)

φ t :

Total porosity (frac)

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Funding

This research work was funded by Shahjalal University of Science and Technology (SUST) Research Center, Project ID: AS/2020/1/58.

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Authors and Affiliations

  1. Department of Petroleum and Mining Engineering, Shahjalal University of Science and Technology, Sylhet, Bangladesh

    Labiba Nusrat Jahan, Tanveer Alam Munshi, Sree Sujon Sutradhor & Mahamudul Hashan

Authors
  1. Labiba Nusrat Jahan
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  2. Tanveer Alam Munshi
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  3. Sree Sujon Sutradhor
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  4. Mahamudul Hashan
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Contributions

TAM contributed to software and writing original draft; LNJ contributed to supervision, funding acquisition, and writing and editing original draft; MH contributed to supervision, conceptualization, funding acquisition, and writing original draft.

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Correspondence to Mahamudul Hashan.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Communicated by Prof. Jadwiga Anna Jarzyna (ASSOCIATE EDITOR) / Prof. Michał Malinowski (CO-EDITOR-IN-CHIEF)

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Jahan, L.N., Munshi, T.A., Sutradhor, S.S. et al. A comparative study of empirical, statistical, and soft computing methods coupled with feature ranking for the prediction of water saturation in a heterogeneous oil reservoir. Acta Geophys. 69, 1697–1715 (2021). https://doi.org/10.1007/s11600-021-00647-w

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