Estimation of porosity of rocks based upon axiomatic local linear model tree (a lolimot model) approach

  • Authors

    • Hossein Hossein Iranmanesh School of Industrial Engineering, College of Engineering, University of Tehran(U.T), Tehran, Iran
    • Ali Mollajan School of Industrial Engineering, College of Engineering, University of Tehran(U.T), Tehran, Iran
    2020-09-02
    https://doi.org/10.14419/ijet.v9i3.30836
  • Axiomatic Design Theory, Fuzzy Linear Regression, Local Linear Model Tree (Lolimot Model) Rocks Prosoity.

  • Shear and Compressional Wave Velocities along with other Petrophysical Logs, are considered as upmost important data for Hydrocarbon reservoirs characterization. In this study, porosity of the extracted rocks form concerned wells is interest as it can indicate the oil capacity of the wells of interest. In this study, we employ the principles of Axiomatic Design theory, specially the first (independence) axiom, to more simplify the measurement system. Also, to clarify the strength of Axiomatic Design theory in reducing the complexity of the system and optimizing the measurement system, we utilize the The Lolimot model (LOcal LInear MOdel Tree) as a model from the neural network family and apply it before and after implementing the basic logic of Axiomatic Design (AD) theory. In addition, in order to illustrate strength of the proposed method emphasizing the effectiveness of a method which benefit from both AD theory and Lolimot model together, the existing system used to measure the rock porosity is addressed and actual data related to one of wells located in southern Iran is utilized. The results of the study show that integrating the Axiomatic Design principles with the LOLIMOT method leads to the least complex and most accurate results.

     

     

  • References

    1. [1] Ameen, M.S., Smart, B.G.D., Somerville, J.M., Hammilton, S., Naji, N.A., 2009. Predicting rock mechanical properties of carbonates from wireline logs. Mar. Pet. Geol. 26, 430–444. https://doi.org/10.1016/j.marpetgeo.2009.01.017.

      [2] Annan, J., Chunan, T., 2008. Forecasting peak acceleration of blasting vibration of rock mass based on PSO-SVM, Control and Decision Conference, CCDC, 2541–2545.

      [3] Archer N.P. and Wang S. (1993). Application of the backpropagation neural network algorithm with montonicity constraints for two-group classification problems. Decision Sciences, 24(1), 60-75. https://doi.org/10.1111/j.1540-5915.1993.tb00462.x.

      [4] Bandyopadhyay, S., Pal, S.K., 2007. Classification and Learning Using Genetic Algorithms. Springer, pp. 320.

      [5] Bhattacharyya S. and Pendharkar P.C. (1998). Inductive, evolutionary, and neural computing techniques for discrimination: a comparative study. Decision Sciences29(4), 871-899. https://doi.org/10.1111/j.1540-5915.1998.tb00880.x.

      [6] Birch, F., 1960. The velocity of compressional waves in rocks 10 kbars: Part 1. J. Geophys. Res. 65, 83–1102. https://doi.org/10.1029/JZ065i004p01083.

      [7] Boonen, P., Bean, C., Tepper, R., Deady, R., 1998. Important implications from a comparison of LWD and wireline acoustic data from a Gulf of Mexico well. In: Transition of 39th SPWLA Annual Logging Symposium, Keystone, CO.

      [8] Brocher, T.M., 2005. Empirical relations between elastic wavespeeds and density in the earth’s crust. Bull. Seismol. Soc. Am. 95, 2081– 2092. https://doi.org/10.1785/0120050077.

      [9] Brocher, T.M., 2005. Empirical relations between elastic wavespeeds and density in the earth’s crust. Bull. Seismol. Soc. Am. 95, 2081– 2092. https://doi.org/10.1785/0120050077.

      [10] Brocher, T.M., 2008. Key elements of regional seismic velocity models for long period ground motion simulations. J. Seismol. 12 (2), 217–221. https://doi.org/10.1007/s10950-007-9061-3.

      [11] Brocher, T.M., 2008. Key elements of regional seismic velocity models for long period ground motion simulations. J. Seismol. 12 (2), 217–221. https://doi.org/10.1007/s10950-007-9061-3.

      [12] Burke L. (1991). Introduction to artificial neural systems for pattern recognition. Computers and Operations Research, 18(2), 211-220. https://doi.org/10.1016/0305-0548(91)90091-5.

      [13] Burlini, L., Fountain, D.M., 1993. Seismic anisotropy of metapelites from the Ivrea-Verbano zone and Serie dei Laghi (northern Italy). Phys. Earth Planet 78, 301–317. https://doi.org/10.1016/0031-9201(93)90162-3.

      [14] Carroll, R.D., 1969. The determination of acoustic parameters of volcanic rocks from compressional velocity measurements. Int. J. Rock Mech. Min. Sci. 6, 557–579. https://doi.org/10.1016/0148-9062(69)90022-9.

      [15] Carroll, R.D., 1969. The determination of acoustic parameters of volcanic rocks from compressional velocity https://doi.org/10.1016/0148-9062(69)90022-9.

      [16] Castagna, J.P., Batzle, M.L., Kan, T.K. 1993. Rock physics-The link between rock properties and AVO response. In: Castagna, J.P., and Backus, M., (Eds.), Offset-dependent reflectivity-Theory and practice of AVO analysis: Investigations in Geophysics, vol. 8, pp. 135–171. https://doi.org/10.1190/1.9781560802624.

      [17] Castagna, J.P., Batzle, M.L., Kan, T.K. 1993. Rock physics-The link between rock properties and AVO response. In: Castagna, J.P., and Backus, M., (Eds.), Offset-dependent reflectivity-Theory and practice of AVO analysis: Investigations in Geophysics, vol. 8, pp. 135–171. https://doi.org/10.1190/1.9781560802624.

      [18] Christensen, N.I., 1974. Compressional wave velocities in possible mantle rocks to pressures of 30 kilobars. J. Geophys. Res. 79, 407–412. https://doi.org/10.1029/JB079i002p00407.

      [19] Christensen, N.I., 1974. Compressional wave velocities in possible mantle rocks to pressures of 30 kilobars. J. Geophys. Res. 79, 407–412. https://doi.org/10.1029/JB079i002p00407.

      [20] D.S. Savic D.S. and W. Pedrycz W. (1991). Evaluation of fuzzy linear regression models. Fuzzy Sets and Systems, 39, 51-63. https://doi.org/10.1016/0165-0114(91)90065-X.

      [21] Eberhart R.C. and Dobbins R.W. (1990). Neural Network PC Tools: A Practical Guide. Academic Press.

      [22] Eissa, A., Kazi, A., 1988. Relation between static and dynamic Young’s moduli of rocks. Int. J. RockMech. Min. Sci. 25 (6), 479–482. https://doi.org/10.1016/0148-9062(88)90987-4.

      [23] El-Haik, B. S., and Yang, K., The components of complexity in engineering design, IIE Transactions, 1999, Vol. 31, No. 10, pp. 92 https://doi.org/10.1080/07408179908969893.

      [24] EL-HAIK, B. S., Axiomatic Quality: Integrating Axiomatic Design with Six-Sigma, Reliability, and Quality Engineering, New Jersey: John Wiley & Sons, 2005. https://doi.org/10.1002/0471714682.

      [25] Feng, X., 1995. A neural network approach to comprehensive classification of rock stability, blastability and drillability. Int. J. Min, Reclama. EnviroN 9 (2), 57–62. https://doi.org/10.1080/09208119508964719.

      [26] H. Tanaka H., S. Uejima S., and K Asai K. (1982). Linear regression analysis with fuzzy model. IEEE Transactions on Systems, Man, and Cybernetics, 12, 903-907. https://doi.org/10.1109/TSMC.1982.4308925.

      [27] Han I., Chandler J.S., and Liang T.P. (1996). The impact of measurement scale and correlation structure on classification performance of inductive learning and statistical methods. Expert Systems with Applications, 10(2), 209-221. https://doi.org/10.1016/0957-4174(95)00047-X.

      [28] James, G.A., Wynd, J.G., 1965. Stratigraphic nomenclature of the Iranian oil consortium agreement area. AAPG Bull., 71.

      [29] Ji, S.C., Salisbury, M.H., 1993. Shear-wave velocities, anisotropy and splitting in the high grade mylonites. Tectonophysics 221, 453–473. https://doi.org/10.1016/0040-1951(93)90173-H.

      [30] Ji, S.C., Wang, Q., Xia, B., 2002. Handbook of Seismic Properties of Minerals, Rocks and Ores. Polytechnic International Press, Montreal, pp. 630.

      [31] Kang, Y., Wang, J., 2010. A support-vector-machine-based method for predicting large-deformation in rock mass. Inst. of Rock & Soil Mech., Chinese Acad. of Sci. 3, 1176–1180. https://doi.org/10.1109/FSKD.2010.5569148.

      [32] Kang, Y., Wang, J., 2010. A support-vector-machine-based method for predicting large-deformation in rock mass. Inst. of Rock & Soil Mech., Chinese Acad. of Sci. 3, 1176–1180. https://doi.org/10.1109/FSKD.2010.5569148.

      [33] Kern, H., 1982. P- and S-wave velocities in crustal and mantle rocks under the simultaneous action of high confining pressure and high temperature and the effect of the rock microstructure. In: Schreyer, W. (Ed.), High-Pressure Research in Geosciences. E. chweizerbart’sche Verlagsbuchhandlung, Stuttgart, pp. 15-45.

      [34] Malaek, S.M.B., Mollajan, A., Ghorbani, A. and Sharahi, A., 2015. A new system engineering model based on the principles of axiomatic design. J Ind Int Inf, 3(2). https://doi.org/10.12720/jiii.3.2.143-151.

      [35] Mangasarian O.L., and Wolberg W.H. (1990). Multisurface method of pattern separaction for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences, 87, 9193-9196. https://doi.org/10.1073/pnas.87.23.9193.

      [36] Mangasarian O.L., Setiono R., and Wolberg W.H. (1990). Pattern recognition via linear programming: theory and application to medical diagnosis. Large-Scale Numerical Optimization, 22-30.

      [37] Markham I.S. and Ragsdale C.T. (1995). Combining neural networks and statistical predictions to solve the classification problem in discriminant analysis. Decision Sciences, 26(2), 229-242. https://doi.org/10.1111/j.1540-5915.1995.tb01427.x.

      [38] Mohammadi, H., Rahmannejad, R., 2009. The estimation of rock mass deformation modulus using regression and artificial neural network analysis. Arab. J. Sci. Eng 35 (1A), 67–77.

      [39] Niu, W., Li, T., 2010. An Intelligent Rock Mass Classification Method based on Support Vector Machines and the Development of

      [40] Niu, W., Li, T., 2010. An Intelligent Rock Mass Classification Method based on Support Vector Machines and the Development of Website for Classification, Information Technology in Geo-Engineering, Proceedings of the 1st International Conference (ICITG), Shanghai.

      [41] Patuwo E., Hu M.Y., and Hung M.S. (1993). Two-group classification using neural networks. Decision Sciences, 24(4), 825-845. https://doi.org/10.1111/j.1540-5915.1993.tb00491.x.

      [42] Peters G. (1994). Fuzzy linear regression with fuzzy intervals. Fuzzy Sets and Systems, 63, 44-55. https://doi.org/10.1016/0165-0114(94)90144-9.

      [43] Rasouli, V., Zacharia, J., Elike, M., 2011. The influence of perturbed stresses near faults on drilling strategy: a case study in Blacktip field North Australia. J. Pet. Sci. Eng. 76, 37–50. https://doi.org/10.1016/j.petrol.2010.12.003.

      [44] Rechlin, A.J., Lu¨ th, S., Giese, R., 2011. Rock mass classification based on seismic measurements using Support Vector Machines, Harmonising Rock Engineering and the Environment, Chapter 31. CRC Press. https://doi.org/10.1201/b11646-407.

      [45] Rechlin, A.J., Lu¨ th, S., Giese, R., 2011. Rock mass classification based on seismic measurements using Support Vector Machines, Harmonising Rock Engineering and the Environment, Chapter 31. CRC Press. https://doi.org/10.1201/b11646-407.

      [46] Sadooni, N.F., 1993. Stratigraphic sequence, MICROFACIES, and petroleum prospect of the Yamama formation, lower cretaceous, southern Iraq. AAPG Bull., 77. https://doi.org/10.1306/BDFF8F92-1718-11D7-8645000102C1865D.

      [47] Saemi, M., Ahmadi, M., Yazdian-Varjani, A., 2007. Design of neural networks using genetic algorithm for the permeability estimation of the reservoir. J. Pet. Sci. Eng. 59, 97–105. https://doi.org/10.1016/j.petrol.2007.03.007.

      [48] Salchenberger L.M., Cinar E.M., and Lash N.A. (1992). Neural networks: a new tool for predicting thrift failure. Decision Sciences, 23(4), 899-916. https://doi.org/10.1111/j.1540-5915.1992.tb00425.x.

      [49] Schrage L (1991). LINDO: An Optimization Modeling System, The Scientific Press, fourth edition.

      [50] Sharahi, A., Tehrani, R. and Mollajan, A., 2014. An Axiomatic Model for Development of the Allocated Architecture in Systems Engineering Process. World Academy of Science, Engineering and Technology, International Science Index, Industrial and Manufacturing Engineering, 8(10), pp.3210-3220.

      [51] Singh, R., Kainthola, A., Singh, T.N., 2012. Estimation of elastic constant of rocks using an ANFIS approach. Appl. Soft Comput. 12, 40–45. https://doi.org/10.1016/j.asoc.2011.09.010.

      [52] Steinwart, I., 2008. Support Vector Machines. Los Alamos National Laboratory, information Sciences Group (CCS-3). Springer.

      [53] Steinwart, I., 2008. Support Vector Machines. Los Alamos National Laboratory, information Sciences Group (CCS-3). Springer.

      [54] Subramanian V., Hung M.S., and Hu M.Y. (1993). An experimental evaluation of neural networks for classification. Computers and Operations Research, 20(7), 769-782. https://doi.org/10.1016/0305-0548(93)90063-O.

      [55] Suh, N.P., “Axiomatic Design: Advances and Applicationsâ€, 1st Edition, Oxford University Press, 2001.

      [56] Tam K.Y. and Kiang M.K. (1992). Managerial applications of neural networks: the case of bank failure predictions. Management Science, 38(7), 926-947. https://doi.org/10.1287/mnsc.38.7.926.

      [57] Tanaka H. and Ishibuchi H. (1992). Possibilistic regression analysis based on linear programming. in J. Kacprzyk and M. Fedrizzi ed., Fuzzy Regression Analysis, 47-60, Physica-Verlag, Heidelberg.

      [58] Wantland, D., 1964. Geophysical Measurements of Rock Properties in situ. In: Judd, W.R., (Ed.). State of Stress in Earth’s Crust, Proceedings of the International Conference, Santa Monica, California, pp. 409–450.

      [59] Wantland, D., 1964. Geophysical Measurements of Rock Properties in situ. In: Judd, W.R., (Ed.). State of Stress in Earth’s Crust, Proceedings of the International Conference, Santa Monica, California, pp. 409–450.

      [60] Watanabe, T., Kasami, H., Ohshima, S., 2007. Compressional and shear wave velocities of serpentinized peridotites up to 200 MPa. Earth Planets Space 59, 233–244. https://doi.org/10.1186/BF03353100.

      [61] Website for Classification, Information Technology in Geo-Engineering, Proceedings of the 1st International Conference (ICITG), Shanghai.

      [62] Wilson R.L. and Sharda R. (1994). Bankruptcy prediction using neural networks. Decision Support Systems, 11, 545-557. https://doi.org/10.1016/0167-9236(94)90024-8.

      [63] Yasar, E., Erdogan, Y., 2004. Correlating sound velocity with the density, compressive strength and Young’s modulus of carbonate rocks. Int. J. Rock Mech. Min. Sci. 41, 871–875. https://doi.org/10.1016/j.ijrmms.2004.01.012.

      Zoback, M., 2007. Reservoir Geomechanic, Cambridge University Press, 450p. https://doi.org/10.1017/CBO9780511586477

  • Downloads

  • How to Cite

    Hossein Iranmanesh, H., & Mollajan, A. (2020). Estimation of porosity of rocks based upon axiomatic local linear model tree (a lolimot model) approach. International Journal of Engineering & Technology, 9(3), 785-803. https://doi.org/10.14419/ijet.v9i3.30836