Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya

Madegwa James Etyang; Edward Gachangi Njenga

doi:doi:10.11648/j.ajtas.20160505.12

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Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya

Madegwa James Etyang, Edward Gachangi Njenga

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)

Received: 15 July 2016 Accepted: 22 July 2016 Published: 6 August 2016

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Abstract

To measure the output of a geothermal well, also known as amount of megawatts of a well, discharge tests are done between two to four months after drilling of the well to collect the relevant types of data which includes wellhead pressure, lip pressure and the weir height. After collection of these data, [8] formula is applied in determining the well output. These data exhibits skewness and excess kurtosis also known as heavy – tailedness, an attempt to fit ordinary least squares (OLS) model to such data leads to model misspecification. Therefore, in this study, robust non-parametric estimation has been used to fit these data as applied by [1]. The model is known to be robust to outliers which characterize the wells data, robustness signifies insensitivity to deviations from the strict model assumptions. A comparison between the robust method used and OLS method has also been made with graphical illustrations. The results show that locally weighted regression (loess) method used with a smoothing parameter of 0.07 and a polynomial of order 2 fits the geothermal well discharge data. It was confirmed that geothermal well discharge data is characterized by outliers which may affect the ultimate determination of the value of a well output and therefore there is need for further statistical data processing to remove the errors before Russel James method is applied.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 5)
DOI	10.11648/j.ajtas.20160505.12
Page(s)	260-269
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Locally Weighted Regression, Wellhead Pressure, Lip Pressure, Weir Height, Geothermal Well Output

References

[1]	Cleveland W. S., 1979. Robust Locally Weighted Regression and Smoothing Scatterplots. Journal of the American Statistical Association, 74: 829 – 836.
[2]	Cleveland W. S. and Devlin S. J., 1988. Locally weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Association, 83: 596-610.
[3]	Cleveland W. S., and Loader C. L., 1996. Smoothing by local regression: principles and methods. In Hardle W. and Schimek M. G., editors, Statistical Theory and Computational Aspects of Smoothing, pages 10-49. Springer, New York.
[4]	Grant M. A., Donaldson I. G. and Bixley P. F., 1982: Geothermal reservoir engineering. Academic Press Ltd., New York, 369.
[5]	Heya M. M., 2002. Geothermal exploration and development in Kenya. Ministry of Energy, Kenya.
[6]	Houssein D. E., 2008. Geothermal resource assessment through well testing and production response modelling, United Nations University, MSC thesis.
[7]	Jacoby W. G., 2000. Loess: a non-parametric, graphical tool for depicting relationships between ariables, Department of Government & International Studies, University of South Carolina, Columbia, USA.
[8]	James R., 1962. Steam water critical flow through pipes, Proceedings of the Institution of Mecanical engineers, London 176-26, 739-748.
[9]	Lagat J., Mbia P. and Muturia C. L., 2010: Menengai prospect: Investigations for its geothermal potential. Contributions from: Njue L., Mutonga M., Malimo S., Kanda I.
[10]	Mungania J., 2004. Geological studies of Menengai geothermal prospect, Kenya Electricity Generating Company Ltd., internal report, 18.
[11]	Ofwona C. O., Kipyego E. K. and Suwai J. J., 2011. Preliminary well test data of Menengai exploration wells, Kenya Geothermal Conference Paper.
[12]	Suwai J. J., 2011. Preliminary reservoir analysis of Menengai geothermal field exploration wells, Geothermal Training Programme, Reporting.

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Madegwa James Etyang, Edward Gachangi Njenga. (2016). Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya. American Journal of Theoretical and Applied Statistics, 5(5), 260-269. https://doi.org/10.11648/j.ajtas.20160505.12

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ACS Style

Madegwa James Etyang; Edward Gachangi Njenga. Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya. Am. J. Theor. Appl. Stat. 2016, 5(5), 260-269. doi: 10.11648/j.ajtas.20160505.12

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AMA Style

Madegwa James Etyang, Edward Gachangi Njenga. Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya. Am J Theor Appl Stat. 2016;5(5):260-269. doi: 10.11648/j.ajtas.20160505.12

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@article{10.11648/j.ajtas.20160505.12,
  author = {Madegwa James Etyang and Edward Gachangi Njenga},
  title = {Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {260-269},
  doi = {10.11648/j.ajtas.20160505.12},
  url = {https://doi.org/10.11648/j.ajtas.20160505.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.12},
  abstract = {To measure the output of a geothermal well, also known as amount of megawatts of a well, discharge tests are done between two to four months after drilling of the well to collect the relevant types of data which includes wellhead pressure, lip pressure and the weir height. After collection of these data, [8] formula is applied in determining the well output. These data exhibits skewness and excess kurtosis also known as heavy – tailedness, an attempt to fit ordinary least squares (OLS) model to such data leads to model misspecification. Therefore, in this study, robust non-parametric estimation has been used to fit these data as applied by [1]. The model is known to be robust to outliers which characterize the wells data, robustness signifies insensitivity to deviations from the strict model assumptions. A comparison between the robust method used and OLS method has also been made with graphical illustrations. The results show that locally weighted regression (loess) method used with a smoothing parameter of 0.07 and a polynomial of order 2 fits the geothermal well discharge data. It was confirmed that geothermal well discharge data is characterized by outliers which may affect the ultimate determination of the value of a well output and therefore there is need for further statistical data processing to remove the errors before Russel James method is applied.},
 year = {2016}
}

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TY  - JOUR
T1  - Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya
AU  - Madegwa James Etyang
AU  - Edward Gachangi Njenga
Y1  - 2016/08/06
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.12
DO  - 10.11648/j.ajtas.20160505.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 260
EP  - 269
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.12
AB  - To measure the output of a geothermal well, also known as amount of megawatts of a well, discharge tests are done between two to four months after drilling of the well to collect the relevant types of data which includes wellhead pressure, lip pressure and the weir height. After collection of these data, [8] formula is applied in determining the well output. These data exhibits skewness and excess kurtosis also known as heavy – tailedness, an attempt to fit ordinary least squares (OLS) model to such data leads to model misspecification. Therefore, in this study, robust non-parametric estimation has been used to fit these data as applied by [1]. The model is known to be robust to outliers which characterize the wells data, robustness signifies insensitivity to deviations from the strict model assumptions. A comparison between the robust method used and OLS method has also been made with graphical illustrations. The results show that locally weighted regression (loess) method used with a smoothing parameter of 0.07 and a polynomial of order 2 fits the geothermal well discharge data. It was confirmed that geothermal well discharge data is characterized by outliers which may affect the ultimate determination of the value of a well output and therefore there is need for further statistical data processing to remove the errors before Russel James method is applied.
VL  - 5
IS  - 5
ER  -

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Author Information

Madegwa James Etyang

Department of Mathematics, Kenyatta University, Nairobi, Kenya
Edward Gachangi Njenga

Department of Mathematics, Kenyatta University, Nairobi, Kenya

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APA Style

Madegwa James Etyang, Edward Gachangi Njenga. (2016). Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya. American Journal of Theoretical and Applied Statistics, 5(5), 260-269. https://doi.org/10.11648/j.ajtas.20160505.12

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ACS Style

Madegwa James Etyang; Edward Gachangi Njenga. Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya. Am. J. Theor. Appl. Stat. 2016, 5(5), 260-269. doi: 10.11648/j.ajtas.20160505.12

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AMA Style

Madegwa James Etyang, Edward Gachangi Njenga. Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya. Am J Theor Appl Stat. 2016;5(5):260-269. doi: 10.11648/j.ajtas.20160505.12

Copy | Download

@article{10.11648/j.ajtas.20160505.12,
  author = {Madegwa James Etyang and Edward Gachangi Njenga},
  title = {Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {5},
  pages = {260-269},
  doi = {10.11648/j.ajtas.20160505.12},
  url = {https://doi.org/10.11648/j.ajtas.20160505.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160505.12},
  abstract = {To measure the output of a geothermal well, also known as amount of megawatts of a well, discharge tests are done between two to four months after drilling of the well to collect the relevant types of data which includes wellhead pressure, lip pressure and the weir height. After collection of these data, [8] formula is applied in determining the well output. These data exhibits skewness and excess kurtosis also known as heavy – tailedness, an attempt to fit ordinary least squares (OLS) model to such data leads to model misspecification. Therefore, in this study, robust non-parametric estimation has been used to fit these data as applied by [1]. The model is known to be robust to outliers which characterize the wells data, robustness signifies insensitivity to deviations from the strict model assumptions. A comparison between the robust method used and OLS method has also been made with graphical illustrations. The results show that locally weighted regression (loess) method used with a smoothing parameter of 0.07 and a polynomial of order 2 fits the geothermal well discharge data. It was confirmed that geothermal well discharge data is characterized by outliers which may affect the ultimate determination of the value of a well output and therefore there is need for further statistical data processing to remove the errors before Russel James method is applied.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Application of Loess Procedure in Modelling Geothermal Well Discharge Data from Menengai Geothermal Wells in Kenya
AU  - Madegwa James Etyang
AU  - Edward Gachangi Njenga
Y1  - 2016/08/06
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160505.12
DO  - 10.11648/j.ajtas.20160505.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 260
EP  - 269
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160505.12
AB  - To measure the output of a geothermal well, also known as amount of megawatts of a well, discharge tests are done between two to four months after drilling of the well to collect the relevant types of data which includes wellhead pressure, lip pressure and the weir height. After collection of these data, [8] formula is applied in determining the well output. These data exhibits skewness and excess kurtosis also known as heavy – tailedness, an attempt to fit ordinary least squares (OLS) model to such data leads to model misspecification. Therefore, in this study, robust non-parametric estimation has been used to fit these data as applied by [1]. The model is known to be robust to outliers which characterize the wells data, robustness signifies insensitivity to deviations from the strict model assumptions. A comparison between the robust method used and OLS method has also been made with graphical illustrations. The results show that locally weighted regression (loess) method used with a smoothing parameter of 0.07 and a polynomial of order 2 fits the geothermal well discharge data. It was confirmed that geothermal well discharge data is characterized by outliers which may affect the ultimate determination of the value of a well output and therefore there is need for further statistical data processing to remove the errors before Russel James method is applied.
VL  - 5
IS  - 5
ER  -

Copy | Download