# A study for estimating reservoir transmissivity based on the recovery process of a wellbore water level after water injection: Numerical modeling of the temperature recovery component

Research output: Contribution to journalArticle

### Abstract

The author reports a numerical modeling study considering the recovery process of a wellbore water level due to temperature recovery after water injection into a geothermal well. This study intends to estimate the transmissivity of a geothermal reservoir based on this recovery process. We assume that the real recovery process of a wellbore water level after water injection consists of two components: the component of pressure recovery in the geothermal reservoir and that of temperature recovery at each depth in the well. The former component can be estimated by modeling the latter component and eliminating it from the recovery process of a wellbore water level. The numerical model takes into account heat transfer due to advection in a well and conduction in rocks. Heat exchange between the well and rocks is estimated based on an empirical equation. The numerical techniques and code developed originally for this study are validated by referring to the analytic solutions of simplified problems and heat balance. The numerical solution of the recovering water level is characterized by the slope of the linear trend line defined in the Horner plot. Numerical experiments are demonstrated for revealing the sensitivities of this slope to both the dimensional and dimensionless parameters. An empirical equation is derived based on these numerical experiments.

Original language English 141-156 16 Journal of the Geothermal Research Society of Japan 39 3 https://doi.org/10.11367/grsj.39.141 Published - Jan 1 2017 Yes

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water injection
transmissivity
water level
estimating
recovery
water
modeling
temperature
pressure recovery
rocks
slopes
heat balance
rock
plots
heat transfer
trends
experiment
conduction
heat

• Geophysics

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In: Journal of the Geothermal Research Society of Japan, Vol. 39, No. 3, 01.01.2017, p. 141-156.

Research output: Contribution to journalArticle

title = "A study for estimating reservoir transmissivity based on the recovery process of a wellbore water level after water injection: Numerical modeling of the temperature recovery component",
abstract = "The author reports a numerical modeling study considering the recovery process of a wellbore water level due to temperature recovery after water injection into a geothermal well. This study intends to estimate the transmissivity of a geothermal reservoir based on this recovery process. We assume that the real recovery process of a wellbore water level after water injection consists of two components: the component of pressure recovery in the geothermal reservoir and that of temperature recovery at each depth in the well. The former component can be estimated by modeling the latter component and eliminating it from the recovery process of a wellbore water level. The numerical model takes into account heat transfer due to advection in a well and conduction in rocks. Heat exchange between the well and rocks is estimated based on an empirical equation. The numerical techniques and code developed originally for this study are validated by referring to the analytic solutions of simplified problems and heat balance. The numerical solution of the recovering water level is characterized by the slope of the linear trend line defined in the Horner plot. Numerical experiments are demonstrated for revealing the sensitivities of this slope to both the dimensional and dimensionless parameters. An empirical equation is derived based on these numerical experiments.",
author = "Mitsuo Matsumoto",
year = "2017",
month = "1",
day = "1",
doi = "10.11367/grsj.39.141",
language = "English",
volume = "39",
pages = "141--156",
journal = "Journal of the Geothermal Research Society of Japan",
issn = "0388-6735",
publisher = "The Geothermal Research Society of Japan",
number = "3",

}

TY - JOUR

T1 - A study for estimating reservoir transmissivity based on the recovery process of a wellbore water level after water injection

T2 - Numerical modeling of the temperature recovery component

AU - Matsumoto, Mitsuo

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The author reports a numerical modeling study considering the recovery process of a wellbore water level due to temperature recovery after water injection into a geothermal well. This study intends to estimate the transmissivity of a geothermal reservoir based on this recovery process. We assume that the real recovery process of a wellbore water level after water injection consists of two components: the component of pressure recovery in the geothermal reservoir and that of temperature recovery at each depth in the well. The former component can be estimated by modeling the latter component and eliminating it from the recovery process of a wellbore water level. The numerical model takes into account heat transfer due to advection in a well and conduction in rocks. Heat exchange between the well and rocks is estimated based on an empirical equation. The numerical techniques and code developed originally for this study are validated by referring to the analytic solutions of simplified problems and heat balance. The numerical solution of the recovering water level is characterized by the slope of the linear trend line defined in the Horner plot. Numerical experiments are demonstrated for revealing the sensitivities of this slope to both the dimensional and dimensionless parameters. An empirical equation is derived based on these numerical experiments.

AB - The author reports a numerical modeling study considering the recovery process of a wellbore water level due to temperature recovery after water injection into a geothermal well. This study intends to estimate the transmissivity of a geothermal reservoir based on this recovery process. We assume that the real recovery process of a wellbore water level after water injection consists of two components: the component of pressure recovery in the geothermal reservoir and that of temperature recovery at each depth in the well. The former component can be estimated by modeling the latter component and eliminating it from the recovery process of a wellbore water level. The numerical model takes into account heat transfer due to advection in a well and conduction in rocks. Heat exchange between the well and rocks is estimated based on an empirical equation. The numerical techniques and code developed originally for this study are validated by referring to the analytic solutions of simplified problems and heat balance. The numerical solution of the recovering water level is characterized by the slope of the linear trend line defined in the Horner plot. Numerical experiments are demonstrated for revealing the sensitivities of this slope to both the dimensional and dimensionless parameters. An empirical equation is derived based on these numerical experiments.

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U2 - 10.11367/grsj.39.141

DO - 10.11367/grsj.39.141

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JO - Journal of the Geothermal Research Society of Japan

JF - Journal of the Geothermal Research Society of Japan

SN - 0388-6735

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