Thermal Profiles in Water Injection Wells: Reduction in the Systematic Error of Flow Measurements during the Transient Regime
This article presents an analytical solution for calculating the flow rate in water injection wells based on the established thermal profile along the tubing. The intent is to minimize the intrinsic systematic error of classic quasi-static methodologies, which assume that all thermal transience on w...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-11-01
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| Series: | Sensors |
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| Online Access: | https://www.mdpi.com/1424-8220/23/23/9465 |
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| author | German Alberto Echaiz Espinoza Gabriel Pereira de Oliveira Verivan Santos Lima Diego Antonio de Moura Fonseca Werbet Luiz Almeida da Silva Carla Wilza Souza de Paula Maitelli Elmer Rolando Llanos Villarreal Andrés Ortiz Salazar |
| author_facet | German Alberto Echaiz Espinoza Gabriel Pereira de Oliveira Verivan Santos Lima Diego Antonio de Moura Fonseca Werbet Luiz Almeida da Silva Carla Wilza Souza de Paula Maitelli Elmer Rolando Llanos Villarreal Andrés Ortiz Salazar |
| author_sort | German Alberto Echaiz Espinoza |
| collection | DOAJ |
| description | This article presents an analytical solution for calculating the flow rate in water injection wells based on the established thermal profile along the tubing. The intent is to minimize the intrinsic systematic error of classic quasi-static methodologies, which assume that all thermal transience on well completion has passed. When these techniques are applied during the initial hours of injection well operation, it can result in errors higher than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>20</mn><mo>%</mo></mrow></semantics></math></inline-formula>. To solve this limitation, the first law of thermodynamics was used to define a mathematical model and a thermal profile was established in the injection fluid, captured by using distributed temperature systems (DTSs) installed inside the tubing. The geothermal profile was also established naturally by a thermal source in the earth to determine the thermal gradient. A computational simulation of the injection well was developed to validate the mathematical solution. The simulation intended to generate the fluid’s thermal profile, for which data were not available for the desired time period. As a result, at the cost of greater complexity, the systematic error dropped to values below <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula> in the first two hours of well operation, as seen throughout this document. The code was developed in Phyton, version 1.7.0., from Anaconda Navigator. |
| first_indexed | 2024-03-09T01:43:20Z |
| format | Article |
| id | doaj.art-b50a7851fa1147828257e00a48ebb560 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-09T01:43:20Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-b50a7851fa1147828257e00a48ebb5602023-12-08T15:26:06ZengMDPI AGSensors1424-82202023-11-012323946510.3390/s23239465Thermal Profiles in Water Injection Wells: Reduction in the Systematic Error of Flow Measurements during the Transient RegimeGerman Alberto Echaiz Espinoza0Gabriel Pereira de Oliveira1Verivan Santos Lima2Diego Antonio de Moura Fonseca3Werbet Luiz Almeida da Silva4Carla Wilza Souza de Paula Maitelli5Elmer Rolando Llanos Villarreal6Andrés Ortiz Salazar7Department of Electronics Engineering, Universidad Nacional de San Agustin de Arequipa, Arequipa 04002, PeruDepartment of Computer Engineering and Automation, Federal University of Rio Grande do Norte (DCA-UFRN), Natal 59072-970, RN, BrazilDepartment of Computer Engineering and Automation, Federal University of Rio Grande do Norte (DCA-UFRN), Natal 59072-970, RN, BrazilDepartment of Computer Engineering and Automation, Federal University of Rio Grande do Norte (DCA-UFRN), Natal 59072-970, RN, BrazilDepartment of Computer Engineering and Automation, Federal University of Rio Grande do Norte (DCA-UFRN), Natal 59072-970, RN, BrazilDepartment of Petroleum Engineering, Federal University of Rio Grande do Norte (DPET-UFRN), Natal 59072-970, RN, BrazilDepartment of Natural Sciences, Mathematics, and Statistics, Federal Rural University of Semi-Arid (DCME-UFERSA), Mossoró 59625-900, RN, BrazilDepartment of Computer Engineering and Automation, Federal University of Rio Grande do Norte (DCA-UFRN), Natal 59072-970, RN, BrazilThis article presents an analytical solution for calculating the flow rate in water injection wells based on the established thermal profile along the tubing. The intent is to minimize the intrinsic systematic error of classic quasi-static methodologies, which assume that all thermal transience on well completion has passed. When these techniques are applied during the initial hours of injection well operation, it can result in errors higher than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>20</mn><mo>%</mo></mrow></semantics></math></inline-formula>. To solve this limitation, the first law of thermodynamics was used to define a mathematical model and a thermal profile was established in the injection fluid, captured by using distributed temperature systems (DTSs) installed inside the tubing. The geothermal profile was also established naturally by a thermal source in the earth to determine the thermal gradient. A computational simulation of the injection well was developed to validate the mathematical solution. The simulation intended to generate the fluid’s thermal profile, for which data were not available for the desired time period. As a result, at the cost of greater complexity, the systematic error dropped to values below <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula> in the first two hours of well operation, as seen throughout this document. The code was developed in Phyton, version 1.7.0., from Anaconda Navigator.https://www.mdpi.com/1424-8220/23/23/9465oil reservoirthermal profilegeothermal profileflow rate injection |
| spellingShingle | German Alberto Echaiz Espinoza Gabriel Pereira de Oliveira Verivan Santos Lima Diego Antonio de Moura Fonseca Werbet Luiz Almeida da Silva Carla Wilza Souza de Paula Maitelli Elmer Rolando Llanos Villarreal Andrés Ortiz Salazar Thermal Profiles in Water Injection Wells: Reduction in the Systematic Error of Flow Measurements during the Transient Regime Sensors oil reservoir thermal profile geothermal profile flow rate injection |
| title | Thermal Profiles in Water Injection Wells: Reduction in the Systematic Error of Flow Measurements during the Transient Regime |
| title_full | Thermal Profiles in Water Injection Wells: Reduction in the Systematic Error of Flow Measurements during the Transient Regime |
| title_fullStr | Thermal Profiles in Water Injection Wells: Reduction in the Systematic Error of Flow Measurements during the Transient Regime |
| title_full_unstemmed | Thermal Profiles in Water Injection Wells: Reduction in the Systematic Error of Flow Measurements during the Transient Regime |
| title_short | Thermal Profiles in Water Injection Wells: Reduction in the Systematic Error of Flow Measurements during the Transient Regime |
| title_sort | thermal profiles in water injection wells reduction in the systematic error of flow measurements during the transient regime |
| topic | oil reservoir thermal profile geothermal profile flow rate injection |
| url | https://www.mdpi.com/1424-8220/23/23/9465 |
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