### Abstract

Heterogeneous equation systems in a pair of coupled co‐ordinate systems are solved by a finite element method. The specific physical application studied is the effect of temperature on single‐well chemical tracer (SWCT) tests to measure residual oil saturation (volume fraction of immobile oil phase) remaining after waterflooding of an oil reservoir. Since temperature effects are caused by injecting cooler surface fluid down a well into a warm reservoir, the vertical temperature profile in the wellbore as well as the temperature distribution in the porous oil‐bearing layer must be considered. The entire system is modelled to account for the different transport mechanisms. However, it is expedient to divide the connected geometrical region into two model domains. The equations for each submodel are expressed in an appropriate set of co‐ordinates. The variational formulation of each model is then discussed. A significant temperature effect on the estimation of residual oil saturation occurs when the radial temperature and concentration wave propagation speeds in the porous formation are about the same. In this case the temperature gradient is located across the chemical tracer bank, causing the chemical reaction rate to vary radially. The temperature effects are demonstrated for two actual field tests in complex reservoirs.

Original language | English |
---|---|

Pages (from-to) | 769-790 |

Number of pages | 22 |

Journal | International Journal for Numerical Methods in Fluids |

Volume | 11 |

Issue number | 6 |

DOIs | |

Publication status | Published - 1990 |

Externally published | Yes |

### Fingerprint

### Keywords

- Finite Element
- Heterogeneous Equations
- Residual Oil Saturation
- Single‐well Chemical Tracer Test

### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics

### Cite this

*International Journal for Numerical Methods in Fluids*,

*11*(6), 769-790. https://doi.org/10.1002/fld.1650110605

**Finite element formulation for transport equations in a mixed co‐ordinate system : An application to determine temperature effects on the single‐well chemical tracer test.** / Park, Y. J.; Deans, H. A.; Tezduyar, Tayfun E.

Research output: Contribution to journal › Article

*International Journal for Numerical Methods in Fluids*, vol. 11, no. 6, pp. 769-790. https://doi.org/10.1002/fld.1650110605

}

TY - JOUR

T1 - Finite element formulation for transport equations in a mixed co‐ordinate system

T2 - An application to determine temperature effects on the single‐well chemical tracer test

AU - Park, Y. J.

AU - Deans, H. A.

AU - Tezduyar, Tayfun E.

PY - 1990

Y1 - 1990

N2 - Heterogeneous equation systems in a pair of coupled co‐ordinate systems are solved by a finite element method. The specific physical application studied is the effect of temperature on single‐well chemical tracer (SWCT) tests to measure residual oil saturation (volume fraction of immobile oil phase) remaining after waterflooding of an oil reservoir. Since temperature effects are caused by injecting cooler surface fluid down a well into a warm reservoir, the vertical temperature profile in the wellbore as well as the temperature distribution in the porous oil‐bearing layer must be considered. The entire system is modelled to account for the different transport mechanisms. However, it is expedient to divide the connected geometrical region into two model domains. The equations for each submodel are expressed in an appropriate set of co‐ordinates. The variational formulation of each model is then discussed. A significant temperature effect on the estimation of residual oil saturation occurs when the radial temperature and concentration wave propagation speeds in the porous formation are about the same. In this case the temperature gradient is located across the chemical tracer bank, causing the chemical reaction rate to vary radially. The temperature effects are demonstrated for two actual field tests in complex reservoirs.

AB - Heterogeneous equation systems in a pair of coupled co‐ordinate systems are solved by a finite element method. The specific physical application studied is the effect of temperature on single‐well chemical tracer (SWCT) tests to measure residual oil saturation (volume fraction of immobile oil phase) remaining after waterflooding of an oil reservoir. Since temperature effects are caused by injecting cooler surface fluid down a well into a warm reservoir, the vertical temperature profile in the wellbore as well as the temperature distribution in the porous oil‐bearing layer must be considered. The entire system is modelled to account for the different transport mechanisms. However, it is expedient to divide the connected geometrical region into two model domains. The equations for each submodel are expressed in an appropriate set of co‐ordinates. The variational formulation of each model is then discussed. A significant temperature effect on the estimation of residual oil saturation occurs when the radial temperature and concentration wave propagation speeds in the porous formation are about the same. In this case the temperature gradient is located across the chemical tracer bank, causing the chemical reaction rate to vary radially. The temperature effects are demonstrated for two actual field tests in complex reservoirs.

KW - Finite Element

KW - Heterogeneous Equations

KW - Residual Oil Saturation

KW - Single‐well Chemical Tracer Test

UR - http://www.scopus.com/inward/record.url?scp=0025573801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025573801&partnerID=8YFLogxK

U2 - 10.1002/fld.1650110605

DO - 10.1002/fld.1650110605

M3 - Article

AN - SCOPUS:0025573801

VL - 11

SP - 769

EP - 790

JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

SN - 0271-2091

IS - 6

ER -