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

Y. J. Park, H. A. Deans, Tayfun E. Tezduyar

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2 Citations (Scopus)

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 languageEnglish
Pages (from-to)769-790
Number of pages22
JournalInternational Journal for Numerical Methods in Fluids
Volume11
Issue number6
DOIs
Publication statusPublished - 1990
Externally publishedYes

Fingerprint

Temperature Effect
Transport Equation
Thermal effects
Finite Element
Formulation
Saturation
Well flooding
Propagation Speed
Domain Model
Wave Speed
Temperature Profile
Reaction Rate
Variational Formulation
Temperature Distribution
Chemical Reaction
Volume Fraction
Thermal gradients
Temperature
Wave propagation
Wave Propagation

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

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title = "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",
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.",
keywords = "Finite Element, Heterogeneous Equations, Residual Oil Saturation, Single‐well Chemical Tracer Test",
author = "Park, {Y. J.} and Deans, {H. A.} and Tezduyar, {Tayfun E.}",
year = "1990",
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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.

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