Hypothesis 1: no porescale mixing

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Investigation of Pore-Scale (Local) Mixing (SPE
99782)
Raman K. Jha Steven L. Bryant Larry W.
Lake Abraham John Department of Petroleum and
Geosystems Engineering The University of Texas at
Austin
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Role of Mixing in Porous Media

• Dilutes the injected solvent slug and reduces its
  displacement efficiency
• Understanding mixing important for
• determining the effectiveness of miscible floods
• better design and control of miscible flood
  processes

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Mechanisms of Mixing in Porous Media

• A complex process involving an interplay of
• Mechanical Mixing
• velocity differences within pores
• path differences
• Molecular Diffusion
• random movement of solute molecules

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Conventional Quantification of Mixing

• Flow averaged concentration histories measured in
  laboratories
• Core-scale mixing termed as dispersion used to
  quantify mixing
• No information about origin of core scale mixing

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Hypotheses for Solute Mixing
Hypothesis 1 Streamline Flow Hypothesis

• No interaction among solute particles on
  different streamlines
• Core scale mixing an artifact of particle
  residence time distribution

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Hypotheses for Solute Mixing
Hypothesis 2 Local Mixing Hypothesis

• Streamline flow with random jump of particles to
  neighboring streamlines
• Core scale mixing a result of local mixing

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Approach

• Measure local solute concentration history using
  a thin probe
• Investigate mixing mechanism by solving Navier
  Stokes and convection diffusion equations in pore
  space

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Experimental Studies

• Standard tracer step change experiments in a sand
  column
• Overall (cup-mixing) concentration history
  obtained
• A thin electrical conductivity probe developed to
  measure local solute concentration
• Local solute concentration history measured at
  several radial and axial positions

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Experimental Measurements

• Gradual rise in local solute concentration
• Local mixing same as core scale mixing

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Experimental Measurements

• Mixing zone grows with distance traveled
• Local mixing same as core scale mixing
• Local mixing hypothesis valid

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Discussion on Experimental Results
Mixing Cell Theory
If diffusion to
equalizes concentration within each pore For our
experiments
Complete local mixing because of molecular
diffusion
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Computational Studies

• To corroborate experimental observations
• To understand mixing mechanism over a wider range
  of flow conditions
• Navier-Stokes and convection-diffusion equations
  solved in surrogate pore space to simulate
  miscible flow
• Simulations carried out for a range of flow
  velocities and diffusion coefficients

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Simulations on an Ordered Pack

• Fluid injected at inlet face at
• Outlet face at atmospheric pressure
• Navier-Stokes equation solved to obtain steady
  state velocity profile

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Simulations on an Ordered Pack

• Concentration profile obtained by solving
  convection-diffusion equation

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Simulations on an Ordered Pack
Qualitatively similar to experimental conditions
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Simulations on an Ordered Pack

• Diffusion enhances mixing

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Simulations on an Ordered Pack
For homogeneous media local and overall mixing
are same for complete local mixing
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Simulations on a Disordered Pack
Wide variation in local velocity
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Simulations on a Disordered Pack
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Simulations on a Disordered Pack
Local Mixing differs with position in
heterogeneous medium
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Simulations on a Disordered Pack
Diffusion enhances local mixing and reduces
effect of local heterogeneity on solute transport
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Simulations on a Disordered Pack
For diffusion dominated process all the local and
overall curves collapse into one
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Simulation of Slug Injection Process
Incomplete mixing inside the pore body at higher
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Conclusions

• Evidence of non-zero local mixing in experiments
• Mixing a result of velocity variations within the
  pores and molecular diffusion
• The converging-diverging flow around sand grains
  causes the solute front to stretch, split and
  rejoin

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Conclusions

• Diffusion tends to reduce radial variation in
  solute concentration
• For slow fluid velocity diffusion is able to
  homogenize solute concentration inside each pore
• In limit of very high fluid velocity (or no
  diffusion) local mixing tends to zero