Pore-scale modelling of WAG: impact of wettability

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Pore-scale modelling of WAGimpact of wettability

• Rink van Dijke and Ken Sorbie
• Institute of Petroleum Engineering
• Heriot-Watt University
• WAG Workshop FORCE, Stavanger, 18 March 2009

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Introduction

• 3-phase (immiscible) flow processes, e.g.
• water-alternating-gas injection (WAG) improved
  oil recovery
• NAPL in unsaturated zone ground water
  remediation
• modelled with Darcys law
• capillary pressure and relative permeability
  functions
• difficult to measure
• pore-scale modelling

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Introduction

• Pore-scale modelling
• pore space structure
• connectivity (topology)
• geometry (pore sizes and shapes)
• flow mechanisms
• capillary forces
• conductance (viscous forces)
• wettability (contact angles)
• incorporated in
• idealized network models (quasi-static invasion
  percolation or dynamic)
• capillary bundle models

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Introduction

• Capillary forces
• invasion of a single tube (cylinder)
• rule for displacement of water by oilwith
  capillary entry pressure according to
  Young-Laplace

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Introduction

• Wettability
• wettability of pore surface defined in terms of
  oil-water contact angle (measured through water)
• water-wet if
• oil-wet if

water
oil
SOLID SURFACE
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Introduction

• Wettability
• in 3-phase flow contact angles
• related by Bartell-Osterhof equation
• constitute capillary entry pressures for
  gas-water and gas-oil displacements, e.g.
• determine presence of wetting films and spreading
  layers

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Introduction

• Micromodel experiments
• understand flow mechanisms
• validate pore-scale network models
• Sohrabi et al. (HWU)

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Outline effects of wettability

• Saturation-dependencies of three-phase capillary
  pressures and relative permeabilities
• Intra-pore physics
• fluid configurations
• capillary entry pressures and layer criteria
• non-uniform wettability
• Network displacement mechanisms
• phase continuity and displacement chains
• WAG simulations
• comparison simulations and WAG micromodel
  experiments
• Concluding remarks

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Saturation-dependencies

• Traditional example (Corey et al., 1956)

• Curved oil isoperms
• Straight water and gas isoperms

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Saturation-dependencies

• Traditional assumptions for saturation-dependencie
  s
• Water-wet system water wetting to oil wetting to
  gas ? water in small pores, gas in big pores

pore occupancy (number fraction)
water
oil
gas
pore size r
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Saturation-dependencies

• Wettability distributions in porous medium often
  correlated to pore size
• mixed-wet with larger pores oil-wet (MWL) may
  occur after primary drainage and aging (similarly
  MWS)

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Saturation-dependencies

• Paths in saturation space gas flood into oil,
  followed by water flood into gas and oil
• capillary bundle model

water-wet
oil-wet
I
II
III
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Saturation-dependencies

• Regions in saturation space iso-capillary
  pressure curves

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II
gas is intermediate-wetting
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Saturation-dependencies

• Regions in saturation space iso-relative
  permeability curves

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II
gas is intermediate-wetting
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Saturation-dependencies

• numerical example FW capillary bundle

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Intra-pore physics

• Films and layers
• water-wet micromodel WAG flood
• water wetting films around both oil and gas
• possible oil layers separating water and gas

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Intra-pore physics

• Fluid configurations in angular pores
• water-wet pores, e.g. strongly water-wet
  all close to 0
• water wetting films around both oil and gas
• possible oil layers separating water and gas
  affected by oil spreading coefficient
• oil-wet pores, e.g. weakly oil-wet close to
  90 degrees, close to 0
• no oil wetting films around water
• only oil wetting films around gas
• ensures phase continuity along pores

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Intra-pore physics

• true 3-phase capillary entry pressures (improved
  Y-L)
• gas-oil entry pressure depends on water wetting
  film pressure
• determined by free energy calculation (MS-P)
• also criterion for (oil) layers

bulk displacement
layer displacement
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Intra-pore physics

• consistent relation 3-phase pressure differences
  and occupancies

oil-water bulk displacement
gas-oil bulk displacement (true varying)
gas-oil bulk displacement, with layer (constant)
layer displacement
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Intra-pore physics

• mixed-wet bundle of triangular pores
• small pores strongly water-wet
• large pores weakly oil-wet

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Intra-pore physics

• water injection
• no difference true (3-phase) and constant
  (2-phase) during invasion of water-wet pores
• huge differences during invasion of oil-wet
  pores
• true simultaneous w-gto and w-gtg
• volume effectoil films

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Intra-pore physics

• nonuniform wettability
• after primary - after imbibition drainage
• strongly affects water flood Sor (Ryazanov et
  al., 2009)

surface rendered oil-wet aging(Kovscek)
oil layers (2-phase)
oil
water
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Intra-pore physics

• non-uniform wettability
• layers in 3-phase configuration
• consistent entry pressures and layer criteria

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Intra-pore physics
high Pow drainage
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Network displacement mechanisms

• phase continuity
• connectivity
• films and layers (wettability)
• water-wet micromodel WAG flood

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Network displacement mechanisms

• connected, trapped and disconnected phases
• phase cluster map

disconnected oil cluster
water cluster connected to outlet
invading gas cluster
outlet
inlet
trapped oil cluster
oil cluster connected to outlet
disconnected water cluster
disconnected gas cluster
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Network displacement mechanisms

• multiple displacement chains displace
  disconnected clusters
• based on target pressure difference
• determining lowest target requires shortest path
  algorithm

e.g. gas-gtoil-gtgas-gtwater
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Network simulations

• 3-phase flow simulator 3PhWetNet regular
  lattice, arbitrary wettability,
  capillary-dominated flow
• few free parameters describing essence of
  pore-scale displacements (needs anchoring)
• coordination number z
• pore size distribution
• volume and conductanceexponents
• wettability (contact angledistribution)
• film and layers (notional)

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Network simulations

• Network model
• parameters anchored to easy-to-obtain data
  network structure and wettability
• example mixed-wet North Sea reservoir data

water flood
gas flood
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Network simulations

• Network model
• predict difficult-to-obtain data, e.g. 3-phase kr
  and Pc

three-phase gas relperms
three-phase gas injection displacement paths
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WAG network simulations

• mixed-wet
• no films or layers
• varying coordinationnumber z
• high residual, but additional recovery during WAG
  for z3

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WAG network simulations

• displacement statistics (chain lengths), z5
• few multiple, many double displacements
• continuing phase movement but no additional
  recovery

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WAG network simulations

• displacement statistics (types), z5
• mainly 3 displacement types, corresponding to
  doubles, e.g. g-gto and o-gtw during gas flood

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WAG occupancy statistics (z5)
after water flood 1
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WAG occupancy statistics (z5)
during gas flood 1
gas intermediate-wetting
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WAG occupancy statistics (z5)
end of gas flood 1
oil moved into water-wet pores
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WAG occupancy statistics (z5)
end of water flood 2
oil moved back into oil-wet pores
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WAG network simulations

• WAG occupancy statistics (z5) end gas flood 2
• oil and gas in both water-wet and oil-wet pores

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WAG network simulations

• Chain lengths (z3)
• significant
  number of multiple chains

z5
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WAG network simulations

• Displacementtypes (z3)

z5
additional types of displacements g-gto for water
and o-gtg for gas floods
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WAG simulation micromodel experiment
water-wet
oil-wet

• weakly wetted little evidence of (continuous)
  water and oil wetting films (around water)
• spreading oil assume oil layers and oil wetting
  films around gas

mN/m
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WAG simulation micromodel experiment

• Fractionally-wet
• 50 water-wet oil-wet pores
• angles distributed between 60-120 degrees
• oil layers and oil wetting films around gas
• Comparison simulated and experimental
  recoveries
• recoveryceases afterWAG 2

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WAG simulation micromodel experiment

• Displacement chain lengths
• many multiples (few films low phase continuity)
• multiples dying out after WAG 3

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WAG simulation micromodel experiment

• Type of displacements
• all types of displacements occur
• many displacements involving oil movement
• after WAG 3 mainly w-gtg, g-gtw

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WAG simulation micromodel experiment

• fluid distributions aftergas flood 1
• narrow gas finger in both simulation and
  experiment
• significant amount of oil displaced
• multiple displacements e.g. gas-gtoil-gtgas-gtwater

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WAG simulation micromodel experiment

• fluid distributions after water flood 1
• water disperses gas
• slightly more extensive in experiment

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WAG simulation micromodel experiment

• fluid distributions after gas flood 2
• different gas finger appears
• additional oil production

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WAG simulation micromodel experiment

• fluid distributions after gas flood 3
• new gas finger in simulation
• some additional oil displaced (jump in
  recovery)
• after this flood mainly water displacing gas and
  vice versa

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Conclusions

• Mixed wettability leads to three types of pore
  occupancy and corresponding saturation-dependenci
  es of three-phase capillary pressures and
  relative permeabilities
• difficult to capture in empirical model
• True three-phase capillary entry pressures and
  layer criteria essential for consistent and
  accurate modelling
• Phase continuity driver for WAG at pore-scale
• strongly affected by network connectivity and
  presence films and layers precise wettability
• multiple displacement chains
• new fluid patterns during each cycle
  (micromodels)
• recovery ceases after few WAG floods, oil
  movement may continue

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Near-miscible WAG micromodel
After 2 hours
After 1 hour

• Continued gas injection in strongly water-wet
  experiment
• Much oil displaced through film flow mass
  transfer (?)

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