Imbibition Assisted Recovery

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Imbibition Assisted Recovery

• Orkhan H Pashayev
• Petroleum Engineering Department
• Texas AM University

February 2004
Masters Division
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Presentation Outline

• Introduction
• Problem Statement
• Background and Literature Review
• Objectives
• Numerical Modeling
• Grid Sensitivity
• Matching Experimental Results
• Numerical Analyses of Spontaneous Imbibition
• Imbibition Upscaling
• Conclusions

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Problem Statement

• An understanding the role of imbibition in
  Naturally Fractured Reservoirs in order to
  achieve maximum recovery
• Lack of knowledge in upscaling laboratory
  imbibition experiments to field dimensions

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Background and Literature Review

• Two methods of modeling Naturally Fractured
  Reservoirs
• Numerical model with sufficiently refined grid to
  adequately represent matrix/fracture geometry
• Dual Porosity Model (Warren and Root, 1963)

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Background and Literature Review

• Expulsion of oil from matrix block to the
  surrounding fractures by capillary imbibition of
  water is the most important oil recovery in
  Naturally Fractured Reservoirs

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Background and Literature Review

• Transfer Functions
• Transfer functions that use Darcys Law
• Diffusivity transfer functions
• Empirical transfer functions
• Scaling transfer functions

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Background and Literature Review

• Scaling transfer functions
• Rapoport (1952)
• Graham and Richardson (1959), Mattax and Kyte
  (1962)
• Hamon and Vidal (1986), Bourblaux and Kalaidjian
  (1995), Akin and Kovsek (1998), etc
• Du Prey (1978), Kazemi (1992), Ma et.al (1996),
  etc

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Objectives

• Conduct numerical studies with matrix block
  surrounded by fractures to better understand the
  characteristic of spontaneous imbibition
• Evaluate dimensionless time tD and investigate
  the limitations of the upscaling laboratory
  imbibition experiments to field dimensions

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Presentation Outline

• Introduction
• Problem Statement
• Background and Literature Review
• Objectives
• Numerical Modeling
• Grid Sensitivity
• Matching Experimental Results
• Numerical Analyses of Spontaneous Imbibition
• Imbibition Upscaling
• Conclusions

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Simulation Parameters

• Two phase black-oil commercial simulator, CMG
• Core 3.2cm x 3.2cm x 4.9cm
• K 74.7
• SWi 41.61
• F 15.91
• µOIL 3.52 cp
• µWATER 0.68 cp
• APIOIL 31

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Grid Sensitivity Analyses

• Cartesian grid system

Simulation Run No. of gridblocks in I, J and K directions No. of gridblocks in I, J and K directions No. of gridblocks in I, J and K directions Total No. of gridblocks
Simulation Run I - Direction J - Direction K - Direction Total No. of gridblocks
1 7 7 7 343
2 12 12 12 1,728
3 16 16 16 4,096
4 20 20 20 8,000
5 20 20 25 10,000
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Grid Sensitivity Analyses

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Grid Sensitivity Analyses

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Grid Sensitivity Analyses

10000
8000
4096
1728
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Reservoir Grid

• I 20, J 20, K 20
• No. of gridblocks 8000
• Grid dimensions
• I 1x0.01cm 18x0.178cm 1x0.01cm
• J1x0.01cm 18x0.178cm 1x0.01cm
• K1x0.01cm 19x0.259cm

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Matching Experimental Results

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Matching Experimental Results

• The following logarithmic capillary pressure
  relationship was used

• PC - threshold capillary pressure
• SW water saturation

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Matching Experimental Results

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Gravity Effect

• Bond number
• ?WATER 1 g/cc
• ?OIL 0.8635 g/cc
• ?WATER ?OIL 0.8635 g/cc

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Different Boundary Conditions

• All Faces Open
• Two Ends Closed
• Two Ends Open
• One End Open

No Flow Surfaces
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Different Boundary Conditions

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Different Boundary Conditions

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Heterogeneities

• One End Open
• Case 1 K1 gt K2 gt K3 gt K4
• Case 2 K1 lt K2 lt K3 lt K4

water
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Heterogeneities

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Presentation Outline

• Introduction
• Problem Statement
• Background and Literature Review
• Objectives
• Numerical Modeling
• Grid Sensitivity
• Matching Experimental Results
• Numerical Analyses of Spontaneous Imbibition
• Imbibition Upscaling
• Conclusions

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Spontaneous Imbibition Upscaling
Theory

• Recovery behavior for a large reservoir matrix
  block could be predicted from lab experiments
• Mattax and Kyte
• Ma et.al

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Spontaneous Imbibition Upscaling

• All Faces Open, Two Ends Closed, Two Ends Open
  and One End Open
• Semi-log plot
• Normalized Recovery vs. Dimensionless Time

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Spontaneous Imbibition Upscaling
Comparison

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Spontaneous Imbibition Upscaling
Varying Mobility Ratio

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Spontaneous Imbibition Upscaling
Varying Mobility Ratio

• Mobility Ratio - not included
• Need to include mobility ratio into the
  formulation of dimensionless time

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Spontaneous Imbibition Upscaling
Varying Mobility Ratio

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TEO
Spontaneous Imbibition Upscaling

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TEC
Spontaneous Imbibition Upscaling

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Spontaneous Imbibition Upscaling
Heterogeneous Core

• One End Open
• Case 1 K1 gt K2 gt K3 gt K4
• Case 2 K1 lt K2 lt K3 lt K4

water
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Spontaneous Imbibition Upscaling
Heterogeneous Core

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Presentation Outline

• Introduction
• Problem Statement
• Background and Literature Review
• Objectives
• Numerical Modeling
• Grid Sensitivity
• Matching Experimental Results
• Numerical Analyses of Spontaneous Imbibition
• Imbibition Upscaling
• Conclusions

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Conclusions

• It was observed that time required to saturate
  core to Sw60 increases exponentially as the
  number of faces available for imbibition decrease
• Results proved that using characteristic length
  in the equation of dimensionless time, instead of
  length of the core improves upscaling of
  spontaneous imbibition

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Conclusions

• Further investigation revealed that upscaling
  correlations could be significantly improved by
  taking into account end-point mobilities and
  mobility ratio
• Spontaneous imbibition recovery is higher for a
  flow in the direction of decreasing permeability
  than in the case of a flow in the direction of
  increasing permeability

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Conclusions

• Some discrepancy observed in correlations, while
  upscaling heterogeneous core, indicated that
  existing transfer functions can not precisely
  account for heterogeneities in the core

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Acknowledgement

• Finally I would like to express my sincere
  gratitude and appreciation to my advisor Dr.
  David Schechter and Dr. Erwin Putra.

Thank You!
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Imbibition Assisted Recovery

• Orkhan H Pashayev
• Petroleum Engineering Department
• Texas AM University

February 2004
Masters Division