Flow Based Micro-Simulation

SPE Qatar Section Technical Presentation: Flow Based Micro-Simulation: An Effective Approach to Understand and Quantify the Impact of Micro-Scale Heterogeneities on Secondary and Tertiary Oil Recovery Mechanisms 12 December 2016 Sheraton Grand Doha, Al Corniche St., Doha, Qatar

Water Flooding

Flow Based Micro-Simulation: An Effective Approach to Understand and Quantify the Impact of Micro-Scale Heterogeneities on Secondary and Tertiary Oil Recovery Mechanisms Mayur Pal* *Maersk

Oil Qatar, Doha, Qatar

Acknowledgment Maersk Oil Qatar Michael Gunningham (SPE) & Christian Perrin (Co-Author on the Papers)

References 1.) Mayur Pal, et.al., Validation of multiscale mixed finite-element methods, Int. J. Numer. Meth. Fluids, Vol 77, Issue 4, pages 206-223, 10th Feb 2015. 2.) Mayur Pal and Christian Perrin, Flow-based micro-simulation: A novel approach to understand and quantify the impact of micro-scale heterogeneity on secondary and tertiary recovery mechanisms, SPE Reservoir Characterization Workshop, 11th -12th Oct, 2016, Doha, Qatar.

Agenda • The necessity of focusing on the real heterogeneity of our reservoir – Case of sub-log heterogeneities

• Impact of grid size on our flow simulations while preserving heterogeneities • The SPC approach: an innovative methodology to quantify micro-porosity in a microporous reservoir • The multiscale method: Time-efficient simulation methodology while preserving heterogeneities – Simulation on the case of sub-log heterogeneities

• Workflow for implementing findings of field scale

What is the reality behind our simplified porosity grids?

Three different realistic scenarios honoring 30 20 % log porosity 20 over 2 ft vertical window 10 Tabular heterogeneity

GR

Commonly observed in carbonate platform top facies

PHIE

Typical oil bearing facies

Nodular heterogeneity Commonly observed in carbonate bioturbated facies

20 p.u.

Typical transition facies

Cell: 2ft x 50m x 50m

Random heterogeneity Commonly observed at thin section scale Typical micrograinstone microporous facies

PHIE resolution ~ 3 ft

Upscaled grid

All these textures can be described in a geostatistical sense, and implemented and tested in a box model.

Impact of heterogeneities on production P

I P

P

I

I

The log-derived uniform scenario

water production

P

I

time

Various possible scenarios that can be deterministically defined by proper reservoir characterization

Impact of heterogeneities on production P

I P

P

I

I

The log-derived uniform scenario

water production

P

I

time

Various possible scenarios that can be deterministically defined by proper reservoir characterization

How to preserve water flooding accuracy for heterogeneous Reservoirs and impact of upscaling ? Fine Scale Fine Scale Perm

Fine Scale Flow

Upscaled Upscaled Flow

Upscaled Perm

1 Fine scale (oil) 0.9

Fine scale (w) Upscaled (oil) Upscaled (w)

0.8 0.7

Upscaled

0.6

Cut

Fine Scale

0.5 0.4 0.3 0.2 0.1 0 0

50

100

150

200

250

300

Time (Days)

350

400

450

500

Discretization of thin section image into SPC’s • Thin section discretized into 9 colour Classes • we show next the colour Classes can then be attributed to a Specific Porosity • SPC: Specific Porosity Class clean cement 6.81 % dirty cement 11.57 % red Hue 15.39 % micrite_1 16.25 %

micrite_2 23.21 % micrite_3 16.51 % micrite_4 8.46 % micrite 5 1.7 % open porosity 0.10 %

Initial thin section scan tight micrite

loose micrite

reconstructed thin section

open porosity blue saturation

Representation of the Thin section SPC distribution * See IPTC – 1375 for Details

Example of SPC distribution on a cored well

SPC control on porosity

Computing specific porosity and permeability • • • •

Each SPC areComponent distribution relate to log porosity Each component has specific porosity SPC Permeability of each SPC is described by Kozeny’s permeability model Reasonable fit between plug (Φ, K) and thin section-derived (Φ, K) THIN SECTION COMPONENTS from image analysis

..

..

..

* See IPTC – 1375 for Details

THIN SECTION COMPONENTS continuous interpolation

Computing specific porosity and permeability of a Highly Heterogeneous Sample Thin Section dsicretized into SPC

Impact of Upscaling on the permeability of a Highly Heterogeneous Sample in a Simulation Grid W2

Permeability Log10 scale -8

-9

-10

-11

-12

-13

-14

-15

W1

275x500x1

55x100x1

How to preserve water flooding accuracy for heterogeneous reservoirs in a Simulation model ? •

Is there way to bypass upscaling and preserve fine heterogeneity ? Multi-scale method*

•

Permeability 2500

2000

1500

1000

500

-11

-10

-9

-8

-7

-6

-5

I

Coarse/Upscaled

P

Finescale (oil)

P

0.9

0.8

Multiscale (water) Pseudo coarse (oil)

0.7

Pseudo coarse (water)

0.6

Fine-scale

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

I

log10 x-permeability (mD)

P

Finescale (water) Multiscale (oil)

Multiscale

100 partitions (weighted)

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

I

1

Cut

-12

Pseudo coarse grid ... PVI = 0.13948 Finescale Weighted METIS Multiscale ... PVI = 0.13948 ... PVI = 0.13948 1 1

0 -13

0.5

0.4

0.3

0.2 -6

-7

-8

-9

-10

-11

-12

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

0.1

* See SPE 163626-MS, 163669-MS

0

0

50

100

150

200

250 Time (Days)

300

350

400

450

500

Multiscale vs. Upscaling

•

Local effective parameters

•

Local basis function

•

Only one parameter per call

•

More than one parameter per cell

•

Loss of fine scale information

•

No loss of fine scale information

Multiscale Simulation Need: •

Be able to run large models

•

Preserve fine scale heterogeneity

•

Preserve multiscale structure

•

Approach: Multiscale Method

•

Based on scale separation

•

•

Fine Scale

•

Pseudo Coarse Scale

Basis Functions

Incorporate fine scale information into the coarse scale formulation via basis functions

Fine Grid

Multiscale

Upscaled Grid

Mathematical Background Given a fine grid with Poro/Perm •

Construct a pseudo coarse grid partitioning

•

Solve local flow problems to generate a basis function  IJfor velocity and  IJ for pressure

 IJ  kIJ   IJ •

  I ( x)    J ( x )

Reconstruct fine scale velocity and pressure from coarse solution

I

J

Multiscale Method Workflow Basis Functions*

Pseudo-coarse grid generation

Generate basis functions

Incorporate fine scale information into the coarse scale formulation via basis functions

Solve pressure and velocity at coarse scale

Reconstruct fine scale pressure and velocity

Use velocity to solve for saturation *Lie et al.,2010

Carbonate Sector Model – Simulation Results Fine-scale model [Grid size: 20x20x93]

Well-placement pattern

Coarse-scale model [Grid size: 5x5x11]

Multiscale model [Grid size: 5x5x11 & 20x20x93]

* See SPE 163626-MS, 163669-MS *Mayur Pal et.al., Validation of multiscale mixed finite-element methods, Int. J. Numer. Meth. Fluids, Vol 77, Issue 4, pages 206-223, 2015.

Water-cut

Oil-production rate

Water saturation

Scalability & Efficiency - incompressible 2-phase ms Geological model 721,999 Active Cells (253x258x38) 14km x14kmx0.100km

Full Field Model

Sector Model

Full field model – 721,999 Active Cells (253x258x38) AMG Fails on fine scale due to Matlab memory restrictions

Size sector model – 20x20x12, Coarse grid – 3x3x3 Fine scale solution with AMG – 200.07 Seconds

Mimicking 27 years of production with 1000 pressure steps

Mimicking 27 years of production with 1000 pressure steps

CPU costs SPE 10 & theoretical MS Speedup Pressure Solver Vs No. of Partitions Pressure solver CPU cost 0.3

0.25 Finescale

CPU cost (secs)

Unstructured Multiscale 0.2 Structured Multiscale

0.15

0.1

0.05

0

20

40

60

80

100 Number of partitions

120

140

160

180

200

Pre-processor CPU cost 0.7

0.6

0.5

CPU cost (secs)

Complexity of the linear solver 0.4

t(n) = O(nα) AMG (practical) O(n1.2 )

0.3

Unstructured

Cholesky

O(n1.5 )

0.2

Structured

0.1

0

0

20

40

60

80

100 Number of partitions

120

140

160

Complexity of the Ms solver 180

200

D . NC . 2 α . NS α + D α NC α Fine-scale (Basis functions)

Coarse-scale

Applying the workflow on a very Heterogeneous sample Simulation on a heterogeneous rock sample Thin Section

* See IPTC – 1375 and SPE 163626-MS, 163669-MS for Details

Simulation - 10 Days

Upscaled Multi-scale

W2

W1

Permeability Log10 scale -8

-9

-10

-11

-12

-13

-14

-15

Simulation - 1 Day

Multi-scale

Upscaled

Simulation - 2 Day

Multi-scale

Upscaled

Simulation - 3 Day

Multi-scale Multi-scale

Upscaled

Simulation - 4 Day

Multi-scale

Upscaled

Simulation - 5 Day

Multi-scale

Upscaled

Simulation - 7 Day

Multi-scale

Upscaled

Simulation - 9 Day

Multi-scale

Upscaled

Simulation - 10 Day

Multi-scale

Upscaled

Heterogeneity description, quantification, and choice of right simulation scale • •

Who is doing it? Core is the main material available to observe / quantify sublog heterogeneities –

•

As long as the heterogeneities are not defined, we don’t know if the flow experiments on core samples are representative of the flow response implemented in the model. –

–

•

High resolution image tool can do the job (cm resolution in good conditions)

Full-core sample is not the solution either as long as the heterogeneity is not understood REV

A strategy should be agreed between petro-physicists / Geologist and RE’s for the core sampling – – – –

BE INNOVATIVE ! Don’t follow the books RE’s can before hand evaluate the impact of possible heterogeneities • Use mini-models or box models with representative elementary volume (REV) Geologist can anticipate the distribution of heterogeneities that are often constrained by facies and depositional environments Petro-physicists need to adapt their plugging and sampling strategy accordingly • a ‘statistical’ (every foot) sampling might not help in characterizing the heterogeneities • Prefer a deterministic sampling towards a statistical sampling

Summary Workflow for quantifying impact of heterogeneity on water flooding

Step 1

Step 2

Step 3

Step 4

Step 5

• Heterogeneity Scale Identification • Heterogeneity Quantification • Box modelling at Relevant Heterogeneity Scale • Quantify Impact, honoring constraints, at reservoir grid scale • Implement findings on field scale