MCERI: Model Calibration and Efficient Reservoir Imaging

Multiscale Parameterization and

Streamline-Based Dynamic Data

Integration for Production Optimization

Norne Field E-Segment

Eric Bhark

Alvaro Rey

Mohan Sharma

Dr. Akhil Datta-Gupta

MCERI

Approach to case study

• Objective

Develop optimal production strategy (2005 to 2008)

Production and seismic data integration

• Conceptual approach

Deterministic perspective

Single, history matched model (to 12/2003)

Global parameters defined

• Faults and transmissibility multipliers

• Saturation regions

– Relative perm, capillary pressure

• Large-scale permeability & porosity

heterogeneity with multipliers

Data integration

• Minimal calibration of prior

2/23

MCERI

Structured workflow

Production data integration

• Calibrate permeability heterogeneity to fluid rates (to 12/04)

• Multiscale parameterization (global to local scales)

Seismic data integration• Match (time lapse) changes in acoustic impedance by

adjusting water front movement (Sw)

• Streamline-based techniques

Production optimization strategy

• Optimize constrained well rates through forecast period

• Objective of improving sweep efficiency (fluid arrival time equality along streamlines)

3/23

MCERI

Production data integration:

Overview

• Calibrate prior permeability model

Multiscale approach of global-to-local adjustment

Update at sensitive locations and scales

• Production data

Three-phase rates

• 12/1997 to 12/2004

Producers E-3H, E-3AH, E-2H

• Heterogeneity parameterization

Reduce parameter dimension of high-resolution model

Address parameter correlation, insensitivity

4/23

MCERI

Parameterization

• Grid-connectivity-based transform (GCT)

Parameterization by linear transformation

Characterize heterogeneity as weighted linear combination of basis vectors

• GCT basis vectors

Generalization of discrete Fourier basis vectors for generic grid geometries

• Parameterization analogous to frequency-domain transformation

• Modal shapes, harmonics of the grid

5/23

Reservoir property

=

w1 w2

+ +

w3

+

w4

… +

w15

… +

w10

Calibrated

parameters

Bhark, E. W., B. Jafarpour, and A. Datta-Gupta (2011), A Generalized Grid-Connectivity-Based

Parameterization for Subsurface Flow Model Calibration, Water Resour. Res., doi:10.1029/2010WR009982

1 2 3 4 10 15

MCERI

• Parameterize layers individually

Maintain prior vertical variability, stratification

Prevent vertical smoothing

• For each layer (21 active of 22 total):

Define perm multiplier (1) field as calibrated field

Retain prior heterogeneity at full spatial detail

Calibration approach

6/23

Prior (ln md)

Multiplier

( )

m

i

iiw

1

cells

param.

n

m

MCERI

• Adaptive refinement of multiplier fields (layers)

From coarse (global) to fine (local) scale

Successive addition of higher-frequency basis vectors

=w1

Constant (zero frequency) basis vector

21 parameters total

zonation

7/23

Calibration workflow

Layer 1

multiplier

MCERI

w2

=w1

+

w5

7/23

+ …

Calibration workflow

• Adaptive refinement of multiplier fields (layers)

From coarse (global) to fine (local) scale

Successive addition of higher-frequency basis vectors

Layer 1

multiplier

MCERI

w2

=w1

+

w5

+ …

w10

7/23

+ …

Calibration workflow

• Adaptive refinement of multiplier fields (layers)

From coarse (global) to fine (local) scale

Successive addition of higher-frequency basis vectors

• Between gradient-based minimization iterates (Quasi-Newton)

– Gradient from one-sided perturbation of transform parameters

• Based on data sensitivity (gradient contribution)

Cease (layer-by-layer) upon data insensitivity to addition of detail

Layer 1

multiplier

MCERI

Calibration results (71 param)

L2 L10 L20 L21 L22

Calibrated multiplier fields:

Permeability fields (Multiplier .* Prior):

8/23

MCERI

Production data misfitWATERCUT

OIL RATE

E-3H E-2H E-3AH

E-3H E-2H E-3AH

9/23

Lower

OWC

MCERI

Structured workflow

Seismic data integration• Match (time lapse) changes in acoustic impedance by

adjusting water flood movement (Sw)

• Streamline-based techniques

10/23

MCERI

Seismic data integration:

Overview

• Seismic inversion of reflection data

Acoustic impedance at grid cell resolution

• Dr. Gibson of Texas A&M Geophysics Dept.

• 2001 – 2003 time lapse interval

• Changes in Z (dynamic changes)

• Calibration to seismic data

Sequential integration of acoustic impedance

• Objective function weighting

– Multiple sources seismic inversion uncertainty

– Limitations in PEM

Gradient-based workflow

• Calibrate inter-well permeability based on streamline-derived sensitivities

– Grid cell resolution local calibration

11/23

Difference of

averages:

2003 - 2001

MCERI

Data misfit

Model (k)Update (LSQR)

Simulation

PEM Z(Gassman)

SL-based sensitivities

Streamline-based workflow

kkkk

P

P

S

S

S

S

g

g

w

w

ZZZZ

Water front evolution

• Positive time-lapse

changes (Sw)

Sensitivity formulation

• Two-phase (water-oil)

PEM

• Consider only variation

with saturation (Kf)

So Sw Sg

Numerical differencingPrior

Model

12/23

Streamline-derived

(analytical)

wS

Z

k

wS

kLkkGZ 21seis1

MCERI

Sensitivity formulation

• Well rates Cell saturations Acoustic impedance

Cell permeability near streamlines traced from production wells

• Trace streamlines from producers

Velocity field from finite-difference simulation

• At each cell

Map Sw, k, to intersecting streamline

Compute time of flight ()

per segment:

tzyx ,,,SS ww

Transform to streamline coordinates

,SS ww t

dru

outlet

inlet

Define semi-analytical formulation for Sw at each cell

0

ww F

t

S

13/23k

S1

k

S 'w

w

tt

MCERI

Increase in acoustic impedance

• Replacement of oil by water

Decrease in acoustic impedance

• Occurs in areas initially water-saturated infer pressure effect

Results: Seismic data integration

K = 5-9

Pre-calibrated Model Observed Calibrated Model

K = 11

14/23

Difference:

2003-2001

MCERI

Production data misfit revisited

No degradation in match quality

• Confirmation that (local, inter-well) permeability

updates for seismic data integration are consistent

with calibration from production data integration

15/23

WATERCUT

E-3H E-2H E-3AH

MCERI

Structured workflow

Production optimization strategy

• Optimize constrained well rates through forecast period

• Objective of improving sweep efficiency (front arrival time equality along streamlines)

16/23

MCERI

Optimal Production Strategy:

Overview

• Review reservoir flow pattern, connectivity

• ‘Base Case’ strategy for rate optimization

From investigation of production enhancement opportunities

• Optimal rate strategy

1) Maximize sweep (RF)

• Equalizing fluid arrival time at producers

(from injectors, aquifer)

2) Maximize NPV (indirectly)

• Accelerating production

i.e., minimize arrival time

17/23

Producer

Injector

Injector

MCERI

Reservoir Flow Pattern

Aquifer outside

of E-segment

Aquifer

Tra

cin

gfr

om

Pro

du

cers

Tra

cin

g fro

m

Inje

cto

rs

18/23

Calibrated model:

End of history

at Dec. 2004

MCERI

1) Produce at last available rates

(Dec. 2004)

RF = 47.8%

2) E-3H sidetrack well in layer 10

Highest remaining oil pore volume

3) F-1H gas injection

Higher NPV than water injection

– Lower injection/production costs

Improvement pre-optimization:

RF = 48.5%

Increment of 0.7%

Incremental NPV increase: 872 MM$

Base Case Production Strategy

19/23

Economic Parameters

Discount Rate 10 %

Oil Price 75 $/BBL

Gas Price 3 $/Mscf

Water Prod/Inj Cost 6 $/BBL

Gas Inj Cost 1.2 $/Mscf

Sidetrack 65 MM$

Production Constraints

Max. Inj FBHP 450 Bar

Min. Prod FBHP 150 Bar

Max. Water Inj Rate 12000 Sm3/day

Max. Liquid Prod Rate 6000 Sm3/day

Max. Water Cut 95 %

Max. GOR 5000 Sm3/Sm3

MCERI

j

iij

q

tS

q

Rate optimization workflow

• Consider 6-month time intervals

• Trace streamlines (using velocity field)

Compute fluid arrival time at producers

• Compute obj. fn.

Penalize water, gas production

• Minimize obj. fn. using SQP

Analytical sensitivities

Single forward simulation

iwii ftt ,' 1 qq

20/23

prodN

i

ittJ

1

2'qqq

MCERI

Rate optimization workflow

21/23

j

iij

q

tS

q

• Consider 6-month time intervals

• Trace streamlines (using velocity field)

Compute fluid arrival time at producers

• Compute obj. fn.

Penalize water, gas production

• Minimize obj. fn. using SQP

Analytical sensitivities

Single forward simulation

• Progress to next time interval

prodN

i

ittJ

1

2'qqq

iwii ftt ,' 1 qq

MCERI

300

344

434

0

100

200

300

400

500

Norm Wt.-0 Norm Wt.-100 Norm Wt.-1000

Incre

menta

l N

PV

, M

M $

Case

48.88 49.19 49.24

40

45

50

55

Norm Wt.-0 Norm Wt.-100 Norm Wt.-1000

Recovery

Facto

r (b

ased o

n O

IIP

), %

Case

Production acceleration

prodprod N

i

i

N

i

i tttJ

1

2

1

2qqqq

• Rate opt. improves recovery factors

Delays gas breakthrough (and shut-in) at E-2H and E-3H-sidetrack

• Acceleration ( ) improves NPV

Disproportionate increase – pressure support from higher gas injection rate

compensates for water injection (BHP upper limits reached)

Recovery factor Incremental NPV(over base case)

22/23

(up 0.3%)

MCERI

Summary

• Production data integration

Global to local permeability calibration

• Multiscale parameterization

Minimally update (pre-calibrated) prior model

• (Sequential) Seismic data integration

Match change in acoustic impedance between 2001 and 2003

Calibrate cell permeability based-on streamlines traced from producers

• Cell saturations through water front movement

Well-captured positive changes

• Production schedule optimization

Established base scenario of E-3H-sidetrack (large remaining oil pore

volume) and F-1H gas injection (lower costs)

Improved RF and NPV by equalization and reduction of fluid travel times

23/23

MCERI: Model Calibration and Efficient Reservoir Imaging

Norne Comparative Study

Eric Bhark

Alvaro Rey

Mohan Sharma

Dr. Akhil Datta-Gupta

MCERI

Backup slides: GCT

27/X

MCERI

Grid-connectivity-based transform basis

(1) Model (or prior) independent

Can benefit from prior model information

(2) Applicable to any grid geometry (e.g., CPG, irregular unstructured,

NNCs, faults)

(3) Efficient construction for very large grids

(4) Strong, generic compression performance

(5) Geologic spatial continuity

28

Highlights of new basis

M

N

M v

v

v

u

u

u

2

12

1

2

1

=

MCERI

Concept: Develop as generalization of discrete Fourier basis

KEY: Perform Fourier transform of function u by (scalar) projection

on eigenvectors of grid Laplacian (2nd difference matrix)

Basis development

• Interior rows Second difference

Periodic operator (circulant matrix)

• Exterior rows Boundary conditions control

eigenvector behavior

29

MCERI

• Decompose L to construct basis functions (rows of )

Always symmetric, sparse

Efficient (partial) decomposition by restarted Lanczos method

Orthogonal basis functions;

• In general (non-periodic) case

Eigen(Lanczos)vectors vibrational modes of the model grid

Eigenvalues represent modal frequencies

Basis development

vΦvΦuvΦuT 1

5 10 15 20 25 30 35 40 45 50

5

10

15

20

25

30

35

40

45

50

Grid LaplacianCPG Unstructured

2-point connectivity (1/2/3-D)

30

MCERI

• Modal shape modal frequency

• Constant basis Zero frequency

• Discontinuities honored

Basis vec. 1 Basis vec. 2 Basis vec. 3 Basis vec. 4 Basis vec. 5

Corner-point Grid

(Brugge)

Basis functions: Examples

Basis vec. 9

31

MCERI

Parameterize

multiplier field

Additional

spatial

detail?

NO

Add higher-

frequency modes to

basis

YES

Calibrated Model

(1) START: Prior model

Prior spatial hydraulic

property model

Update in transform

domain

Back-transform

multiplier field to

spatial domain

Flow and transport

simulation

Mu

ltis

cale

ite

rate

Unit-multiplier field at

grid cell resolutionG

rad

ien

t-b

ased

itera

te

Streamline-,

sensitivity-based

inversion (GTTI)

Structured workflow

Data misfit

tolerance?

NO

YES

(2) Regional update (3) Local update

FINISH

32

MCERI

Leading basis functions by modal frequency

Leading basis functions by prior model compression performance1 2 3 4 5 6 7 8 9

3D CPG 1 2 3 4 5 6 7 8 9

Coefficient spectrum: scalar proj. of prior onto 500 leading basis functions

Honoring prior by basis element selection

33

Sp

ec

tra

l

co

eff

icie

nt

Basis function by modal frequency Basis function by compression

MCERI 34/X

Pressure misfit

MCERI

E-3AH Pressure

• There is an apparent constant shift

Simulated pressure is over-estimated

• Potential Solutions

Add (negative skin), completion specific

• Skin required to lower pressure 20+ bars (e.g., s = -10) results in high

rate fluctuation as drawdown becomes too large

Add WPIMULT < 1.0

• Same result as for skin

Lower Pinit

• Improves match, but

lowered to 150 bars

MCERI

E-3AH Pressure

• Early FMT match indicates

that Pinit is consistent with

prior model specs

• This is despite isolation of

EQLNUM 3 (see below)

which would permit a very

different pressure across

the NOT formation

MCERI

Backup slides:

SL-based AI integration

37/X

MCERI

Seismic inversion

• Selected components

QC/filtering of sonic, density logs

• Well acoustic impedance

– Conditioning data

Stochastic inversion (genetic algorithm)

• Solve for acoustic impedance maps at 2001, 2003

• Average of 5 realizations

Compute change at grid cell resolution

• Observation data for model calibration

• Focus on dynamic changes

• Reduce affect of static, poorly resolved parameters

Gao, K. Acoustic impedance inversion using Petrel for the Norne Oil Field,

Texas A&M Geophysics Dept.

3rd Layer 10th layer Bottom layer

Difference of

averages:

2003 - 2001

12/24

MCERI

(Qualitative) Results

Pre-calibration Calibrated

Saturation

Changes

(Cellular Grid)

Acoustic

impedance

(Seismic volume)

Sli

ce

J =

49

Slice

J =

45

Assessment of WOC in E-segment (Ile, Tofte)

Change in Z (2001 – 2003) with Sw following production & seismic integration

• Orthogonal intersection of seismic volume slice and grid slice

• Increase in calibrated WOC more consistent with observed acoustic impedance

15/X

Pre-calibration Calibrated

MCERI

• Well rates Cell saturations Acoustic Impedance

Sensitivity (Z/k) computed along streamlines traced from producers

• Trace through velocity field at grid cell resolution

Sensitivity matrix is sparse

• non-zero components correspond to cells intersected by streamlines (localization)

tzyx ,,,SS ww

Sensitivity formulation

/SS ,SS wwww tt

kS

k

S '

ww

tt

1

Semi-analytical

13/X

I J

Transform to characteristic coordinates

t,SS ww

Define semi-analytical formulation for Sw

MCERI

Time-lapse sensitivity

• Sw depends on front location & previous state of saturation

• Perturbation in Sw

41/X

1-n

wnw

nw S,

τSS

t

1-nw1-n

w

nw

nw'n

w SS

SτS

1S

t

τS

1

S

S

S

SτS

1

S

SτS

1S

0w'

0w

M-nw

2-nw

1-nw1-n

w'

1-nw

nwn

w'n

w ttt

0S

S

FS w

w

ww =τ

+t

• 2-phase incompressible

• perturbations in properties do

not affect streamline geometry

• Mapping of Sw b/w SL’s at different ‘steady-state’ intervals

MCERI

Seismic data integration

42

Layer 10

Layer 20

MCERI

• Construct sparse sensitivity matrix

Gradient-based minimization (LSQR)

• For each cell at which acoustic impedance measured

Compute sensitivity for all cells along intersecting streamline(s)

Sensitivity definition

No

bs

Cell

s w

ith

in s

eis

mic

cu

be

NparamActive model cells

xx

xxx

xx

xx

xxx

xxx

xx

xxx

xxx

x

xx

xxx

xx

x

x

xx

x

kS

1

k

S 'w

w

tt

14/X

MCERI

Prod. data misfit

44/X

Oil rate

Gas rate

MCERI

Backup slides:

Production Optimization

45/X

MCERI

Reservoir Flow Pattern

46

Aquifer

Aquifer

Based on calibrated model at end of history ( Dec-2004)

MCERI

RF NPV Increm.

(%) (MM $) (MM $)

1 Do Nothing: Production based on last available voidage rates 47.8 3998 -

2 Case 1 + Sidetrack + Water Injection: Recomplete E-3H in layer 10 horizontally 48.8 4438 440

3 Case 1 + Gas Injection: Inject gas through F-1H (at same voidage as w ater inj.) 48.0 4574 576

4 Case 1 + Sidetrack + Gas Injection 48.5 4870 872

Case Production Strategy

Base Case

20/24

Base case for optimization

• E-3H sidetrack in layer 10

Highest remianing oil pore volume

• F-1H gas injection

Shut-in of E-2H (Feb. 2008) and E-

3H-sidetrack (Feb. 2007)

Higher NPV than water injection

• Lower injection/production costs

Production Constraints

Max. Inj FBHP 450 Bar

Min. Prod FBHP 150 Bar

Max. Water Inj Rate 12000 Sm3/day

Max. Liquid Prod Rate 6000 Sm3/day

Max. Water Cut 95 %

Max. GOR 5000 Sm3/Sm3

Economic Parameters

Discount Rate 10 %

Oil Price 75 $/BBL

Gas Price 3 $/Mscf

Water Prod/Inj Cost 6 $/BBL

Gas Inj Cost 1.2 $/Mscf

Sidetrack 65 MM$

MCERI

Enhancement scenarios tested

• Sidetrack (300m)

E-3H in layers 1-3

E-3AH in layer 5, 6, 7, 8, 9, 10

• Currently in layers 1 and 2

F-3H in layer 2, 3 for injection to support E-3AH

• Currently in layer 20

• Conversion of F-3H into gas injector

Layer 20

48/X

MCERI

Analytical sensitivity

• Producer i, well (prod. or inj.) j

• When j is producer:

Assume streamlines do not shift for perturbation in well rates

• Travel time at i sensitive only to change in well rate at producer j = i

• When j is injector:

Nfls,i,j connect wells i and j

• Requires only single forward simulation

49/X

00

0

,,

1

,,

fsl

fsl

jfsl

N

l

jil

ij

N

NqNS

jifsl

ji

jiqS

j

i

ij

0