27/10/2017

1

Using computational heuristics to recover a variable surface relaxivity from tomographic images for NMR loggingFrancisco J. Benavides Murillo

fbenavides@id.uff.br

PhD Candidate. Computer Sciences. UFFLAR laboratory

Universidade Federal Fluminense

Advisors: Dr. Rodrigo Bagueira, Dr. Ricardo Leiderman

1

Agenda

� NMR deliverables

� NMR simulation workflow

� Our problem

� Our proposal

� Software

2

27/10/2017

2

Formation evaluation by NMR

� Deliverables

� Mineralogy independent porosity

� Pore size distribution

� Irreducible water saturation

� Formation Permeability

� Advantages

� Does not need to wait for laboratory results

� Continuous record of formation’s rock properties

� Available in logging while drilling (LWD)

3

http://accutech.metadot.com/index.pl?r=1

www.spe.org/jpt/article/10327-technology-update-24

NMR simulation to produce a PSD

4

Pore size distribution

1

��,�= ��

�

�

Digital rock

Random Walk

NMR decay

T2 Distribution

27/10/2017

3

Our problem� A mismatch between laboratory measurements and simulated results (RW

method)

5

0,000

0,200

0,400

0,600

0,800

1,000

0,001 0,01 0,1 1 10

Bin magnitude

Time T2 (s)

Reference Constant

1

��,�= ��

�

Petrographic thin section

Our proposal

� Surface relaxivity varies with pores size

� Pore size is associated to the collision rate ξ of the fluid molecules saturating the porous media

� ��(�) can be expressed as a combination of sigmoid functions

� Pore size can be recovered from the collision rate

� � =4�

Δ

6

0

10

20

30

40

50

0 0,5 1

Relaxivity (µm/s)

ξ…

0

10

20

30

40

50

60

0 0,5 1

Relaxivity (µm/s)

ξ…

0

10

20

30

40

0 0,5 1

Relaxivity (µm/s)

ξ…

27/10/2017

4

Iterative computational heuristics� A genetic algorithm optimization

� A large set of RW simulations must be performed

7

0,0000,2000,4000,6000,8001,000

0,001 0,1 10

Bin magnitude

Time (s)

Random Walk( )ξρ2

GA Same DSP

Experimental results (AC, DP)

8

0

20

40

60

80

100

1 3 5 7 9 11 13 15Surface relaxivity (µm/s)

Pore radius (µm)A

0,0000

0,0050

0,0100

0,0150

0,0200

0,0250

0,0300

0,001 0,010 0,100 1,000 10,000

Bin magnitude

T2 (s)B

0

50

100

150

200

250

1 3 5 7 9 11 13 15Surface relaxivity (µm/s)

Pore radius (µm)A

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,001 0,010 0,100 1,000 10,000

Norm

alized bin magnitude

T2 (s)B

0,0000

0,0050

0,0100

0,0150

0,0200

0,0250

0,0300

0,0350

0,001 0,010 0,100 1,000 10,000

Bin magnitude

T2 (s)D

0,0000

0,0100

0,0200

0,0300

0,0400

0,0500

0,0600

0,0700

0,001 0,010 0,100 1,000 10,000

Bin magnitude

T2 (s)D

27/10/2017

5

Pore size distributions� Varying surface relaxivity � Constant surface relaxivity

9

0,0000,0250,0500,0750,1000,1250,1500,1750,2000,2250,250

Volume fraction

Radius (µm)

0,0000,0250,0500,0750,1000,1250,1500,1750,2000,2250,250

Volume fraction

Radius (µm)

0,0000,0250,0500,0750,1000,1250,1500,1750,2000,2250,250

Volume fraction

Radius (µm)

Simulation software

10

27/10/2017

6

Collision rate distribution

11

Computational heuristics

12

27/10/2017

7

13

Conclusions� A new varying surface relaxivity concept was introduced

� This approach produces a more precise PSD from a rock sample

� The oil industry can apply this approach on the formation evaluation by NMR

� A new Software Tool specialized in NMR: https://www.youtube.com/watch?v=kR7FmL6KSII

14

27/10/2017

8

Acknowledgements

� Advisors: Dr. Rodrigo Bagueira and Dr. Ricardo Leiderman

� Universidade Federal Fluminense

� Universidad Nacional de Costa Rica

� Sponsored by Shell, registered as ``Aplicação de técnicas avançadas deRessonância Magnética Nuclear (RMN) assistidas por ferramentascomputacionais na avaliação petrofísica de rochas carbonáticas`` (ANP18999-3) under the ANP R&D levy as “Compromisso de Investimentos comPesquisa e Desenvolvimento”

15