Nicholas Déry & Paul Glover. Université Laval, Québec, Canada

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1 Nichola Déry & Paul Glover Univerité Laval, Québec, Canada

2 The Helmholtz Smoluchowki equation relate the treaming potential coupling coeicient i (SPCC) to zeta potential Pore luid dielectric permittivity Pore luid conductivity Pore luid vicoity No implicit dependance on grain ize C C ΔV ε r ε o ζ = = * Δ P ησ ΔV ε ζ = = Δ P η σ + 2Σ Λ ( ) 1999 Revil produced equation implying a grain ize dependent model Thi preentation: SPCC a a unction o grain ize Thi preentation: SPCC a a unction o pore ize Thi preentation: SPCC a a unction o pore throat ize 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 2/17

3 Previou experimental determination only two Bull & Gortner (1932) Bolève et al (2007) Thi preentation: A et o new high quality SPCC meaurement a a unction o grain ize and pore throat ize. 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 3/17

al., 2006) Λ d F C = ΔV d ε 2mF Δ P η ( d σ + 4 Σ m F ) = ζ Coïncident or phere and

4 SPCC a a unction o grain diameter Λ = Revil (1999) equation imply the model d ( F 1 ) 3 F 1 C = ΔV Δ P = d ε ( d σ + 6ΣΣ ( F 11 ) ) η σ ζ Our model (t (ater Glover et al., 2006) Λ d F C = ΔV d ε 2mF Δ P η ( d σ + 4 Σ m F ) = ζ Coïncident or phere and F>>1 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 4/17

5 SPCC a a unction o pore radiu Ourmodel or all geometrie ΔV C = = Δ P η rε ζ a ( rσ a + 4Σ 2) 4 Our model or pherical particle (a=8/3) ΔV C = = ΔP η r ε ζ ( rσ + Σ 3) 2 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 5/17

6 SPCC a a unction o pore throat diameter Our model or all geometrie C = η d M ε ζ a PT i ( d M aσ + 8Σ 2) PT i a=8/3 or pherical particle C = η 1.627d PT ε ζ ( 1.627d aσ + 8Σ 2) PT Random a C = η dpt ε ζ a ( 3 1) dpt ε ζ a( ) C = ( dpt a ( 3 1) σ + 8Σ 2 ( 2 1 ) η dpt a( ) σ + 8Σ 2 ( 4 2 3) Cubic ( ) Hexagonal 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 6/17

7 Bull and Gortner (1932) Bolève et al. (2007) 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 7/17

8 12 grain ize by laer diractometry Meaured pore throat diameter (Hg) Calculated pore radii ( (ater Glover and Walker, 2009) Meaured poroity (Hg and He) Meaured permeabilitie 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 8/17

9 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 9/17

NaCl electrolyte ph 6.9 C = 2 10 4 and 2 10 3 mol/l σ = 2.44 10 3 and 2.

electrode Keithley microvoltmeter logger 4 low rate 2 direction 12 grain

10 NaCl electrolyte ph 6.9 C = and mol/l σ = and S/m T=25 o C Omega PX302 preure tranducer Cypre Ag/AgCl g electrode Keithley microvoltmeter logger 4 low rate 2 direction 12 grain ize 2 luid 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 10/17

11 High quality experimental data it the grain diameter dependent SPCC model excellently C = mol/l 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 11/17

12 High quality experimental data it the grain diameter dependent SPCC model excellently C = mol/l 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 12/17

13 High quality experimental data it the pore throat diameter dependent SPCC model excellently C = mol/l 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 13/17

14 High quality experimental data it the pore throat diameter dependent SPCC model excellently C = mol/l 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 14/17

15 The claical HS model cannot predict the SPCC a a unction o grain ize However, there are ew data available to tet the model New high quality meaurement have been done a a unction o Grain ize Pore throat diameter Pore ize or 12 particle ize 2 pore luid alinitie 4 low rate each in 2 low direction 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 15/17

16 The Revil (1999) grain ize dependent model agree with the new high quality experimental data excellently The new Glover and Déry grain ize dependent model i an approximation o that by Revil (1999) It alo perorm very well A new pore radiu dependent model ha been developped. A new pore throat diameter dependent model ha alo been developped The pore throat diameter dependent model agree with the new high quality experimental data excellently too 1. Introduction 2. Theory 3. Previou 4. Experiment 5. Reult 6. Concluion 16/17

17 Thi work ha been made poible thank to unding by the Natural Science and Engineering Reearch Council o Canada (NSERC) Dicovery Grant Programme 1. Introduction 2. Databae 3. Theory 4. Plenary 5. Individual 6. Concluion 17/17

A study on the Variation of Streaming Potential Coefficient with Physical Parameters of Rocks

A study on the Variation of Streaming Potential Coefficient with Physical Parameters of Rocks VNU Journal o Science: Mathematics Physics, Vol. 33, No. 1 (2017) 60-68 A study on the Variation o Streaming Potential Coeicient with Physical Parameters o Rocks Luong Duy Thanh 1,*, Rudol Sprik 2 1 Thuy