Quantifying shale matrix permeability: challenges associated with gas slippage

Transcription

1 Quantifying shale matrix permeability: challenges associated with gas slippage Eric A Letham and R Marc Bustin The University of British Columbia, Canada

2 Why is K m important? K m can be control on production Need accurate input parameters to model production (Bustin and Bustin, 2012)

3 K m of fg rocks is difficult to quantify because: Anisotropy Heterogeneity / scale (Chalmers and Bustin, 2012) ~20 cm

4 Low Flow Rates Stress Sensitivity (Munson, unpublished) Different Flow Regimes

5 K m far more sensitive to stress in fg rocks Very sensitive! (Munson, unpublished)

6 Need to quantify K m at reservoir stress 50 Initial reservoir pressure Pore pressure (Mpa) 0 Time

7 Permeability effective stress laws Permeability = f(effective stress) Effective stress = f(pore pressure, confining pressure) Pore pressure and confining pressure combined into a single variable, effective stress Can predict K m at high pressures using low pressure data

8 Permeability effective stress laws In its simplest form: Effective stress = confining pressure pore pressure If initial reservoir pore pressure is 50 MPa & overburden pressure is 70 MPa Effective stress = = 20 MPa Can quantify K m at initial reservoir pressure by measuring K m in the lab at 7 MPa pore pressure & 27 MPa confining pressure Effective stress = 27 7 = 20MPa

9 Often more complicated than that. Effective stress = confining pressure α * pore pressure α < 1 K m more sensitive to change in confining pressure than change in pore pressure α > 1 K m more sensitive to change in pore pressure than change in confining pressure

10 Or even more complicated. Nonlinear effective stress law Of little practical utility Can t predict K m without measuring at exact pressure conditions of interest

11 ESLs in the literature for fg rocks? Very few published For low K m rocks, often takes more than a month per ESL Kwon et al., 2001, for Wilcox shale, coefficient of 1 Heller et al., 2014, various shales, coefficients between 0.85 and 0.15

12 Summary for those who fell asleep: K m of fine grained rocks sensitive to stress Need to quantify K m at in situ reservoir stress and range of stress states experienced during production for accurate modeling parameters K m difficult to measure in the lab, especially at high pressure Effective stress laws, if linear, can help

13 Gas Slippage (Klinkenberg Effect)

14 Permeability (md, m 2 ) Symptoms of gas slippage x Predicted Real Data by Darcy's Law Predicted by Darcy's Law Pore Pressure (MPa) Darcy s Law Q = K A μ δp δx

15 Velocity profile for a liquid Gas slippage velocity profile Liquid Zero velocity at pore wall Gas in small pore Non-zero velocity at pore wall Permeability enhancement

16 Permeability (md, m 2 ) Permeability (md, m 2 ) What is gas slippage? x Real Data Predicted by Darcy's Law Pore Pressure (MPa) x Inverse Pore Pressure (MPa -1 ) λ = T k B 2πPr 2 where: λ is mean free path P is pressure T is temperature k B is Boltzmann s constant r is diameter

17 How could gas slippage result in misleading ESLs? ESLs meant to evaluate K m variation resulting from pore structure changes induced by stress change Slippage, if present, causes K m to vary due to fluid property changes (mean free path) resulting from changing pore pressure, which also causes stress change Superposition of two counteracting processes

18 Klinkenberg s Sample L ~50% Klinkenberg s Sample A ~20% (Klinkenberg, 1941)

19 Percent of Total Pore Volume Really small pores = lost of gas slippage Pore Diameter (nanometers) 10 1

20 Experimental Method K m measured over wide range of pore and confining pressures Pore pressures low enough to easily recognize gas slippage Multiple measurements at single simple effective stresses

21 Experimental Method Cont d Synthetic Data Assuming α = 0.8, effective stress decreases nonlinearly with decreasing inverse pore pressure If stress and therefore pore structure changes are responsible for permeability change, result should be nonlinear Klinkenberg plots

22 Linear Klinkenberg plots indicate that either α = 1, or permeability variation due to slippage dominates in comparison to changes due to stress

23 Linear Klinkenberg plots, so simplest assumption is α = 1 Can derive permeability effective stress law using intercept of Klinkenberg plots

24 What if we assume slippage is insignificant at pore pressures > 7MPa??

25

26 Apparent Permeability ESL

27 Impact of gas slippage on GRI method permeability measurements

28

29 Type equation here. K a = K ( 1 b + ) P p b = K a P p K P p K a = K (1 + b P p )

30

31

32

33

34

35

36 Permeability (md) 1.5 x Intercept = 1e Inverse Pore Pressure (psi -1 )

37 Permeability (md) 1.5 x Intercept = e-06 Intercept = 1e Inverse Pore Pressure (psi -1 )

38 Conclusions Gas slippage causes significant permeability variation in fine grained lithologies, even at pore pressures higher than 7 Mpa Gas slippage naturally drives apparent permeability effective stress laws towards values less than one. Published laws for fine grained lithologies that ignore gas slippage are misleading. GRI method permeability measurements are made at very low pore pressures where gas slippage has extreme impacts on permeability

39 References Bustin, A., Bustin, RM., 2012, Importance of rock properties on the producibility of gas shales, International Journal of Coal Geology 103, Chalmers, G., Bustin, RM., Geological evaluation of Halfway-Doig-Montney hybrid gas shaletight gas reservoir, northeastern British Columbia. Marine and Petroleum Geology 38, Heller, R., Vermylen, J., Zoback, M., Experimental investigation of matrix permeability of gas shales. AAPG Bulletin 98, doi: / Klinkenberg, L.J., The Permeability Of Porous Media To Liquids And Gases. Drilling and Production Practice. Kwon, O., Kronenberg, A.K., Gangi, A.F., Johnson, B., Permeability of Wilcox shale and its effective pressure law. J. Geophys. Res. 106, doi: /2001jb Vairogs, J., Hearn, C.L., Dareing, D.W., Rhoades, V.W., Effect of Rock Stress on Gas Production From Low-Permeability Reservoirs. Journal of Petroleum Technology 23, doi: /3001-pa Zoback, M.D., Byerlee, J.D., Permeability and Effective Stress: GEOLOGIC NOTES. AAPG Bulletin 59,