Experimental and simulation interpretation ofcapillary pressure and relative permeabilityfrom waterflooding experiments

Pål Ø. Andersen1,2, Presenter.IEA-EOR, Copenhagen Sep 2018

Co-authors: Kenny Walrond1, Eliana Vasquez1, Citra Nainggolan1, RezaAskerinezhad3, Dag C. Standnes1, Svein M. Skjæveland1,2, Ingebret Fjelde2,3

1 Dep. of Energy Resources, University of Stavanger2 The National IOR Centre of Norway, University of Stavanger3 NORCE Research, Norway

Contents

• Context• Aims• Mathematical model• Experimental setup• Results• Conclusions

Context: Capillary End Effects• Multiphase core flooding experiments

• Capillary pressure (CP) often neglected: • simple Buckley-Leverett analysis using

relative permeabilities (RP)

• CP can have significant impact oninterpretation

• Pc = 0 at the outlet [Leverett 1941]• Affects transient and steady state behavior.• Accumulation of wetting phase at outlet• Magnitude of end effects can be reduced by

increasing factor (Length * viscosity * rate)Rapoport & Leas, 1953: Measured recovery at water breakthrough of oil-wet cores. Stabilizationat high scaling factor (end effects becomenegligible).

Richardson et al., 1952: Measuredin situ accumulation of oil (wetting) at outlet during co-injection of gas and oil

Context: water flooding• Oil displaced by water in mixed-wet

media

• Steady state:• No time derivatives• Oil immobile• Water produced with same rate as

injected

• Saturation and pressure gradients depend on:

• Distribution of capillary pressurederivative and water mobility

• Not on oil mobility

Context: Analytical solution

• Steady state

• Simple saturation functioncorrelations

• Allows full integration to giveexplicit solutions

• sw(x), pw(x)• sw,avr and DP

• The analytical solution ispresented in Andersen et al.(2017)

Aims

• Conduct experiments under optimal conditions for testing the analytical solution:

• Maximize end effects• Measure capillary number over several orders of magnitude

• Done using • High permeability sandstone core• Injection rate from very low to vary high values• Oil-wet system

• Compare estimation of saturation functions from • Full history matching (Sendra)• Analytical solution

Summary of the Analytical Solution• Sw(x) depends on a new

capillary number N (adv/capforces) and value of m+n

• At high rates sw(x>L_E) = 1-Sor

• End effects reach inlet atthe critical value N=1

LE<LC

Average saturation• Becomes Linear with 1/N for

N>1=critical value

• Extension of intercept methodby Gupta and Maloney (2016)

• Unique slope in this region

• Capillary end effects can be scaled by new capillary numberN_canew

Scaled pressure drop• Also different trends whether

end effects have reached inlet

• Scaled dP (by dP without CEE)• proportional to 1/N (large N)• goes to 1 (large N)• given by mobility at Seq (very low

N)

Calculation of krw and J from analytical model• Assume 3+ steady state measurements of

rate, pressure drop and average saturation• Based on linear slope and intercept in high

rate region: • Sor• Krw(1-Sor)• m (curvature of Pc)• n (curvature of water rel perm)

• Based on critical point where linear region begins (N=1):

• J0 (coefficient of Pc)

• From core preparation• Swi

• Only undetermined parameter is Seq• Extrapolate measurements with model• Or spontaneous imbibition test

Estimation by points within critical N

Estimation by points outside critical N

Experimental setup• Bentheimer sandstone core, nC10 oil and NaCl

brine• Preparation

• Inject NaCl brine K(water)• Inject NaCl with Quilon to make strongly oil-

wet and displace with ordinary NaCl brine• Desiccate to Swi ~10%• Inject nC10 and measure kro(Swi) after

alteration

• Ambient temperature• Spontaneous imbibition to determine Sweq• Displace n-decane with NaCl brine at constant

rate• Measure DP and oil production vs time• Increase rate when production and pressure

drop have stabilized

• Initial and final weight to QC saturations

Results• Spontaneous imbibition

confirms strongly oil-wet state: Sweq ~ Swi

• Rate-dependent production confirms end effects

• Stable low production at low rates

• Incremental oil at increased rates

• 12 steady state measurements of Sw,avrand DP

• Rates varied over 3 orders of magnitude (0.4 to 500 PV/d)

• Good overall history match with Sendra

Relevant core

Spont Imb

Low rates

High rates

Interpretation by analytical solution• Match

• DP and Sw at given Q (absolute values)

• Overall trend (variation with Q)

• Determine critical rate to 1.6 mL/min.

• Until then end effects cover entire core.

• No point has obtained Sor

Sw linear vs 1/Q towards 1-Sor

End point determined by krwmax only

Sw nonlinear vs 1/Q

Results comparison• krw

• Similar end points and exponents• Sendra estimates too high Sor

• Pc• Sendra predicts threshold in Pc

curve (indicative of strong wetting state)

• Analytical solution gives lower magnitude, but similar slope

kri Sendra

krwanalytical solution

Pc Sendra

Pc analytical solution

Conclusions

• An experimental setup was designed and conducted successfully to give rate dependent production due to strong capillary end effects

• The results (pressure drop and oil production) were interpreted using full history matching and an analytical solution

• The corresponding saturation functions were comparable

• More tuning can improve the match

References• Andersen, P. Ø., Standnes, D. C., & Skjæveland, S. M. (2017). Waterflooding oil-saturated core samples-

Analytical solutions for steady-state capillary end effects and correction of residual saturation. JPSE,157, 364-379. doi: 10.1016/j.petrol.2017.07.027

• Gupta, R., Maloney, D.R., 2016. Intercept method - a novel technique to correct steady-state relativepermeability data for capillary end effects. SPE REE, 675 (19), 316-330. doi:10.2118/171797-PA.

• Leverett, M.C., 1941. Capillary behavior in porous solids. Trans. AIME 142, 152-169.doi:10.2118/941152-G.

• Rapoport, L.A., Leas, W.J., 1953. Properties of linear water floods. JPT, 5, 139-148. doi:10.2118/213-G.

• Richardson, J.G., Kerver, J.K., Hafford, J.A., Osoba, J.S., 1952. Laboratory determination of relativepermeability. JPT, 4, 187-196. doi:10.2118/952187-G.

The 2018 user partners and observers:

Acknowledgement:The authors acknowledge the Research Council of Norway and the industry partners, ConocoPhillips Skandinavia AS, Aker BP ASA, Eni Norge AS, Total E&P Norge AS, Equinor ASA, Neptune Energy Norge AS, Lundin Norway AS, Halliburton AS, Schlumberger Norge AS, Wintershall Norge AS, and DEA Norge AS, of The National IOR Centre of Norway for support.