Sensitivity analysis of effective fluid and rock bulk modulus due to changes in pore pressure, temperature and saturation

Abstract Fluid substitution plays a vital role in time-lapse seismic modeling and interpretation. It is, therefore, very important to quantify as exactly as possible the changes in fluid bulk modulus due to changes in reservoir parameters. In this paper, we analyze the sensitivities in effective fluid bulk modulus due to changes in reservoir parameters like saturation, pore-pressure and temperature. The sensitivities are analyzed for two extreme bounds, i.e. the Voigt average and the Reuss average, for various fluid combinations (i.e. oil–water, gas–water and gas–oil). We quantify that the effects of pore-pressure and saturation changes are highest in the case of gas–water combination, while the effect of temperature is highest for oil–gas combination. Our results show that sensitivities vary with the bounds, even for same amount of changes in any reservoir parameter. In 4D rock physics studies, we often neglect the effects of pore-pressure or temperature changes assuming that those effects are negligible compare to the effect due to saturation change. Our analysis shows that pore-pressure and temperature changes can be vital and sometimes higher than the effect of saturation change. We investigate these effects on saturated rock bulk modulus. We first compute frame bulk modulus using the Modified Hashin Shtrikman (MHS) model for carbonate rocks and then perform fluid substitution using the Gassmann equation. We consider upper bound of the MHS as elastic behavior for stiffer rocks and lower bound of the MHS as elastic behavior for softer rocks. We then investigate four various combinations: stiff rock with upper bound (the Voigt bound) as effective fluid modulus, stiff rock with lower bound (Reuss bound) as effective fluid modulus, soft rock with upper bound as effective fluid modulus and soft rock with lower bound as effective fluid modulus. Our results show that the effect of any reservoir parameter change is highest for soft rock and lower bound combination and lowest for stiff rock and upper bound combination.

[1]  A. Nur,et al.  A physical model for porosity reduction in sandstones , 1998 .

[2]  A. Nur,et al.  Critical porosity; a key to relating physical properties to porosity in rocks , 1998 .

[3]  V. A. Clark.  The effect of oil under in-situ conditions on the seismic properties of rocks , 1992 .

[4]  Martin Landrø,et al.  Estimation of pressure-saturation changes for unconsolidated reservoir rocks with high VP/VS ratio , 2014 .

[5]  Madhumita Sengupta.  Integrating rock physics and flow simulation to reduce uncertainties in seismic reservoir monitoring , 2000 .

[6]  S. N. Domenico,et al.  Effect of brine-gas mixture on velocity in an unconsolidated sand reservoir. [Laboratory velocity measurements in unconsolidated sand at various brine saturations] , 1976 .

[7]  G. Mavko,et al.  Influence of porosity and pore fluid on acoustic properties of chalk: AVO response from oil, South Arne Field, North Sea , 2004, Petroleum Geoscience.

[8]  B. Smith,et al.  Modeling Seismic Velocity in Ekofisk Chalk , 1998 .

[9]  I. Fabricius.  How burial diagenesis of chalk sediments controls sonic velocity and porosity , 2003 .

[10]  J. Anderson,et al.  The capabilities and challenges of the seismic method in chalk exploration , 1999 .

[11]  G. Mavko,et al.  Rock Physics of Chalk - Modelling the Sonic Velocity of the Tor Formation, Danish North Sea , 2000 .

[12]  Raymond D. Mindlin,et al.  Compliance of elastic bodies in contact , 1949 .

[13]  F. Gaßmann.  Uber die Elastizitat poroser Medien. , 1961 .

[14]  Zhijing Wang,et al.  Seismic properties of pore fluids , 1992 .

[15]  J. Poirier,et al.  Effet de la saturation eau-gaz sur les proprietes acoustiques des roches : Etude aux frequences sonores et ultrasonores , 1993 .

[16]  M. Batzle,et al.  Constrained and Simplified Gassmann's Equations , 2002 .

[17]  Michael Batzle,et al.  Gassmann's fluid substitution and shear modulus variability in carbonates at laboratory seismic and ultrasonic frequencies , 2006 .

[18]  A. Marsala,et al.  Shear sonic interpretation in gas-bearing sands , 1995 .

[19]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[20]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[21]  Ian Jack,et al.  Time-lapse seismic in reservoir management , 1997 .

[22]  Zhijing Wang.  3. Seismic Properties of Carbonate Rocks , 1997 .

[23]  W. Murphy.  Acoustic measures of partial gas saturation in tight sandstones , 1984 .

[24]  Lawrence W. Teufel,et al.  Effect of Reservoir Depletion And Pore Pressure Drawdown On In Situ Stress And Deformation In the Ekofisk Field, North Sea , 1991 .

[25]  A. Nur,et al.  Acoustic signatures of patchy saturation , 1998 .

[26]  G. Eberli,et al.  Changes of shear moduli in carbonate rocks: Implications for Gassmann applicability , 2005 .

[27]  S. Jenkins,et al.  Time‐lapse monitoring of the Duri steamflood: A pilot and case study , 1997 .

[28]  R. Nolen-Hoeksema.  Modulus—porosity relations, Gassmann’s equations, and the low‐frequency elastic‐wave response to fluids , 2000 .

[29]  A. Nur,et al.  Wave Velocities in Sediments , 1990 .