SEG/San Antonio 2007 Annual Meeting

Transcription

1 Interaction of seismic background noise with osciating pore fuids causes spectra modifications of passive seismic measurements at ow frequencies Marce Frehner*, Department of Earth Sciences, ETH Zurich, Stefan M. Schmahoz, Department of Earth Sciences, ETH Zurich Yuri Podadchikov, Physics of Geoogica Processes (PGP), University of Oso Summary Studies of passive seismic data in the frequency range beow Hz have shown that the frequency content of the ever-present seismic background noise changes above hydrocarbon reservoirs. Different expanations for this observation have been proposed. In this study, the effect of osciating pore fuids, i.e. oi, on the seismic background noise is investigated. A non-wetting fuid drop entrapped in a pore can osciate with a characteristic eigenfrequency. Capiary forces act as the restoring force driving the osciations. A 1D wave equation is couped with a inear osciator equation, which represents these pore fuid osciations. The resuting inear system of equations is soved numericay with expicit finite differences. The most energetic part of the seismic background noise, i.e. frequencies around.1-.3hz, is used as the externa source. This part is presumaby reated to seismic surface waves generated by ocean waves. It is shown that the resuting eastic wave initiates osciations of the fuid drops. The osciatory energy of the pore fuid is transferred continuousy to the eastic rock matrix. In consequence, seismic waves in the eastic rock carry a second frequency, the eigenfrequency of the pore fuid osciations on top of the appied externa frequency. Both frequencies can be measured at the earth surface. The presented mode is considered as a possibe expanation for observed spectra modifications above hydrocarbon reservoirs. Time evoution of the pore fuid osciations seems to be reated to the thickness of the hydrocarbon reservoir. a, b). The main finding of these studies is the osciatory movement of fuids when an externa force is appied. The frequencies of these osciations can be reasonaby ow. The driving force is the surface tension force acting on the interface between the wetting and the non-wetting fuid phase. The resuts of these works were used by the oi and gas industry to deveop a new enhanced oi recovery (EOR) method termed wave stimuation of oi or vibratory mobiization (Iassonov and Beresnev, 3; Beresnev et a., 5; Li et a., 5). The genera idea of the method is to excite osciations of the entrapped oi with a vibratory device. Inertia forces occurring with osciations eventuay are strong enough to overcome the capiary pressure. This way the oi drops are enabed to eave the pore constrictions. The method and many appication resuts are reviewed in Beresnev and Johnson (1994). Biot (196) and many foowing pubications consider fuy saturated porous rocks where no osciations can take pace. The main focus of these pubications is to better understand the dynamics of the second or sow P- wave that is a specia feature of Biot s poro-eastic theory. Pore fuid osciations considered in the presented work ony occur in partiay saturated rocks. The effect of these osciations on seismic waves traveing through a porous rock is investigated together with the effect they cause at the earth surface. Naturay induced osciations are considered that are generated by the ever-present seismic background noise. Introduction Spectra modifications of seismic background noise in the frequency range beow Hz have been observed above hydrocarbon reservoirs (right gray bar in Figure 1) (Dange et a., 3; Boch and Akrawi, 6). A new direct hydrocarbon indication method was deveoped using spectra of ow frequency seismic noise measurements. The physica expanation for these modifications is the subject of current discussions (Graf et a., 7). Seismic attenuation phenomena in poro-eastic media, subsurface refection patterns and phase transition effects (Suntsov et a., 6) have been discussed as possibe causes. The behavior of non-wetting fuids entrapped in capiary tubes and in ideaized pore spaces were thoroughy studied in the past (Dvorkin et a., 199; Graham and Higdon, Figure 1: Fied measurements of seismic background noise. One measurement above (red) and one nearby (bue) a proven oi reservoir. Left gray bar: Ocean-wave peak; Right gray bar: Modification due to reservoir. Spectraseis survey for Petrobras, Potiguar Basin, Brazi, 4 137

2 Seismic noise and pore fuid osciations Methods Couping between pore fuid osciations and eastic rock Various theoretica investigations showed that a nonwetting fuid drop, i.e. oi, entrapped in a capiary tube can osciate (Hipert et a., ; Beresnev, 6; Graham and Higdon, a, b). Both siding and pinned contact ines were considered. In both cases the radii of the menisci change when the fuid drop is dispaced out of its equiibrium position. In the case of siding contact ines a variabe width of the capiary tube has to be assumed to obtain the change of radii. This change of radii of the menisci changes the capiary pressure at the corresponding menisci which eads to a restoring force that drives the osciation. Hipert et a. () demonstrated a resonant behavior of such osciations and Hozner et a. (7) showed that possibe eigenfrequencies range down to reasonaby ow vaues (<1Hz). For simpicity, osciations of pore fuids in this work are approximated with a inear one-dimensiona osciator mode with the eigenfrequency ω. The eigenfrequency of the osciations are assumed to be constant for a pores. The pore fuid osciations are couped to a one-dimensiona inear eastic soid. A sketch of the rheoogica mode is given in Figure. The beam on the eft hand side represents a one dimensiona inear eastic soid which is couped to a one dimensiona inear osciator. The osciations infuence the behaviour of the eastic soid and vice versa. In the continuous imit of an infinite number of pore fuid osciators the tota kinetic energies E kin and tota potentia energies E pot of the fuid and soid subsystems are given by f 1 f f s 1 s s kin = ( ), ( 1 ) ( ) φρ kin = φ ρ E S u dx E u dx (1) f 1 f f s s 1 s s pot = ( ), φρ ω pot = σ ε E S u u dx E dx Superscript f and s denote fuid and soid parts of the system, respectivey. u i are dispacements and u i are their time derivatives. is the tota ength of the one-dimensiona mode. φ is porosity of the eastic rock and ρ f and ρ s is fuid and soid mass density, respectivey. S is the fiing eve of the pores and is a number between and 1. σ s is the stress in the eastic rock and ε s is the strain, i.e. spatia derivative of soid dispacement. Stress and strain are ineary reated, i.e. a inear rheoogy is assumed for the soid. Nonconnected pores are assumed that do not aow pressure waves to propagate in the fuid. Equations (1) ony consider the soid and fuid subsystems. When the fiing eve of the pores S is smaer than 1, a third phase is present in the system. Here it is assumed to be a gaseous phase. Both its kinetic and potentia energy is sma compared to the fuid and soid phases and is negected. For the continuous twocomponent system Hamiton s variationa principe can be appied to the Lagrangian functiona L (Fetter and Waecka, 198). t t t Ldt = ( T U ) dt = L dxdt () δ δ δ t1 t1 t1 T and U are tota kinetic and tota potentia energies of the couped system, respectivey. t 1 and t are two points in time. L is the Lagrangian density and has dimension of energy per unit ength. Assuming sma variations Equation () spits into two equations for the soid and fuid. Partia integration is carried out omitting the resuting boundary terms by appying zero-boundary conditions. Variations δu i arise as common mutipiers for a terms. Since variations are arbitrary the remaining terms have to be equa to zero. The resuting equations are the Euer-Lagrange equations for the continuous two-component system. L d L d L i i = i (3) u dt u dx ε The Lagrangian density L (Equation ) is substituted into the Euer-Lagrange equations. The fina equations of motion resut. f f u f f s Sφρ = Sφρ ω ( u u ) t (4) s s s u u f f s ( 1 φ) ρ = E Sφρ ω + ( u u ) t x x The first of Equations (4) is amost identica to a inear onedimensiona osciator equation. It differs in the sense of its formuation in terms of reative dispacement and averaged density (Sφρ f ). The eft hand side together with the first term of the right hand side of the second of Equations (4) is simiar to a one-dimensiona wave equation (Szabo, 1985). It is aso written in terms of the averaged density ((1-φ)ρ s ). The additiona term on the right hand side is aso written in terms of reative dispacement and inks the fuid and the soid motion. Figure : Schematic rheoogica mode for couping between eastic deformation and pore fuid osciations. Eastic bar with Young s moduus E is couped with a inear osciator of eigenfrequency ω. Two dispacements have to be considered, one for the eastic subsystem u s and one for the osciatory fuid subsystem u f. 138

3 Seismic noise and pore fuid osciations Numerica methods and setup Using two kinematic equations for u f and u s and the constitutive equation, Equations (4) are expanded to five first order inear partia differentia equations. They are discretized using the finite difference method on a onedimensiona staggered grid (Virieux, 1986). Discretization in time is done expicity with a predictor-corrector method. Boundary conditions can be rigid (a veocities equa Zero) or non-refecting (Ionescu and Ige, 3) (Figure 3). Three receivers are paced in the mode together with an externa source at the position of receiver R 1. Since the mode is one-dimensiona and the ayers on top and at the bottom are inear eastic, the distances of R 1, R 3 and S from the porous ayer do not change character of the recorded signa apart from adding a time shift. Therefore these distances are chosen to be sma (7m) to optimize numerica resoution. The source term is added to the second of Equations (4) and acts as an additiona force. The Fourier spectrum of a typica measurement of seismic noise shows a very distinct peak at around.1-.3hz (eft gray bar in Figure 1). This high energy spectra peak is a goba feature that can be measured everywhere in the word. It is presumaby reated to seismic surface waves generated by ocean waves (Aki and Richards, 198). In this study, seismic background noise is reduced to this most energetic frequency. The externa source term in Equation (4) becomes A ( x) = forx xsource F( x, t) = A ( x) sin( Ωt) (5) A ( x) = 1 forx = xsource Ω = 1.89 (=.3Hz π). The externa source is appied at one point x source in the mode domain. The eigenfrequency of the pore fuid osciations is fixed to 3Hz throughout the mode domain according to Hozner (7). Physica parameters used in the simuations are given in Tabe 1. Figure 3: 1D mode setup for numerica simuations consists of three receivers R 1 -R 3 and one source S identica with position of receiver R 1. Shaded area (i.e. the reservoir) is described by couped system of Equations (4), the rest is purey eastic. Lower and upper boundaries can be rigid (zero dispacement) or non-refecting. Symbo Vaue ω (=3Hz π) ρ f 8 kg m -3 ρ s 8 kg m -3 E 1 1 Pa φ.3 S.9 Ω 1.89 (=.3Hz π) Tabe 1: Vaues used in numerica simuations. Parameters not isted are expained in the text. Numerica resuts Energy conservation and transfer For a first simuation ony the 1m thick shaded area, i.e. the reservoir, of the mode in Figure 3 was used without the eastic ayers and with two rigid boundaries. No source was appied, but a Gaussian curve for the soid veocity was used as initia condition. Figure 4 shows the time evoution of the four energies (thin ines) in the system (Equations 1). Aso, the tota fuid energy and the tota soid energy are shown together with the tota energy of the system (thick ines). The energies of the soid and fuid phase aways add up to constant tota system energy, i.e. the tota energy is conserved. At the same time energy is transferred back and forth between the soid and the fuid subsystems. The beginning with zero energy of the fuid represents the initia conditions. That the osciations of the different energy contributions over time happen with simiar ampitudes shows that the pore fuid osciations infuence the behavior of the soid phase consideraby. Figure 4: Time evoution of the four different energies in the system. A 1m thick homogeneous system with two rigid boundaries is used. No externa source is appied but an initia veocity perturbation in the soid. The tota energy stays constant over time, i.e. energy is conserved. Spectra over time for different reservoir thicknesses Severa numerica simuations with different reservoir thicknesses were performed. At receiver R 3 a Fourier spectrum was cacuated with the recorded soid veocity after different simuation engths. Figure 5 shows the evoving Fourier spectrum for the case of a 5m thick porous ayer. The ampitude of the peak at.3hz stays constant over time whie the ampitudes of a other frequencies, incuding 3Hz, decrease. The decrease of the spectra ampitude at the eigenfrequency of the pore fuid osciations is different for different thicknesses of the reservoir. Figure 6 shows the time evoution of the ratio between the spectra ampitudes of the 3Hz-peak and the.3hz-peak. A thick reservoir initiay creates higher ampitudes of the spectra peak at 3Hz. This ampitude decreases ineary with time on doube-ogarithmic axes. A 139

4 Seismic noise and pore fuid osciations thin reservoir initiay creates ower ampitudes of the spectra peak at 3Hz. The decrease with time is smaer unti the ampitude asymptoticay reaches the vaues for thicker reservoirs. A saturation of this effect occurs at a thickness of around 7m. Whie the wave itsef is monochromatic, the wave front contains a frequencies, incuding the eigenfrequency of the pore fuid osciations. After the wave front has passed, the pore fuid continues to osciate with its eigenfrequency ω and constanty transfers energy to the eastic porous matrix. This resuts in a decrease of the ampitude of the osciations. For further studies two types of non-inear osciators were used to describe pore fuid osciations. These noninearities resut from compex pore geometries and compressibiity assumption. Preiminary resuts show that non-inearities have ony a sma effect on the energy transfer from pore fuids to soid. Figure 5: Spectra of soid veocity at receiver R 3 for a 5m thick reservoir. Different spectra are cacuated after different simuation engths. Longest time signa is 1s (back spectra), shortest is 3.5s (red). Dash-dotted vertica ine: Frequency of externa force; Soid vertica ine: Eigenfrequency of pore fuid osciations. To have modes with a more reaistic externa source, the ow frequency part (<.7Hz) of rea passive measurements of seismic background noise wi be used in the numerica mode. The resuting source is neary monochromatic but with strongy varying ampitudes over time. This ampitude variation acts ike many incident wave fronts. Presumaby, osciations of pore fuids are more excited than in the case with ony one incident wave front. The peak at the eigenfrequency of pore fuid osciations in the soid spectra is expected to be more pronounced. Additiona numerica simuations wi be performed with the reservoir having ower impedance than the eastic surrounding. Standing waves within the reservoir may deveop. They are expected to excite the pore fuid osciations more than in the case without impedance contrast. Natura porous rocks contain a range of pore sizes which eads to varying eigenfrequencies of the fuid osciations. Observed ow frequency spectra modifications of seismic background noise (right gray bar in Figure 1) may be expained as a superposition of severa spectra peaks around 3Hz created by pore fuid osciations with different eigenfrequencies. Concusions Figure 6: Time evoution of the ampitude ratio between 3Hz-peak and.3hz-peak in the spectra in doubeogarighmic representation. Different coors represent different reservoir thicknesses. Spectra are cacuated with the soid veocity at receiver R 3. Discussion Despite Equations (4) are inear. Sti, the monochromatic externa source (Equation 5) acting on the soid phase excites the pore fuid to osciate with its eigenfrequency. These osciations are initiated by the incident eastic wave. The presented mode demonstrates the possibiity of couping between pore fuid osciations and eastic wave propagation. The micro-scae pore fuid osciations are abe to change the frequency content of the arge-scae eastic wave in the ow frequency range. For expaining observed spectra modifications of seismic background noise above hydrocarbon reservoirs, osciations of oi entrapped in pore constrictions must be considered. Acknowedgements Coaboration and financia support of Spectraseis and the Swiss Innovation Promotion Agency KTI is gratefuy acknowedged. Fruitfu discussions with Reto Hozner, Erik H. Saenger and Hoger Steeb heped to improve this work. 131

5 EDITED REFERENCES Note: This reference ist is a copy-edited version of the reference ist submitted by the author. Reference ists for the 7 SEG Technica Program Expanded Abstracts have been copy edited so that references provided with the onine metadata for each paper wi achieve a high degree of inking to cited sources that appear on the Web. REFERENCES Aki, K., and P. G. Richards, 198, Quantitative seismoogy: Theory and methods: W. H. Freeman and Company. Beresnev, I. A., 6, Theory of vibratory mobiization on nonwetting fuids entrapped in pore constrictions: Geophysics, 71, no. 6, N47 N56 Beresnev, I. A., and P. A. Johnson, 1994, Eastic-wave stimuation of oi production - a review of methods and resuts: Geophysics, 59, Beresnev, I. A., R. D. Vigi, W. Q. Li, W. D. Pennington, R. M. Turpening, P. P. Lassonov, and R. P. Ewing, 5, Eastic waves push organic fuids from reservoir rock: Geophysica Research Letters, 3. Biot, M. A., 196, Mechanics of deformation and acoustic propagation in porous media: Journa of Appied Physics, 33, Boch, G., and K. Akrawi, 6, Appication of ow frequency passive seismic surveys in ADCO, UAE: Passive Seismic Workshop, EAGE. Dange, S., M. E. Schaepman, E. P. Sto, R. Carnie, O. Barzandji, E. D. Rode, and J. M. Singer, 3, Phenomenoogy of tremor-ike signas observed over hydrocarbon reservoirs: Journa of Vocanoogy and Geotherma Research, 18, Dvorkin, J., G. Mavko, and A. Nur, 199, The osciations of a viscous compressibe fuid in an arbitrariy-shaped pore: Mechanics of Materias, 9, Fetter, A. L., and J. D. Waecka, 198, Theoretica mechanics of partices and continua: McGraw-Hi Book Company. Graf, R., S. M. Schmahoz, Y. Podadchikov, and E. Saenger, 7, Passive ow frequency spectra anaysis: Exporing a new fied in geophysics: Word Oi, 47 5 Graham, D. R., and J. J. L. Higdon, a, Osciatory fow of dropets in capiary tubes. Part 1. Straight tubes: Journa of Fuid Mechanics, 45, 31 53, b, Osciatory fow of dropets in capiary tubes. Part. Constricted tubes: Journa of Fuid Mechanics, 45, Hipert, M., G. H. Jirka, and E. J. Pate,, Capiarity-induced resonance of oi bobs in capiary tubes and porous media: Geophysics, 65, Hozner, R., P. Esche, S. Dange, M. Frehner, C. Narayanan, and D. Lakeha, 7, Hydrocarbon microtremors interpreted as noninear osciations driven by oceanic background waves: Communications in noninear science and numerica simuation. Iassonov, P. P., and I. A. Beresnev, 3, A mode for enhanced fuid percoation in porous media by appication of owfrequency eastic waves: Journa of Geophysica Research-Soid Earth, 18 Li, W. Q., R. D. Vigi, I. A. Beresnev, P. Iassonov, and R. Ewing, 5, Vibration-induced mobiization of trapped oi gangia in porous media: Experimenta vaidation of a capiary-physics mechanism: Journa of Cooid and Interface Science, 89, Suntsov, A. E., S. L. Aroutunov, A. M. Mekhnin, and B. Y. Metchouk, 6, Passive infra-frequency microseismic technoogy experience and probems of practica use: Passive Seismic Workshop, EAGE. Szabo, I., 1985, Höhere technische mechanik: Springer-Verag. Virieux, J., 1986, P-Sv-wave propagation in heterogeneous media - veocity-stress fnite-difference method: Geophysics, 51,