SEG 1999 Expanded Abstracts

A Model Study for the E�ects of Flow on Seismic Signatures

A rpita Pal�,Vinh Phan and Jerry M. Harris, Stanford University

Summary

The aim of this paper is to explore the link betw eenseismic signatures and time-varying c hanges in reservoirproperties. The e�ects of w ater ooding on seismicsignatures is studied to demonstrate the use of seismicdata for the purpose of monitoring reservoir pressure andsaturation changes.

In troduction

Fluid ow characterization is one of the main aspectsof reservoir prediction and monitoring. In reservoirs,information betw een the w ells is scarce, and seismicmonitoring techniques ha ve tremendous poten tial topro vide data on lateral variations betw eenw ells. Th us,establishing correlations betw een seismic properties onone hand, and lithology, porosit y, permeability and stresson the other will increase the reliabilit y of reservoirpredictions from seismic measurements.

Pressure and uid changes are the important factors inmonitoring production processes. In this study, w e wan tto quantify the seismic sensitivity to changes in satura-tion and pressure. T o do this we use results from a uid ow simulator and empirical models for the dependencyof seismic properties on pressure and saturation.

We use a ow sim ulatorto generate several hundred 3-D snapshots of the reservoir in time. Our problem is tocon vert the reserv oir o w data to seismic data using gen-eral empirical relations and Gassmann's equation. Thenthe e�ects of pressure and saturation changes on Vp andVs can be studied in a syn thetic reservoir. Of course,these general empirical relations for the seismic propertiesshould alw aysbe calibrated with core data. Iden ti�ca-tion of the best seismic attribute to monitor the reservoirchanges is very important. T o accomplish this, we do asensitivit y study to see the e�ect of a shallo w reservoirand a deep reservoir. The traveltime detectabilit yof aseismic event is studied for both reservoirs.

Seismic Forward Modeling

The framework of the seismic forward modeling process,whic h pro vides the seismic properties from the reservoir ow properties is outlined in Fig 1. The problem hereis how to �nd the Vp, Vs and densit y of the rock as afunction of time and space from the pressure, saturationand porosity values pro vided by the ow simulator. Theinput to the seismic modeling process is porosit y ateach cell of a cube (represen ting 3D volume in space),pressure, and saturation at di�erent times at those cellsof the cube. The output is Vp, Vs and density for eac h

cell of the cube at di�erent times. We ha ve 200 timesteps, but only tw o (beginning and end) are discussedherein. We use here a simple model that is typical of aclean sandstone reservoir.

Seismic Algorithm to be follow ed is as giv en belo w:1) Assign dry rock velocities from core calibrated empiri-cal v elocity-porosit y relations.The velocities are assumedto decrease linearly with increasing porosity:

V = A�B � (1)

where � is porosit y,V is the v elocity,A and B are theconstan ts depending on lithology and e�ective pressure.2) Find the density of the uids at pore pressure value P :

�P = �(1 +C(P � Pref ))=FV F (2)

where Pref is the reference pore pressure, �P is the densit yof the uid at pore pressure value P , � is the density atPref , C is the compressibility and FV F is the formationvolume factor.Next, �nd the bulk modulus of the uids at the giv enpore pressure value from the curves giv en in (Wang et al.,1998) for water and oil.F rom the uid saturation values calculate the density ofthe mixture of uid in the rock:

�f =

3Xi=1

Si�i (3)

The bulk modulus of the uid can be found using Wood'sequation (Wood, 1930):

1

Kf

=

3Xi=1

SiKi

(4)

3) Calculate the dry density of the roc k from the porosityand mineral density values at eac h cell of the cube:

�dry = �min(1� �) (5)

Find the density of the saturated rock using the equation:

�sat = �dry + ��f (6)

4) Using the formula (Dutta and Levin, 1987):

Po = g

Z h

0

�b(z)dz (7)

for overburden pressure as a function of depth and bulkdensit y,con vertthe pore pressure to e�ectiv epressure:

SEG 1999 Expanded AbstractsDownloaded 01 Dec 2011 to 171.64.173.107. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/

Flow Simulation and Seismic

Vp, Vs,Density(dry rock)

Bulkdensity(saturatedrock)

EffectivePressure (P)

Vp,Vs(saturatedrock at P)

Bulkmodulusof fluid

Densityof fluid

Saturation offluid

Porosity,PorePressure,Saturation,Lithology

Vp,Vs(dry rock at P)

Fig. 1: Flow chart for forw ard modeling. The arrows represent astep in the whole algorithm. The bo x at the head of the arrow isthe output from step and the box at the tail of the arrow is theinput to that step. in fraction

(Peff = Po� Pp).5) Calculate the velocities for the new pressure value ata later time using the empirical trend in the velocity -pressure relation. The most widely used functional formfor v elocityV versus stress P is giv en b y:

V = V HSh1�

ha

1 + a

iexp

h�P

Pc

ii(8)

where V HS is the velocity at very high e�ectiv e stress(terminal velocity); a is the maximum velocity changebetw een zero stress and very high stress, fraction; andPc is the critical e�ectiv e stress. For clean sst, a=0.15,Pc=4351.13 psi. V HS is calculated from original V andP .6) Extract the bulk modulus of the dry rock from the dryrock velocities and dry rock densities at the new pressurevalue.(Gassmann, 1951) deriv ed the general relation betw eenthe dry rock moduli and the saturated rock moduli withthe assumptions that

� the roc k is isotropic� the mineral moduli are homogeneous� the frequency is low

Ksat

Kmin �Ksat

=Kdry

Kmin �Kdry

+Kfluid

�(Kmin �Kfluid)

1

�dry=

1

�sat(9)

Apply Gassmann equation to �nd the saturated bulkmodulus of the rock using bulk modulus of the dry rock,bulk modulus of the mineral, porosity and bulk modulusof the uid. Then P-wave and S-wave velocities due tow ater ooding at injection pressure can be derived fromthe saturated bulk modulus of the rock and the densityof the saturated rock.

Methodology

The input model is shown in Fig 2. The reservoir is ata depth of either 8000 ft or 1000ft. It consists of tenlayers, each 30ft thic k, in the z direction and is divided

510

1520

2530

5

10

15

20

25

30

1

2

3

4

5

6

7

8

9

10

0.18

0.2

0.22

0.24

0.26

0.28

0.3

0.32

Fig. 2: The syn thetic model with in fractional porosity values

into 30 ft b y 30 ft.cells in (x,y) direction. The center ofeach cell is 50ft apart. The porosity is constant in eachlayer. Two phase uid ow (oil and water) is considered.The oil-water con tact is inside the reservoir. The changein porosit y with pressure is assumed to be negligible.There is one injector w ell and one producer well in theexperiment.

We examined the changes in seismic attributes due tow ater ooding to study the e�ects of pressure and satu-ration c hanges and to identify the best seismic attributefrom which the pressure and saturation changes are recog-nizable and separable. This was done for both a shallow(e.g., 1000 ft.) and for a deep reservoir (e.g., 8000 ft.).

We calculated the change in travel times after w ater ooding, near the w ells. Then, using the appro ximatefrequency of a seismic surv ey w e estimate whether thechange can be detected (without any noise).

Results & Discussion

E�ect of Pressure and Saturation

Figure 3 shows the percen tage changes in the ow pa-rameters (pressure and saturation) and the seismic pa-rameters (P- and S- wave velocity, bulk density and shearmodulus). The changes in velocity are attributable toboth c hanges in uid saturation and the increase in porepressure. We observ edan increase in velocity near theproduction well due to the increase in e�ective pressureand a decrease in velocity near the injection well due todecrease in e�ectiv epressure and change in saturation.As the e�ective pressure of the roc k increases, the roc kbecomes sti�er and so the velocity increases. The veloc-ity decrease due to pore pressure increase is due to theopening of a number of closed pores or microcracks th usmaking the rock softer. Water ooding causes replace-ment of some of the oil by water near the injection welland since water has higher density than oil, the bulk den-sity of the rock increases. It should also be noted that



1020

3010

2030

5

10

(%)Effective Pressure

−10

0

10

20

30

1020

3010

2030

5

10

(%)Water Saturation

0

200

400

600

1020

3010

2030

5

10

S−wave Velocity

−2

−1

0

1

1020

3010

2030

5

10

P−wave Velocity

−0.5

0

0.5

1020

3010

2030

5

10

Shear Modulus

−1

0

1

2

1020

3010

2030

5

10

Bulk Density

0

1

2

3

Fig. 3: The percen tage changes in the input parameters (pressure and saturation), the output parameters (P- and S-wave velocity,bulk densit y) of forw ard modeling and shear modulus. The changes are calculated at the end of water ooding i.e., da y 200.



since bulk density is a function of porosity, the change insaturation cube looks di�erent from the change in bulkdensit y cube, although one is a direct consequence of theother. As a result of this increase in bulk density the v e-locity also decreases. It is also interesting to note thatthe v elocity decrease is more in S-wave velocity than inP-wave velocity, as the increase in bulk modulus of thepore uid o�sets some of the densit y e�ects in case ofP-wave velocity.

Looking qualitatively at the seismic di�erence cubes, weconclude that shear modulus shows best the e�ect of pres-sure change, because Gassmann's theory predicts that theshear modulus is not e�ected by uid change. Th us, theshear modulus can be used to identify the e�ect of pres-sure.

E�ect of Reservoir Depth

T able 1 is the result of the sensitivit y study on a deepreservoir versus a shallo w reservoir. The changes insaturation and pore pressure are kept the same in boththe cases. As seen from the T able 1, by changing the

P ercen tage change Deep Shallo w(%) (8000ft) (1000ft)

P-wave velocity -1 to 1 -1.25 to 2S-w ave velocity -2.5 to 1.5 -3 to 3Bulk density -1 to 3.5 -1 to 3.5P-wave impedance -1 to 3 -1.5 to 2.5S-w ave impedance -1 to 2 -1.75 to 3Lames coeÆcient -10 to 30 -10 to 30Shear modulus -1.5 to 3 -3 to 6Bulk modulus -2 to 7 -3 to 7P/S velocity -0.5 to 2 -1 to 2.25

Table 1: The percent changes of di�eren t seismic attributesafter w ater ooding in both cases.

depth of the reservoir, changes in all seismic parametersexcept for bulk densit y and Lame coeÆcient show anincrease. Th us w e can conclude that a shallow reserv oiris more sensitive to water ooding than a deep reservoir.The change in velocity due to change in pressure isless as the e�ectiv e pressure increases. In the case ofa deep reservoir the e�ectiv e pressure is higher and sothe change in velocity is less and since other parametersdepend on velocity, they also c hange.Bulk density andthe Lame coeÆcient do not change in the tw o cases astheir change is attributable only to change in saturation,whic h is the same in both cases.

V ertical resolution at maximum surface seismic frequencysay 50Hz is 5ms. And vertical resolution at maximumcrossw ell seismic frequency say 1000Hz is 0.25ms. The dif-ference in 2-way tra veltime in actual data (without noise),for both the deep and shallow reserv oirs, is only detectableat crossw ellfrequencies. 4-D time-lapse surface seismiccannot detect this change as the frequency is very low.

T raveltime Deep Shallo wdi�erence (ms) (8000ft) (1000ft)

P-wave (injector) 0.31 0.54P-wave (producer) -0.42 -0.9S-w ave (injector) 1.3 2S-w ave (producer) -1 -2

Table 2: The tw o-w ay traveltime di�erence due to water ood-ing at the producer and injector well in the reserv oir.

Conclusions

The following conclusions can be drawn based on theexperiment. Seismic velocities decrease with porepressure increase. Shear velocity decreases with w atersaturation but compressional velocity �rst decreasesand then increases with w ater saturation. Changes inpressure may be observ ed in shear modulus and thusit can be used to separate the pressure e�ect from thesaturation e�ect. A shallo w reservoir is more sensitiv eto w ater ooding than a deep reservoir. The traveltimedi�erence is detectable at crossw ell frequencies but notat surface seismic frequencies.

References

Dutta, N. C., and Levin, F. K., 1987, Geopressure: Soc.Expl. Geophys.

Gassmann, F., 1951, Elastic waves through a packing ofspheres: Geophysics, 16, 673{685.

Wang, Z., Cates, M. E., and Langan, R. T., 1998, Seismicmonitoring of co2 ooding in carbonate reservoir: Rockph ysics study:Geophysics, 63, no. 5, 1604{1617.

Wood, A. B., 1930, A textbook of sound: G. Bell andSons, London.


Documents

SEG 1999 Expanded Abstracts