towards quantitative evaluation of gas injection using ... · quantitative interpretation. key...

Geophysical Prospecting, 2011, 59, 310–322 doi: 10.1111/j.1365-2478.2010.00925.x

Towards quantitative evaluation of gas injection using time-lapseseismic data

Reza Falahat, Asghar Shams and Colin MacBeth∗Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS, UK

Received April 2010, revision accepted August 2010

ABSTRACTOf particular concern in the monitoring of gas injection for the purposes of stor-age, disposal or improved oil recovery is the exact spatial distribution of the gasvolumes in the subsurface. In principle this requirement is addressed by the use of4D seismic data, although it is recognized that the seismic response still largely pro-vides a qualitative estimate of moved subsurface fluids. Exact quantitative evaluationof fluid distributions and associated saturations remains a challenge to be solved.Here, an attempt has been made to produce mapped quantitative estimates of thegas volume injected into a clastic reservoir. Despite good results using three accu-rately repeated seismic surveys, time-delay and amplitude attributes reveal fine-scaledifferences though large-scale agreement in the estimated fluid movement. These dif-ferences indicate disparities in the nature of the two attributes themselves, which canbe explained by several possible causes. Of most impact are the effects of processingand migration, wave interference effects and noise from non-repeatability of the seis-mic surveys. This subject highlights the need for a more careful consideration in 4Dacquisition, amplitude processing and use of true amplitude preserving attributes inquantitative interpretation.

Key words: Amplitude and time-shift attributes, Gas injection, Quantitative inter-pretation, Time-lapse seismics.

INTRODUCTIO N

Of particular concern in the monitoring of gas injection forthe purposes of storage, disposal or improved oil recovery isthe exact spatial distribution of the gas volumes in the sub-surface and, in particular, away from wells. In principle thisrequirement is addressed by the use of 4D seismic data, al-though it is recognized that the seismic response still largelyprovides a qualitative estimate of these gas distributions. Exactquantitative evaluation of subsurface fluid volumes and asso-ciated saturations remains a challenge to be solved. Past workhas addressed the calibration of 4D seismic for this purposeusing well production data and threshold analysis (Huang

∗E-mail: [email protected]

et al. 2001), laboratory measurements (Langlais, Mezghaniand Lucet 2005), well tie analysis (Meadows 2008) or directcomparison with simulation models (Sengupta and Mavko2003). In these studies, consideration has been given to bothseismic amplitudes (Huang et al. 2001) and reflector time-shifts (Dumont et al. 2001) as possible attributes for monitor-ing purposes but it is found that the results from amplitude andtime-shift analyses differ substantially. These differences areindicative of the degree of calibration of the seismic productand the complexity of the reservoir geology but are central tounderstanding the quantitative nature of the 4D seismic signal.To address this issue, here these two attributes are analysedusing a highly repeatable 4D survey, monitoring gas injection.Specifically, our focus is multiple vintages of seismic used tomonitor methane injected into a saline aquifer in the NorthSea. In this case, use can be made of known well volumes of

310 C© 2010 European Association of Geoscientists & Engineers

Evaluation of gas injection using time-lapse seismic data 311

Figure 1 a), b) and c) NW (left) – SE (right) seismic sections for the area of interest, at the baseline in 1993 (before gas injection) with horizonsand faults, at 2002 after four years of gas injection and their difference. The orange horizon corresponds to the base conglomerate layer pickedin the time-shift analysis. Inset in (a) and (b) is an example of the difference in time picks between the baseline and monitor surveys. d) Gammalog and interpretation of the main T28-ss1, T31-sst1 and T31-ss2 sands of the reservoirs of interest.

this light immiscible gas injected into highly porous reservoirsands known to be reasonably homogeneous, to aid in a goodquality calibration of the final spatial distribution estimates.

D A T A A N A L Y S I S

Description of the data set

Our data set consists of repeated seismic surveys shot over aturbidite reservoir lying at 2 km depth in the North Sea intowhich methane is injected. The multiple reservoir sands ofthe area sit within the Faroe Palaeocene group of the Vailaformation. Previous detailed evaluation of well and seismicdata by the operator of the field has allowed the group to besub-divided into a number of sequences. It is these sandstonebodies that form the reservoir into which gas was injected.The sands are generally clean, fine to medium grained, vary-ing with porosity by only a few per cent with a mean of 27%and a wider range of permeability from 225–600 mD (Lamersand Carmichael 1999; Freeman et al. 2008). The three main

sands of interest are the T31-sst1, T31-sst2 and T28-sst1 andthese are separated by a background of pelagic mudstones(Fig. 1). The sands of T31-sst1 are very thick bedded sand-stones, with a high net-to-gross, whilst the other two sandsshow varying degrees of shale interbedding and hence amal-gamation. Inside the selected structure of interest to our study,each sand body remains hydraulically isolated although somecross-flow is thought to occur at fault locations. These sandsare approximately parallel and are underlain by the base con-glomerate, a key marker for seismic interpretation (see Fig. 1).Our study area is limited by the channel boundary from theeast and west and by faults in the north and south.

Data from a single injection well drilled into the area ofinterest are available. Injection starts in 1998 and contin-ues for the period of the seismic monitoring (Fig. 2a). Thebaseline seismic data were shot in 1993 and three seismicmonitor surveys were acquired thereafter in 1999, 2000 and2002, after 25, 37 and 53 billion cubic feet of gas injectionrespectively. The resultant time-lapse responses have a highrepeatability, defined by an average value of 21% for the

C© 2010 European Association of Geoscientists & Engineers, Geophysical Prospecting, 59, 310–322

312 R. Falahat, A. Shams and C. MacBeth

0

20

40

60

80

100

120

0

10000

20000

30000

40000

50000

60000G

as R

ate

(M

Mscf/

d)

Time since injection (days)

Pre

ssure

(psi)

2000

2500

3000

3500

4000

4500

0 250 500 750 1000 1250 1500

First Monitor Second Monitor Third Monitor

Cu

m.

inj. G

as (

MM

scf)

(a)

(b)

Figure 2 Gas injection data. a) Gas rate (in blue) with cumulativevolume of injected gas (in red) and b) reservoir pressure together withthe times of the monitor surveys.

normalized root mean square (NRMS) non-repeatability met-ric. Fig. 1(a–c) demonstrates the general seismic quality. Inthe portion of the structure where the well is drilled lies thethree distinct and fairly homogeneous T31-sst1, T31-sst2 andT28-sst1 sands into which the gas is injected (Fig. 1d). Becauseof the need to maintain pressure, daily injection gradually de-creases after 1999 and this ensures that the average reservoirpressure is held approximately constant during the acquisitionof the monitor surveys (see Fig. 2b). As each sand body is wellconnected both vertically and laterally, pressure equilibrationis rapidly established controlled by the bounding faults andchannel edges. The pressure at the well also reflects that of thefield in general. Thus, the time-lapse changes visible betweenthe 1999, 2000 and 2002 surveys are mainly due to gas vol-ume or saturation increases. However, any seismic time-lapsechanges taken relative to the baseline survey shot in 1993 alsocontain the start-up pressure effect.

Volumetric analysis using time-shift attributes

A stable reference reflector is chosen for the analysis corre-sponding to the base of the conglomerate layer (see Fig. 1),which appears as a zero-phase trough on the seismic. This

reflector is below the reservoir and is chosen to avoid the ef-fects of tuning influencing the results (as explained in Ghaderiand Landrø 2009). The field operator provided an interpretedpick for this reflector derived from the baseline seismic. Thereflector is then manually re-picked on each of the monitorsusing the baseline interpretation as a guide. Subtraction of theresultant picks from the two surveys then gives the requiredtime-shifts that can be mapped across the area of interestaround the injecting well. Time-shifts of up to 26 ms are mea-sured, corresponding to a velocity slow-down in the reservoirdue to the presence of gas. During the picking procedure onlyan occasional degradation of the signal is noticed (perhapsdue to residual multiples or thinning of the layer) but this haslittle impact on the overall results. There is no obvious signof a change of event character when extending beyond thereservoir zone. The data are well cross-equalized, as can beobserved by the clean difference section in Fig. 1(c), indicatingthat the influence of non-repeatability effects on these pick-ing procedures is low. Indeed analysis (described below) hasshown that events picked above the reservoir on the baselineand monitor seismic vary only by a fraction of a millisecond.

Following the strategy of Huang et al. (2001), we thresholdthe resultant time-shift maps to allow us to define robust con-tiguous areas influenced by the changes in gas volume. Thetime-shift changes remaining after the thresholding proceduredescribe an area, �. , of change on the map. For each cellwithin this area, the corresponding time-shift, �t, is relatedto the change in the in situ gas volume �Vg sampled throughthe reservoir interval and within the cellular area �x�y via

�Vgas ={

SgφNTGVV′

(V − V′)

}�t(x, y)�x�y, (1)

where V is the seismic wave velocity with no gas and V′ theseismic wave velocity in the cell in the presence of the gassaturation Sg (see Appendix B). φ and NTG are the sandporosity and net-to-gross respectively and combine to give theeffective porosity φeff = φNTG. Sg is a strong function ofrock properties for flow, particularly the relative permeabilitycurves.

By integrating (1) over∑

, an estimate of the total vol-ume of injected gas for each seismic time-lapse period canbe obtained. As the reservoirs are fairly homogeneous andtheir petrophysical properties are known to vary only slowlyacross

∑, then the spatial integral of Sg and φeff can be ap-

proximated by their average. This is justified, as inspectionof the operator’s simulation model shows that the net-to-gross distribution is very narrow across the area of interest,with a standard deviation of approximately 0.1. Numerical



simulations have shown that the gas saturation for the reser-voir is narrowly distributed, with a mean close to the maxi-mum attainable value of Smax

g (Appendix A). These assump-tions lead to a formula for the gas volume injected relative tothe initial gas volume Vgas(initial)

Vgas = Vgas(initial) +{Sgφe f f

VV′

(V − V′)

}mean∫∫�

�t(x, y)dxdy,

(2)

which predicts that the integration of the time-shift changesobserved from the seismic data are directly proportional tothe total volume of injected gas Vgas for a chosen survey timeperiod. One modification to this is required when time-shiftsbetween the (pre-injection) baseline and any of the monitorsurveys are being considered. This is because the total mea-sured time-shift, �t, in this case now includes a constant time-shift �tpr due to the effect of a pressure increase on the rockframe and fluids prior to 1999 but after 1998, such that �t =�tgas + �tpr and the time-shift due only to gas saturation�tgas is slightly masked. This effect essentially adds a posi-tive constant, a, to equation (1) as both pressure up and gassaturation soften the reservoir. In practice the combinationof constant factors multiplying the integrand in equation (2)and the pressure factor a are not known in situ with certaintybut can be estimated directly from the data by calibratingthe time-lapse seismic with the known well injection data.Thus, the three combinations of integrated time-shift from the2002–2000, 2002–1999 and 2000–1999 signatures are cross-plotted against the injected volumes independently from the2002–1993, 2000–1993 and 1999–1993 signatures (Fig. 3a).An initial common noise threshold of 0.5 ms is used for thetime-shift maps prior to integration and this is refined upwardsuntil the points in the cross-plot follow a straight line and bothsets of points for the monitor-monitor and monitor-baselinecombinations have identical gradients. This is achieved byfinding the maximum of an objective function that optimizesthe fit of the points to each line and the degree to which bothresultant lines are parallel. Based on this function, the optimalthreshold can be determined accurately to within 5%. It is ob-served that the points involving the baseline survey display anoffset corresponding to the pressure effect anticipated above,whilst the points generated between monitor surveys lie on astraight line that passes very close to the origin (there is nocondition to intersect the origin in our technique). The off-set due to the pressure effect contributes on average 19% (or4 ms) to the total time-shift (for a 1000 psi pressure increase).The common gradient of the lines now gives us an estimateof the calibration coefficient (the factor in the curly bracketsmultiplying �t in equation (1) and the integrand in equation

y = 1.4215x

y = 1.5072x + 0.4784

0

2

4

6

8

10

12

Cumulative Gas Volume (E+6 m3)

Monitor-Monitor Monitor-Base

y = 1829.9x

y = 1865.7x + 529.55

0

2000

4000

6000

8000

10000

12000

14000

Inte

gra

ted

Am

plitu

de

Ch

an

ge (

E+6)

Monitor-Monitor Monitor-Base

(a)

0 2 4 6 8

Cumulative Gas Volume (m3*106)

Inte

gra

ted A

mplit

ude C

hange

(

*10

6)

Inte

gra

ted T

imeshift C

hange

(*

10

6)

(b)

Figure 3 Total injected gas volume versus: a) integrated time-shift;b) integrated amplitude. Data points are for the differences formedby the monitor-baseline combinations 1999–1993, 2000–1993 and2002–1993; and the monitor-monitor combinations 2000–1999,2002–2000 and 2002–1999.

(2)) that can be applied to the time-shift �t(x,y) at each lo-cation and to the monitor-baseline attribute maps to convertthem into a gas volume variation Vgas(x,y) with appropriatecorrection for the pressure effect. As a quality control check,it is found that an estimate of the calibration factor using ap-proximate values from the field match the final derived valuequite well. The gas volume distribution predicted in this wayfor the 2002 survey is shown in Fig. 4(a).

Volumetric analysis using amplitude attributes

A similar relation to equation (1) is also possible for amplitudeattributes. Each reservoir sand is below tuning thickness as thethickness of the individual sands is between 20–39 m (from loginterpretation), compared with the seismic wavelength at thereservoir level of 185 m respectively. Thus, their time-lapsedseismic root mean square amplitude is directly proportional tothe thickness of the gas accumulated between surveys. Here,the difference of the root mean square amplitudes is chosen asit significantly reduces intra-reservoir time-shift effects. Theamplitude equivalent of equation (1) is

�Vgas ={

cSgφNTGVV′

(V − V′)

}�A(x, y)�x�y, (3)



Figure 4 Gas volume maps (in m3) for the period up to July 2002, estimated from: a) time-shift attributes; b) amplitude attributes. c) Theaverage estimated gas volume map; and d) the difference of the maps in (a) and (b).

where c is a constant of proportionality that converts tunedamplitude to time-thickness and is a function of impedancesin the sand, shale and the fixed velocities V and V′ (seeAppendix B). This relation assumes small impedance contrastsat the top reservoir and the gas-water contact. The in situ vol-ume of gas injected can now be calculated in a similar mannerto the time-shifts and the term in the curly brackets in equation(3) estimated empirically using the cross-plots. In practice, aroot mean square amplitude average is selected in a windowbetween the top and base of the reservoir interval. Given thesmall amplitudes involved, this is approximately equal to thesum of the individual root mean square amplitudes for eachreservoir sand and hence the summation of the gas accumu-lation thicknesses. Furthermore, assuming (as before) that thepressure effect on the amplitudes is linearly additive, pressurecan be treated using an identical workflow to the time-shifts.Thus, the amplitude threshold is initially set at 5% of the max-imum and then adjusted upwards as before until the points inthe cross-plot follow a linear trend. In this process the lowerlimit amplitude threshold is required to avoid introducing thespatially broad background noise level. The final cross-plotresults are shown in Fig. 3(b), which also reveal the antici-pated small vertical offset due to the pressure effect on thetime-lapse signatures, contributing in this case to 13% of thetotal amplitude. After determining the corresponding calibra-tion coefficient linking Vgas to �A in a similar manner to the

previous section, the resultant gas volume derived from theamplitude for 2002 can now be mapped in Fig. 4(b).

Comparing the gas volume maps of Figs 4(a) and 4(b), to-gether with their corresponding average and difference, thetime-shift and amplitude attributes are observed to yield dif-ferent results. Indeed, differences between amplitude and time-delay based interpretations are expected and are commonlyobserved. For example Meadows (2008) showed significantlydifferent maps for CO2 injection into a clastic reservoir andNg, Bentley and Krebes (2005) showed major differences inmaps for the injection of a miscible gas and solvent into a car-bonate reservoir but concluded that the time-delays appearto agree closer with their well activity. Finally, Mehdizadehet al. (2010) found different amplitude and time-shift maps inseismic monitoring of an in situ combustion process in heavyoil. They concluded that the time-shift map was noisy relativeto the amplitudes. In our example, the two maps do appear tobe reasonably close but there are still regions of disparity. Forexample, there is a region of no gas change in the southernpart of the amplitude map that is not present in the timeshiftmap. Also, in general, the amplitude map possesses lower spa-tial frequencies. Around the well, gas volume anomalies areshifted towards the east and north-east in the amplitude maprelative to the time-shift map. Both maps possess roughly thesame geometric outline consistent with the flow simulationpredictions (see the next section). The results also show an



excellent correlation with the known fault system and theedges of the channel to the west and east. Whilst the signalsappear to terminate at the fault to the north, there is howevera gap between the lowermost edge of the gas volume and thesouthern fault. The latter observation can be explained usingthe simulation model as a combination of structural and grav-itational effects. However, it is the fine-scale details betweenthe time-shift and amplitude maps that differ greatest, witha general mismatch of many of the local high and low gasconcentrations. As the calibrations using the well injectivitydata and material balance as described above are found to beexcellent, the differences between maps must be due to theinherent nature of the attributes themselves. These differencesare discussed further in the next section.

R E S U L T S A N D D I S C U S S I O N

There are a number of reasons for why the estimates of gas vol-umes derived from the amplitude and time-shift maps do notmatch exactly. These attributes are different average measuresof the gas saturated reservoir sands and the variation cannotbe simply related to errors in the picking of the time-shiftsor in evaluating the amplitudes. Some possibilities are: a) theamplitudes respond to local changes in density and velocity,whereas the time-delays respond only to a depth-averaged ve-locity. If density and velocity are uncorrelated, then there willbe differences in the attributes; b) the amplitudes may be af-fected by variable thin bed tuning effects; c) lateral variationsin the phase or frequency of the seismic wavelet; d) errors arisedue to acquisition (and processing) non-repeatability, whichsuperimpose the uncertainty already present in the evaluationof the amplitude and time-shifts and e) the seismic amplitudesare sensitive to the choices made during processing such as thechoice of a particular velocity model or migration algorithm.These possibilities are discussed in more depth below.

To aid in the understanding of the origin of the differencesbetween the attributes, a simulation model is built from whichseismic data are modelled, amplitudes and time-delays ex-tracted and gas volumes estimated as in the previous section.The simulation model for the area of interest is built basedon the petrophysical and geological characteristics of a largermodel provided by the operator of the field. The field modelis, however, too coarse for our studies as it was intended tocover a larger area, so a finer scale model is required. Thebase conglomerate (see Fig. 1), a key event on the seismic, ispicked, converted to depth and displaced upwards by 30 mto provide the base of the reservoir lowermost reservoir sand.(The conglomerate layer is included later in the seismic mod-

elling but not in the simulation model). As the other seismicdata picks are unclear, the additional layers of the model aredeveloped by extrapolating the well picks for the top and baseof each sand layer. Five faults are also identified from the seis-mic interpretation and added to model. The overall size of thefinal model is 2900 m × 2400 m × 143 m, with a cell size of25 m × 25 m × 2 m. Properties are distributed in the model ac-cording to those extracted from the coarse-scale field model.This uses knowledge that the porosity in the sands is fairlyuniform both horizontally and vertically. Permeability rangesfrom 225–600 md and it is constant laterally across each sandbut varies from sand body to sand body. Net-to-gross followsthe channelized system established in the original model. Fi-nally, the pressure-volume-temperature behaviour tables andrelative permeability data from the original model are used(it will be seen later how critical the choice of relative perme-abilities is in this study). The final resultant predictions of gassaturation from this simulation model are shown in Fig. 5.1 To investigate the first possible explanation for the mis-

match of amplitude and time-shift attributes, P-waveimpedance (IP) against velocity (VP) from the wireline logs(using the density and sonic logs) is plotted (Fig. 6). Sepa-rate cross-plots are made for each individual shale and sandlayer. For these data a small, 1–2%, fluctuation about alinear trend line is noted. As it is likely that the lateral vari-ability in subsurface properties is smaller than the verticalvariability, then this result indicates that lack of correla-tion between IP and VP is an insufficient reason for theobserved differences between attributes. To check that thispoint remains valid for the gas saturated sands, the watersaturated log values are adjusted by Gassmann fluid sub-stitution (Mavko, Mukerji and Dvorkin 2003) to representthose for the gas saturated case. Note, that the injected gasvolume fills the sands and settles quickly into a saturationstate governed approximately by the maximum gas satura-tion Sg = 1-Swir (see Appendix A) between seismic surveys.Figure 7 shows the resultant cross-plots after gas saturationand that a predominantly linear correlation between IP andVP remains, despite the range in IP-VP space covered by thedata (on average a coefficient of variation for IP and VP

from 12–26%). Varying the gas saturation by 10% eitherside of the mean does not affect this result.

2 Another possibility for consideration is that the root meansquare amplitudes are influenced by constructive or destruc-tive wave interference effects and the time-delays are not. Toexamine this, synthetic seismic are modelled directly fromthe simulation model, the root mean square amplitudes andtime-shifts are then calculated and the gas volume estimates



Figure 5 a) Gas saturation for the upper layer predicted from the flow simulation model for July 2002. Model section is shown correspondingto b) the NW(left) – SE(right) seismic sections in Fig. 1 and c) perpendicular to the seismic section. Well locations and vertical trajectories aremarked for reference.

Figure 6 P-wave impedance against P-wave velocity from well-log data for a) reservoir sands; b) shales. Green points indicate properties of thesands and shales respectively used in our simulator to seismic modelling, showing their degree of calibration with the well data.

obtained in a similar manner to the observed data. Anessential component of this modelling involves using theIP-VP cross-plot to calibrate the rock matrix values forthe simulator-to-seismic calculations. These values are

adjusted until there is a match between the log val-ues and those obtained from each cell of the simula-tion model (as shown in Fig. 6). Pressure and satura-tion changes are calculated using flow simulation and



Figure 7 P-wave impedance plotted against P-wave velocity for theupper T31 sand. Water saturated points (blue points) shift to redpoints by changing from water to gas. Green points – gas saturationis varied randomly by 10% from 1-Swir.

then convolutional modelling applied to generate thesynthetic traces using a wavelet derived from the observeddata. Next, the traces are subjected to the same cross-plotvolumetric analysis as that carried out on the observed datain the previous section. The results of this procedure areshown in Fig. 8 and indicate several differences between theestimated spatial distributions across the area of interest.It appears that amplitude estimates are reduced relative tothose from the time-shifts due to intra-reservoir wave in-

terferences. For example, in the southern part of the reser-voir there is a reduction in amplitude due to a gas volumeconcentration, which is completely contradictory to whatis expected. Inspection of this region indicates that this isa zone of gas lying below a shale barrier, which preventsupward movement into the top of the structure. Here, time-shifts are more reliable as destructive interference resultsfrom the particular thicknesses of these layers. Addition-ally, it is observed that there is a correlation between thethickness of the gas-water transition zone and departuresof the amplitude from that expected from our simple modelin Appendix B. This is probably due to the larger variabil-ity of gas saturation values in this zone creating a morenon-linear seismic response. It is anticipated that in prac-tice variations might also arise in the observed data due toreservoir thickness. Furthermore our convolutional mod-elling does not capture the effects of intra-bed multiples orthat of wave conversions. Acquisition offset range variabil-ity has also been tested in the modelling and it is observedthat the reservoir does not show strong amplitude varia-tions with offset and that the estimates closely resemble thenormal incidence results.

3 Lateral changes in the seismic wavelet across a survey andalso between seismic surveys, are other probable reasons for

Figure 8 Gas volume maps (in m3) for the period up to July 2002, estimated from: a) synthetic time-shift attributes, b) synthetic root meansquare amplitude attributes. c) The average estimated gas volume map; and d) differences of the maps.



Figure 9 Normalized root mean square amplitude maps for a window a) 400–600 ms; b) 600–800 ms; c) 800–1000 ms; and d) 400–1000 msin size above the reservoir. These maps assess the impact of acquisition non-repeatability on the seismic.

the gas volume differences. These may arise due to a varietyof processing- or acquisition-related causes. To investigatewavelet effects, we pick and window a second referencehorizon at approximately 700 ms above the reservoir. Tim-ing, phase and amplitude differences of this event are anal-ysed between the baseline and monitor surveys. Time-shiftvariations between vintages are observed to be on aver-age 0.05ms, with a standard deviation of 1.47 ms. Themean phase rotation between surveys is –0.8 degrees, witha standard deviation of 15 degrees. The final measure is across-correlation coefficient taken between wavelets eval-uated in a 300 ms window and across the entire surveyarea, giving a value of 0.93. This analysis confirms thatthe different vintages of data are well cross-equalized andinter-survey differences (in, for example, statics) should notcontribute significantly to the observed disparity in the vol-ume estimates. Further to this study, the seismic waveletused to generate the synthetic data is varied by ±10 degreesin phase and ±5 Hz in frequency. This simulates changesthat may arise due to processing and acquisition. Such vari-ations are found to shift the resultant pattern of volumeestimates slightly and the effects are not large enough to

cause the major discrepancies that are apparent betweenthe observed amplitude and time-shifts.

4 Another reason for differences in the gas volume maps couldbe the presence of seismic noise or non-repeatability noise inthe 4D data. Time-lapse seismic attributes are particularlysusceptible to non-repeatability of the acquisition geometrywhen in the presence of overburden heterogeneity (Domes2010). To consider this, we map non-repeatable noise fromthe 4D seismic by calculating the normalized root meansquare amplitude of the difference data for a range of win-dow sizes above the reservoir and away from the reservoirpressure and saturation changes. These windows are from400–600 ms, 600–800 ms, 800–1000 ms and 400–1000 msin size (see Fig. 9). Interestingly, the various maps show aconsistent pattern of high level (>70%), low spatial fre-quency noise to the north-east and east and a smaller noiselevel elsewhere. The noise map for the 400–1000 ms win-dows (Fig. 9d) is chosen for our analysis as it provides arobust statistical measure of the overall noise. This is nowrescaled to the average amplitude of the synthetic tracesand then added to the synthetic amplitude map to simulatean observed data set (Fig. 10). Comparison of the noise



Figure 10 Root mean square amplitude maps of the difference volume at the top reservoir for: a) synthetic seismic, b) observed seismic, c)synthetic seismic with noise from a window 400–1000 ms above the reservoir.

contaminated synthetics with the observations indicatessome similarities in general character, particularly with therepositioning of the major anomalies. Overall, the noisysynthetic amplitude maps compare well in character withthose obtained from the observed data. It appears thereforethat this non-repeatability noise could be a major contribu-tor to the mismatch. To investigate the impact of time-shifts,the time-shifts previously analysed for the second shallowreference event at 700 ms are normalized and then addedto the time-shifts from the synthetic data (the same pro-cedure as for the amplitudes) (Fig. 11). It is observed thatthis creates a low level, high spatial frequency noise butin this case noise has very little impact on the time-shiftmaps.

5 The final reason for the observed mismatch is seismic pro-cessing. Whilst the processing noise due to non-repeatabilityof acquisition and processing algorithms throughout theworkflow may add to the overall 4D noise levels, seismicamplitudes in general are affected by the choice of velocitymodel and migration algorithm (Kvalheim et al. 2007). Am-

plitudes may shift laterally or vertically depending upon thevelocity model and underlying structural dips. The choiceof migration combined with the heterogeneities in the ve-locity model can alter the spatial frequency content, con-tinuity and smoothness of the amplitude maps. Inspectionof the maps in Fig. 4 and the south-east dip of the struc-ture in the area of interest, suggests structure as a possi-ble cause of movement in the main amplitude changes. Inaddition, Domes (2010) indicated that overburden hetero-geneity may also have some considerable influence on the4D seismic amplitudes and should be taken into account,although insufficient information is available on the over-burden characterization to assess this further. However it isclear that overburden heterogeneity such as channels, faults,or velocity changes due to geomechanical activity can havea significant effect on the amplitudes and time-shifts. Theimpact of these effects is not easily predictable from 4D seis-mic repeatability metrics and ideally should be taken intoaccount in the velocity model when using a full prestackdepth migration (Domes 2010).



Figure 11 Time-shift maps from a) synthetic seismic, b) observed seismic, c) synthetic seismic with noise from a horizon at approximately700 ms above the reservoir added. The scale bar is adjusted so that a comparison with Fig. 10 can be made.

CONCLUSIONS

A surprising result of the flow simulation component of ourstudy is that the saturation values for injected methane occupya fairly narrow range. As a consequence, there is a direct linearrelationship between the injected gas volume and both seismicamplitude differences and time-shifts of the reflector below thereservoir. Indeed, analysis of field data confirms that this rela-tion is very accurate in practice, yields good quality volumetricgas distribution maps and also allows easy separation of pres-sure effects. However, the field data analysis has also revealeddifferences in the mapped gas distributions derived separatelyusing the amplitude and time-shift attributes. Synthetic databased on the reservoir model and further analysis of the ob-served data have been able to replicate some of these differ-ences and identify them as due to inter-layer wave interfer-ences and 4D noise, however there are still some remainingvariations that cannot be adequately explained. An exami-nation of previous studies on this topic points to inaccuratechoices made during the processing and migration of the seis-

mic product as a possible explanation. As a disparity betweenthe results of amplitude and time-shift attributes has also beenseen elsewhere by other researchers, there is a need to care-fully evaluate the impact of decisions made during acquisitionand processing on quantitative interpretation of 4D seismic,particularly when used for reservoir engineering purposes.

ACKNOWLEDGEMENTS

We thank BP, Marathon Petroleum West of Shetlands Ltd andMarubena Oil and Gas (North Sea) Ltd for permission to usethe data. We thank sponsors of the Edinburgh Time LapseProject, Phase III and IV (BG, BP, Chevron, ConocoPhillips,EnCana, Eni, ExxonMobil, Hess, Ikon Science, Landmark,Maersk, Marathon, Norsar, Ohm, Petrobras, Shell, Statoil,Total and Woodside) for supporting this research. We thankSchlumberger-Geoquest for the use of their Petrel and Eclipsesoftware. Reza Falahat acknowledges financial support fromNIOC.



REFERENCES

Domes F. 2010. The influence of overburden on quantitative time-lapse seismic interpretation. PhD thesis, Institute of Petroleum En-gineering, Heriot-Watt University.

Dumont M.H., Fayemendy C., Mari J.L. and Huguet F. 2001. Un-derground gas storage: Estimating gas column height and sat-uration with time lapse seismic. Petroleum Geoscience 7, 155–162.

Freeman P., Kelly S., MacDonald C., Milington J. and Tothill M.2008. The Schiehallion field: Lessons learned modelling a complexdeepwater turbidite, the future of geological modelling in hydro-carbon development. In: The Future of Geological Modelling inHydrocarbon Development (eds A. Robinson, P. Griffiths, S. Price,J. Hegre and A. Muggeridge), pp. 205–219. The Geological Societyof London.

Ghaderi A. and Landrø M. 2009. Estimation of thickness and velocitychanges of injected carbon dioxide layers from prestack seismicdata. Geophysics 74, 17–28.

Huang X., Will R., Khan M. and Stanley L. 2001. Integration of time-lapse seismic and production data in a Gulf of Mexico gas field.The Leading Edge 20, 278–289.

Kvalheim A.K., Sandø I.A., Skogland S.M., Vinje V. and CarpenterM. 2007. Impact of time and depth imaging methods on quantita-tive 4D reservoir management. 69th EAGE meeting, London, UK,Expanded Abstracts, H017.

Lamers E. and Carmichael S.M.M. 1999. The Palaeocene deepwatersandstone play west of Shetland. In: Petroleum Geology of NWEurope: Proceedings of the 5th Conference (eds A.J. Fleet and S.A.R.Boldy), pp. 645–659. The Geological Society of London.

Langlais V., Mezghani M. and Lucet N. 2005. 4D monitoring ofan underground gas storage using an integrated history match-ing technique. SPE Annual Technical Conference and Exhibition,9–12 October 2005, Dallas, Texas, USA, Expanded Abstracts, SPE95838.

Mavko G., Mukerji T. and Dvorkin J. 2003. The Rock Physics Hand-book: Tools for Seismic Analysis in Porous Media. Cambridge Uni-versity Press.

Meadows M. 2008. Time-lapse seismic modelling and inversion ofCO2 saturation for storage and enhanced oil recovery. The LeadingEdge 27, 506–516.

Mehdizadeh H., Srivastava R.P., Vedanti N. and Landro M. 2010.Seismic monitoring of in situ combustion process in a heavy oilfield. Journal of Geophysics and Engineering 7, 16–29.

Morrow N.R. and Melrose J.C. 1991. Application of capillary pres-sure measurements to the determination of connate water satura-tion. In: Interfacial Phenomena in Petroleum Recovery (ed. N.R.Morrow), pp. 257–287. Marcel Dekker Inc.

Ng H.T., Bentley L.R. and Krebes E.S. 2005. Monitoring fluid injec-tion in a carbonate pool using time-lapse analysis: Rainbow Lakecase study. The Leading Edge 24, 530–534.

Sengupta M. and Mavko G. 2003. Impact of flow-simulation pa-rameters on saturation scales and seismic velocity. Geophysics 68,1267–1280.

Timur A. 1968. An investigation of permeability, porosity and resid-ual water saturation relation for sandstone reservoirs. The LogAnalyst 9, 8–17.

APPENDIX A: SATURATION CONDITIONSARIS ING FROM GAS INJECTION

In this study an immiscible gas (methane) is injected into ini-tially water-saturated and almost clean sands. As the processof gas displacement of the water proceeds, the final saturationreaches a limit determined by the irreducible, immobile watersaturation (Swir) for the rock. This irreducible water saturationis a function of a number of interrelated factors such as the sur-face area of the pore space, clay content and placement, grainshape, grain arrangement, wettability, temperature and pres-sure. However, there is also a well recognized connection topermeability and effective porosity and a number of relationsexist in the literature (for example, Timur 1968; Morrow andMelrose 1991). Thus the maximum gas saturation possible inthe sands is Smax

gas = 1 − Swir.Of importance for the seismic interpretation of gas injec-

tion is the saturation state within the gas distribution profile.Statistical analyses of many fine-scale simulations based onthe flow parameters appropriate for this particular reservoir,show that the distribution of gas saturation is narrow, witha mean of 50% and standard deviation of 6% (and a max-imum gas saturation of 56%). There are a smaller numberof lower gas saturations restricted to the gas-water transitionzone. However, due to the large density difference betweenwater and methane, capillary pressure curves for this specificcase show a sharp behaviour in the transition zone (Morrowand Melrose 1991). Therefore, the transition zone is abruptand the vertical thickness over which the gas saturation vari-ation occurs is typically less than a few metres and may beneglected in our analysis. These absolute values of gas satura-tion are strongly influenced by the relative permeability curvesand the balance of viscous, gravitational and injection forces.The saturation distribution remains similar for homogeneoussands and heterogeneous sands defined by a narrow range ofporosity but one order of magnitude range in permeability –provided that the relative permeability curves and the pressuregradients do not strongly vary. Indeed, the fluid flow simu-lations mentioned above have shown that the gas saturationstate is likely to change only very near to the injector (due tothe higher pressure gradients) and at the gas-water transitionzone as a consequence of capillary forces. The consequencesof the above are that the seismic response is relatively insensi-tive to local gas saturation variations but more sensitive to theoverall gas accumulation. The characteristic non-linear seis-mic response associated with variations in small gas saturationstates (Mavko et al. 2003) does not apply in this case. Thisdeduction is the basis of the model used to develop equations(1) and (2) in the main text.



Figure A1 Schematic illustrating injected gas movement in three homogeneous sand reservoirs a) before gas injection; b) after a short time ofgas injection; and c) after a longer period of gas injection.

The shape of the injected gas distribution depends on theinteraction between the forces induced by gas injection, buoy-ancy and capillary forces, together with the conditions of anyactive aquifers and the top and base reservoir seal. Figure A1gives an illustration of how the gas distribution may varywith time. Fine-scale simulations (not shown) have indicateda strong dependence of the shape of this profile on the kv/kh

(ratio of vertical to horizontal permeability) of the reservoir,which in turn is governed by the amount of shale presentin the sands and their degree of erosion. A low kv/kh givesa displacement profile that is more piston-like, particularlyat early injection times. In the general case, for most timesthere is a strong non-linear decrease of gas distribution thick-ness away from the injecting well. This thickening effect nearto the well can be detected in Figs 4 (observed data) and 8(synthetic seismic data). It appears to be more prominent onthe time-shift attribute than the amplitudes. In the observeddata, the influence of complex geology and faults is anticipatedto give rise to some variation from the above behaviour.

APPENDIX B: DERIVATION OF THEAMPLITUDE AND T IME-SHIFT EQUATIONS

Time-shift formula

Consider a homogeneous sandstone reservoir of porosity φ

and thickness H, filled with gas to a constant thickness ofh. There is a uniform distribution of shales in this reservoirgiving an overall net-to-gross of NTG. The volume of gas ina small cell of area �x�y is given by

Vg = h�x�yNTGφSg, (B1)

where Sg is the gas saturation. Calculating the seismic normalincidence travel-times and using these to determine the two-way time thickness of the reservoir gives the following changein thickness after gas saturation

�t = HV

−(

hV′ + (H − h)

V

)= V − V′

VV′ h. (B2)

Inserting the time thickness from equation (B2) into equation(B1) yields the volume in terms of the seismic time-shift data,�t and a property-dependent multiplier.

Vg ={

(NTG)φSgV′V

V − V′

}�x�y�t. (B3)

Amplitude formula

The gas thickness, h, can also be written in terms of the seismicamplitude. Here, assuming that the reservoir is thin relativeto the seismic wavelength (λ/H >>1) and that the propertycontrasts at the top and base reservoir and at the gas-watercontact are small, then the underlying mathematics from tun-ing analysis may be used. Assuming identical shales above andbelow the reservoir (log analysis suggests this to be a reason-able assumption), this leads to an expression for the compositebaseline root mean square amplitude

ABL =(

Zsh − Zw

Z

HV

)SRMS, (B4)

in terms of the shale impedance Zsh, water-saturated sandimpedance Zw, average impedance Z and the root meansquare amplitude SRMS of the time-derivative of the wavelets(t). Using the same analysis, the root mean square amplitudeof the monitor seismic after gas saturation can be written

AMON =(

Zw − Zg

Z

hV′ + Zsh − Zw

Z

(hV′ + (H − h)

V

))SRMS,

(B5)

where Zg is the impedance of the gas-saturated sandstone.This leads to the final formula relating gas thickness h to thetime-lapsed root mean square amplitude change �A = AMON-

ABL

�A = h(

Zw − Zg

ZV′ + Zsh − Zw

ZV

)SRMS, (B6)

which can now be used to replace h in equation (B1) by theobserved amplitude change.


towards quantitative evaluation of gas injection using ... · quantitative interpretation. key...

Documents