estimation of pore-pressure change in a compacting ... · 1institute of petroleum engineering,...

Geophysical Prospecting, 2013, 61, 1022–1034 doi: 10.1111/1365-2478.12037

Estimation of pore-pressure change in a compacting reservoirfrom time-lapse seismic data

Margarita Corzo1,2, Colin MacBeth1,∗ and Olav Barkved3

1Institute of Petroleum Engineering, Heriot-Watt University, Edinburgh, UK, 2Now at: BP Exploration and Production, Houston, USA,and 3BP Exploration, Stavanger, Norway

Received February 2011, revision accepted November 2012

ABSTRACTAn approach is developed to estimate pore-pressure changes in a compacting chalkreservoir directly from time-lapse seismic attributes. It is applied to data from thesouth-east flank of the Valhall field. The time-lapse seismic signal of the reservoirin this area is complex, despite the fact that saturation changes do not have aninfluence. This complexity reflects a combination of pressure depletion, compactionand stress re-distribution throughout the reservoir and into the surrounding rocks. Asimple relation is found to link the time-lapse amplitude and time-shift attributes tovariations in the key controlling parameter of initial porosity. This relation is sufficientfor an accurate estimation of pore-pressure change in the inter-well space. Althoughthe time-lapse seismic estimates mostly agree with reservoir simulation, unexplainedmismatches are apparent at a small number of locations with lower porosities (lessthan 38%). The areas of difference between the observations and predictions suggestpossibilities for simulation model updating or a better understanding of the physicsof the reservoir.

Key words: Pore pressure, Porosity, Time-shift.

INTRODUCTION

One requirement for successful reservoir management is themonitoring of pressure across a field, particularly betweenproduction and injection wells. Pressure monitoring con-tributes to the assessment of field connectivity over time, mon-itoring the performance of wells, placing new wells, assessingthe degree of aquifer or injector support, inferring barriersand compartments, the degree of fault seal and evaluatingthe average pressure state of the field. Over time, pressuremeasurements are also used to update the simulation modeland improve its predictive performance. Pressure measure-ments are normally obtained initially at the wells by produc-tion logging tools (PLTs) and then repeated throughout fieldlife, although repeat logging can be costly or impracticable.

∗E-mail: [email protected]

However in some fields, permanent sensor gauges are in place,which allow more cost efficient and frequent measurements(for example, the Schiehallion field – Gainski et al. 2010).One limitation of measurements derived at wells is the lackof knowledge about the inter-well space, which must be in-ferred and extrapolated from the well data. In compactingchalk fields, there is a particular necessity to monitor pressuredepletion, as a large proportion of the drive mechanism hascome from rock compaction. The recovery factor is influencedby our knowledge of the zones of depletion and the perfor-mance of individual perforations connecting long horizontalwells in the formation (Barkved et al. 2003a).

4D (time-lapse) seismic data provide one way to access pres-sure information between wells. Indeed, previous studies onclastic reservoirs have shown how this may be possible us-ing amplitude variation with offset or restricted offset stacksto separate pressure effects from the masking influence offluid saturation (Landrø 2001; MacBeth, Soldo and Floricich

1022 C© 2013 European Association of Geoscientists & Engineers

Estimation of pore-pressure change from time-lapse seismic data 1023

2006). Past work on clastic reservoirs has also shown thatreservoir-related attributes influenced primarily by pressurecan be calibrated to map pressure in certain cases (Eiken andTøndel 2005). In this respect, geomechanically active reser-voirs are found to be excellent candidates for the use of 4Dseismic data, as pressure depletion leads to a number of pro-nounced physical effects including reduced pore and reser-voir volume, movement of the physical reflectors and changesin the bulk density and velocity changes (Hall et al. 2005;Staples et al. 2007). The combination of these effects gener-ates a strong, stable and measurable time-lapse signal – visi-ble in both seismic amplitudes and reflector time-shifts. Thetime-lapse signal is relatively easy to observe in compactingreservoirs since changes in the elastic properties of the rocksare not just restricted to the reservoir zone but also occur inthe overburden and underburden rocks as they undergo straindeformation (Barkved and Kristiansen 2005). Indeed, in suchcompacting reservoirs it has been shown that the time-shiftsof seismic events in the overburden, measured between base-line and repeat surveys, can be used to invert for a smoothed,long wavelength estimate of the reservoir’s volumetric strain(and hence possibly infer pressure) despite the relatively smallvalues of the time strain measured (Hodgson et al. 2007;Garcia, MacBeth and Grandi 2010). Recently, it has also beendemonstrated that well-resolved pressure estimates can be ob-tained from seismic amplitude or time-shift attributes calcu-lated within or close to the reservoir and these can be used ascomplementary data to production logging tools in a highlycompacting chalk reservoir with long horizontal producingwells (van Gestel et al. 2009).

Fields such as Valhall and Ekofisk in the Norwegian Sea orSouth Arne in the Danish Sea (Herwanger et al. 2009) possessa non-unique relationship between the seismic attributes andpressure depletion due to the physics of chalk deformation. Inparticular, the trajectory of the compaction process with ef-fective stress or pressure change is strongly dependent on theinitial distribution of the reservoir porosity. This makes the4D seismic response difficult to interpret, especially at highereffective stresses (Corzo and MacBeth 2006). Another poten-tial complicating factor in compacting reservoirs is the re-distribution of the stress in the overburden and underburdenas production proceeds. Pressure estimation from 4D seismicsthus requires a more elaborate calibration of the pressure de-pletion response in chalk reservoirs than for clastic reservoirs.This study aims to develop such a calibration and proposes anequation to estimate pressure changes in a compacting chalkreservoir from seismic attributes alone. For this purpose, datafrom the south-east flank of the Valhall field are chosen as the

Table 1 Reservoir rock and fluid properties for theValhall field, Tor Formation obtained from the fieldoperator

PROPERTY VALUE

Overburden stress (MPa) 50Reservoir pressure (MPa) 45.2Effective pressure (MPa) 4.8Bubble point pressure (MPa/psi) 28/4060GOR (scf/stb) 800Initial porosity 0.4Temperature (◦C) 90Oil Gravity API 36Water saturation 0.1–0.5Salinity (ppm) 100 000Formation volume factor 1.62Gas gravity 0.77Density of matrix (g/cm3) 2.71Bulk modulus of calcite (GPa) 65

4D seismic signatures are not influenced by saturation effectsin this area, allowing an opportunity to focus on the pressureeffects alone.

D A T A D E S C R I P T I O N

Production setting and 4D seismic data

The field of interest for the study is Valhall: one of the chalkfields in the Central Graben, North Sea. This field has beenin production since 1982, with the first 20 years of produc-tion by primary depletion. Table 1 gives general details of thereservoir for reference. Our focus is on the south-east flank(Fig. 1a) within the major Tor Formation unit, which is dis-tinguished by a wide variation in thickness (Fig. 1b) and highporosities. At the crestal part of the field, the Tor Formationporosities range from 42–50% in the thickest areas (Farmerand Barkved 1999). The preservation of high porosities in theTor Formation is primarily due to the extreme overpressurein the reservoir. In contrast the reservoir quality on the flanksof the structure is poorer and in particular the initial porositywithin the Tor reservoir in our study area is in the range of35–43%. The matrix permeability in the Tor reservoir gener-ally ranges from 2–10 mD, which rises to between 20–90 mDin the crestal wells possibly as a result of natural fracturing.The reservoir is thinner in the study area than on the crestand varies from 0–40 m in thickness. The Tor interval wasdivided into eight reservoir zones based on detailed biostratig-raphy: Tor-D (zone 1), Hardchalk (zone 2), Tor-M1 (zone 3),

C© 2013 European Association of Geoscientists & Engineers, Geophysical Prospecting, 61, 1022–1034

1024 M. Corzo, C. MacBeth and O. Barkved

Figure 1 Geological settings of the Valhall field. (a) Structural contours of the lower Hod formation – after Farmer and Barkved (1999). Thered box indicates the area of interest for the present work in the south-eastern flank. (b) Schematic and simplified cross-section from the crestof the Valhall structure (after Barkved and Kristiansen 2005). The approximate line location is marked by the dashed line A-A’.

Hardchalk (zone 4), Tor-M2 (zone 5), Tor-M3 (zone 6), Tor-Camp (zone 7) and Hardchalk (zone 8). The producers wereperforated in zones 3 and 5. Zones 2, 4 and 8 are thin, low-porosity (less than 15%) layers, normally present between theproducing layers and characterized by a sharp increase in theP-wave velocity and a slight (a fraction of the velocity) in-crease in the density (as assessed from the wireline logs). Thestructure in the study area is relatively simple as can be ob-served from the seismic section example of Fig. 2(a). In theseismics there is good continuity of the top of the Hardchalklayer at the base of the Tor interval and the overlying Top

Balder formation and both form the main seismic reflectorsfor interpretational purposes. Indeed, these are easily recog-nized in a standard 3D seismic volume and serve as usefulguides when locating the oil bearing zone as the exact top andbase of the Tor interval are generally not well-resolved.

Pressure gauges at the seafloor and infrared sensing withGPS have determined that the subsidence rate in Valhall isaround 25 cm/year. The overpressure and the mechanicallyweak structure of the chalk are the elements that triggerthe reservoir compaction. The pore walls of the chalk arepoorly cemented such that pores will collapse under pressure



Figure 2 (a) Seismic section through the area of interest showing the Top Balder and Top Hardchalk event picks. The approximate positioningsof the well cross-sections inside the Tor interval are shown for reference. (b) Well trajectories displayed relative to the location of the verticalseismic section in (a).

depletion and this mechanism is a strong driving force for pro-duction. Valhall has an overpressure of 19.3 MPa (making itone of the most over-pressured reservoirs in the North Sea)and thus an effective stress on the rock matrix of only 4.8MPa. The selected study area has been produced by primarydepletion since 1994 and is not expected to show fluid-relatedeffects on the 4D seismics since pressure support by water in-jection has not been carried out and the aquifer support isweak. In addition, despite pore pressures being close to thebubble point at some times during the acquisition period ofinterest, there is no evidence of gas out of solution from thewells or the seismic data. This area is therefore suitable to usefor analysing the connection between compaction, pressuredepletion and 4D seismic signatures.

In the area of interest, four horizontal wells (P2, P3, P4and P5) have been drilled into the Tor formation (Fig. 2b,Fig. 3). The spatial separation between the wells is on av-erage 300 m and the maximum horizontal length in contact

with the Tor reaches up to 2500 m. The wells are hydrauli-cally stimulated and opened with proppant materials and arethought to penetrate and connect with the entire Tor inter-val with eight zones of variable reservoir quality. Figure 4shows the cumulative oil production for these wells for theperiod January 2003–March 2006. The wells do not produceconsistently over this period of time but are in production orshut-off in order to maintain a favourable overall productionrate. When a well is shut, the reservoir pressure builds up andhence higher pressures are often observed when the well is re-opened. As a consequence, the pressure depletion pattern inthe reservoir is not expected to be spatially uniform. The seis-mic data available for this study are the first six surveys fromthe Life of Field Seismic, shot between October 2003–June2005 (we label these surveys LoFS1 to LoFS6 in our follow-ing description). The first seismic survey was acquired at thesame time as the production started from wells P4 and P5 butapproximately one month after the wells P2 and P3 were put in



Figure 3 (a) Map of the estimated reservoir pressure when the firstLife of Field Seismic (LoFS) survey was acquired, based on productionlogging. The low pore pressures (blue colour at the top of the picture)observed between wells P2 and P4 are caused by production fromP1 (lying outside the perimeter of this selected area), which is theoldest producer in the area. (b) An estimate of the initial porosityfor zone 5 based on wireline log data and geological modelling. Wellperforations are indicated by the solid red circles.

production. The time interval between the surveys varies from3–6 months.

Preliminary observations

The compaction process is strongly dependent on the initialporosity. This is illustrated in Fig. 5 that shows how poros-ity evolves with pressure for initial porosities of 32% and42%. These predictions are based on porosity loss curves fromthe field’s geomechanical model calibrated using core data,seafloor subsidence records, gravimetric data and radioactivebullet markers (Barkved et al. 2003b). The general conclusionfrom this work is that there appears to be different mechani-cal stress sensitivity characteristics dependent on whether the

Figure 4 LoFS acquisition schedule and cumulative production forthe wells that were drilled in our study area after the Life of FieldSeismic project started. Wells P2 and P3 started to produce one monthbefore the acquisition of the first seismic survey (LoFS1). Wells P4and P5 were put into production during the acquisition of LoFS1.The width of the coloured vertical bars indicates the acquisition timefor each survey.

Figure 5 Comparison of how porosity evolves as the pressure de-creases for initial porosities of (a) 32% and (b) 42% using the poros-ity loss curves calculated for Valhall by the operator. These curves areobtained from the calibrated geomechanical model. The vertical linesdefine the reservoir pressures when the wells were put into productionfor the first time and when the LoFS seismics were acquired. Arrowedintervals relate to Fig. 6.



Figure 6 (a) 4D amplitude anomaly produced by 585 psi of pressuredepletion in perforations 7 and 8 of well P3: LoFS4–LoFS1, (b) 4Damplitude anomaly for a pressure depletion of 555 psi in perforations9 and 10 of well P2: LoFS2–LoFS1. The colour bar is consistent withFig. 8 and indicates difference amplitudes from 0 to the maximum(all positive numbers).

initial porosity is above or below 35% in porosity. Higherinitial porosity rocks give a stronger stress sensitivity, whilstlower porosity rocks are largely stress insensitive for similarpressure ranges. The predictions indicate that for an initialporosity of 42%, the porosity reduces to 39% over the entireLoFS period. We thus expect to observe a strong correlationbetween the initial porosity and the magnitude of the 4D sig-nal. Figure 6 compares the observed 4D amplitude producedby 585 psi of pressure depletion at perforations 7 and 8 of wellP3 versus a pressure depletion of 555 psi at perforations 9 and10 of well P2 (see Fig. 5 for the impact of these pressures onporosity). Despite the similar values of pressure depletion, thesignature at well P3 with initial porosities of 32% is smallerthan that at well P2 for which the initial porosity is 42%. Toreinforce this point, Fig. 7 shows a thresholded 4D amplitude(the LPV1 attribute described in the footnote and later used inour pressure analysis) map and superimposed porosity logs.It is observed that 4D amplitude highs mostly correlate with

1 LPV is a seismic attribute evaluated by calculating the largest posi-tive amplitude value in a windowed section of a seismic trace.

Figure 7 Scaled and thresholded 4D seismic amplitude (�A) map forLoFS2–LoFS1 overlying the scaled neutron porosity log for each well.The brown tick marks on the well trajectory indicate the locations ofperforations. Some perforations are numbered for reference purposesfor the main text.

perforated areas encountering high porosity. The strongesttime-lapse signal is recognized at the toe of well P2 (red circlein Fig. 7) and this is linked to the high porosities encounteredin that area. A low-porosity section drilled by well P4 butnever perforated (blue circle in Fig. 7), shows no 4D response.The best defined 4D amplitudes are located around perfora-tions 7, 9 and 10 for well P2 and perforations 2 and 3 for wellP4. Figure 8 shows how the 4D amplitude evolves throughtime for perforations 9 and 10 in well P2, where the initialporosities are above 42%. The 4D amplitude starts to be no-ticeable at the survey difference LoFS2–LoFS1 and intensifiesthrough time due to production-induced compaction. In con-trast, the 4D amplitude signatures along well P5 do not havea strong 4D signal overall (Fig. 7). This is because in this areathe Tor interval is very thin (around 10 m) and porosities aremostly lower than 35%, except near the toe of the well.

For the pressure estimation study in the next section, twotime-lapse attributes are used: the largest positive value (LPV1)based on amplitudes and the speed-up (SU2) attribute based

2 The SU or speed-up attribute is calculated from the volume oftime-shifts estimated between the monitor and base surveys. It is thedifference between the maximum and minimum time-shifts across the



Figure 8 Evolution of the 4D amplitude (defined by the largest positive value and scaled to one common maximum) through time for perforations9 and 10 in well P2. At the location of these perforations, porosities are higher than 42% and thus the signal is of good quality. The time intervalbetween each seismic survey is roughly 3– 6 months. The colour bar is identical to that in Fig. 6.

on differencing time-shifts. Because the Top Tor interval isdifficult to interpret on the seismics, the amplitude extractionis performed for a 35 ms asymmetric time window definedaround the Top Hardchalk reflector (20 ms above and 15 msbelow this reflector). Time-shifts are generated from a cross-correlation procedure applied to common events above andbelow the reservoir and across the different volumes of seis-mics. These time-shifts represent the change in the two-waytime thickness of the reservoir interval for various combi-nations of the monitor surveys LoFS2, 3, 4, 5 and 6 withthe baseline LoFS1. Empirically, it has been shown that thespeed-up attribute represents the time thickness decrease as-sociated with the reservoir compaction. Figure 9 shows howthe LPV and SU attributes evolve against pressure decreasepredicted according to the simulation of Tran, Settari andNghiem (2004) for different production times. The LPV at-tribute intensifies with depletion in general, however there arespecific regions where pressure depletion is predicted by sim-ulation but undetected on the seismic (highlighted by blackellipses). In addition, whilst the simulation model suggests a

reservoir interval and has been found to be a robust way of measuringthe change in two-way time thickness between the monitor and basesurveys. Further details of these attributes can be found in Corzo(2010).

broader area of pressure depletion, the changes appear to bemore localized. It is possible that this may relate to the na-ture and distribution of the true initial porosity and reservoirthickness. The maps of the SU attribute show close agreementwith the LPV maps but differ from the predictions from thesimulation model. For example, the SU highs observed aroundwells P2 and P5 (indicated by the red circles on the maps ofFig. 9) are stronger than the corresponding features on theLPV attribute map. Conversely, the LPV shows highs in areaswhere the SU attribute detects no response (indicated by thewhite circles on the maps). The LPV anomaly present nearthe toe of well P4 seems to be shifted to the west on the SUmaps (indicated by the black circles on the maps in Fig. 9).This could be explained by the seismic quality deterioratingaround the toe of wells P4 and P5 due to the known gas cloudabove the crest of the field. Also some faulting is observedand the reflectors become broken and weak in this region.This lack of continuity in the reflectors affects the interpre-tation of the reservoir zones and decreases the reliability ofthe 4D seismic attributes. Another factor affecting the seismicattribute extraction is the thickness of the reservoir. The thick-ness variation is difficult to quantify at a seismic scale but maybe assessed from well drilling reports. For P5, it is determinedthat the Tor interval is less than 10 m for the first 1000 m ofthis well. P3 also penetrated a very thin (7 m) Tor reservoir



Figure 9 The LPV attribute derived from seismic amplitudes (left) compared to the SU attribute (middle) and the predicted pressure depletionfrom the flow simulator (right). Each column represents an increase of time interval between the LoFS surveys. The top represents the intervalbetween the first and second surveys LoFS2–LoFS1 and the bottom represents the time interval between the first and last surveys LoFS6–LoFS1.Circled regions highlight the main discrepancies between the seismic attributes and the predicted pressure changes and are described in the maintext.

at the beginning of the horizontal section but the reservoirthickness increases to 15 m towards the toe of this well. Thereliability of the LPV attribute diminishes in very thin areas,where information from the overburden and/or underburdenmight also be inadvertently included in the calculation due tothe use of a constant window size in the calculation (35 ms asdescribed above).

QUANTITATIVE ESTIMATION OFPORE-PRESSURE DEPLETION

The starting point for our analysis is the linear relation pro-posed by MacBeth et al. (2006), which connects any gener-alized seismic attribute �A to a pore-pressure change �P ina non-compacting reservoir. To extend this to the case of thecompacting Valhall field, it is necessary to take into account



not only the pore-pressure changes but also porosity reduc-tion. As discussed in the previous section, initial porosity isconsidered to be an important factor, as this determines howthe porosity varies with pressure. Based on this understanding,the following adaptation of the �A-�P relation is proposedfor our current study:

�A = (C1φi + C2)�P, (1)

where C1 and C2 are fixed constants to be determinedfor the particular reservoir and φi is the initial porosity.To obtain values for the coefficients in equation (1) andto examine the effectiveness of this equation, the mapped4D seismic signatures for the five different combinationsLoFS6–LoFS1, LoFS5–LoFS1, LoFS4–LoFS1, LoFS3–LoFS1and LoFS2–LoFS1 of the available LoFS seismics arecross-plotted against the pressure changes predicted by thesimulator at the perforation locations for each of the fourhorizontal wells P2, P3, P4 and P5 in our study area.

To implement the cross-plotting in practice, the seismic at-tribute (LPV and SU) maps are firstly thresholded to revealonly the maxima of the response. The exact threshold value isdefined independently for the LPV and SU attributes and de-termined from the map of the difference LoFS6–LoFS1 in bothcases, as this is known to have the biggest overall response.Next, rectangular search areas are drawn around each of theperforations and for each well using the seismic response as aguide. These rectangles are roughly 200 × 150 m in dimen-sion (approximately 4 × 3 simulation cells or 8 × 6 seismicbins in size). For consistency, the averages of the LPV and SUattributes are calculated inside the same set of rectangles. Thepressure change and initial porosity from the simulation modelpredictions are also averaged in a similar way. The pressurechange extracted from the simulation predictions is believedto be accurate at the perforations, as there is a good historymatch on the measured pressures. Indeed, pressures at eachof the perforations are known with accuracy from dedicatedproduction logging. Also, there are permanent downhole pres-sure sensors installed in the heel of all wells in our study area.These provide reliable data for the history matching processduring the simulator runs, giving some assurance that the sim-ulated pressure changes used in our method are close to theactual reservoir pore pressure at the perforations (but not nec-essarily accurate away from these perforations due to lateralvariations). The initial porosity values in the simulator modelare a combination of well logs and seismic inversion results.In our calculations, it is firstly assumed that the wells producefrom the entire Tor Formation and therefore an initial poros-ity determined by a thickness-weighted mean for the whole

Figure 10 (a) Straight lines fit to the amplitude LPV attribute trendsas a function of the predicted pore pressure decrease at the well per-forations extracted from the simulation model. (b) Variation of theresultant gradient term (C1) with initial porosity.

formation is appropriate. Later this mean is refined as themost appropriate interval for the average is investigated – thischoice is discussed further below. As each perforation corre-sponds to a different initial porosity, the data set generatedfrom the above procedure permits identification of separatelinear trends between �A and �P for several different initialporosity classes.

It is found that there is sufficient data from the above togroup the fitting process into four classes of initial porosityfor the LPV attribute: 40% and above, 38–40%, 36–38%and below 36%. For the SU attribute, there are three classesof initial porosity: 40% and above, 38–40% and 36–38%. Itis found that by cross-plotting the time-lapsed amplitude (LV)and time-shift (SU) attributes against the estimated change inpressure (�P), the data points for each porosity class followa straight line trend (Fig. 10a and Fig. 11a). Given this obser-vation, a straight line is fit to the points from each porosityclass in a least-squares sense, the gradient of which yields anestimate for the bracketed term C1+C2φι in equation (1) for



Figure 11 (a) Straight lines fit to the time-shift SU attribute trendsas a function of the predicted pore pressure decrease at the well per-forations extracted from the simulation model. (b) Variation of theresultant gradient term (C1) with initial porosity.

that particular mean porosity. Once this procedure has beenperformed for all porosity classes, C1+C2φι is then plottedagainst the mean porosity of each class to determine C1 andC2 (Fig. 10b and Fig. 11b). To quantify the errors involvedwith this two-stage procedure, a range of seismic thresholdsfor the LPV and SU maps are selected within +/−10% ofthe originally selected value, then the data cross-plotted againand the C1 and C2 values determined once more. By doingthis many times, this allows a mean and standard deviation ofthese coefficients to be computed. Applying this procedure tothe LPV maps, the mean value of C1 is found to be 0.052 andits standard deviation 0.001. For C2, the mean is −1.646 andthe standard deviation 0.012. The SU maps produce similarresults. Once C1 and C2 are obtained, equation (1) can nowbe used to predict the pressure change away from the wellperforations from only maps of the seismic attribute changeand the initial porosity taken from the reservoir model. Asthere are now a range of C1 and C2 coefficients, these maps ofpore-pressure change can be output together with their meanand standard deviation. The results for the amplitude (LPV)attributes are shown in Fig. 12(b,c), alongside the predictionsfrom the simulator (Fig. 12a).

Figure 12 Estimated pore pressure from: (a) a coupled flow and ge-omechanical simulator by the operator; (b) the 4D seismic amplitudeattribute LPV, using the initial porosity averaged across zones 1,3,5and 6; (c) the 4D seismic amplitude attribute LPV, using the initialporosity from zone 5 only.

One source of error in the above method is the choice ofwhich zones of the Tor formation to include in the estimateof the initial porosity. At first, the initial porosity is estimatedusing zones 1, 3, 5 and 6 of the eight-layered Tor reservoir.Next, estimates are made using only the penetrated and per-forated zones for the wells (Fig. 12b), as according to thewell reports all wells have been drilled mainly into zones 3and 5. However, since most perforations are made in zone 5,only this zone is used in the final calculation of Figs 10 and11. Calculations using the initial porosity of zone 5 providebetter visual agreement with the simulator prediction. Whilstagreement between the simulator and the 4D seismic data isnot necessarily expected, as the model may not be correct,



the similarity of these data estimates and model predictions iscompelling. Ultimately it is hoped that studies such as this canbe used to update the simulation model.

Another source of uncertainty in the above calculation is thevariation in reservoir thickness. In this respect, as mentionedearlier, it is anticipated that the reliability of the time-shift(SU) attribute should degrade for areas of thin (time-shifts ofless than 1 ms) reservoir such as those encountered in the firsthalf of wells P3 and P4. Indeed, in these areas, the estimates ofpressure change do disagree to some degree with the simula-tion result. An additional uncertainty appears when pressureestimates from the SU and LPV maps disagree – see Fig. 9.For example, around well P5 there is a pressure change esti-mated from the SU attribute but no response is observed inthe LPV attribute. This discrepancy arises despite both seismicattributes having a good chance of capturing pressure effectsin the thick and porous reservoir (according to the well re-ports). One possible explanation is that accurate predictionof pressure change is difficult in areas with weak 4D seismicsignatures. A low-seismic response could be attributed to lackof compaction due to low porosity, or areas where pressureequilibration has not taken place as a consequence of barri-ers due to small-scale faulting. This may suggest an updateto the initial porosities in the model around this well maybe necessary. Finally, the differences between the LPV- andSU-derived pressure change maps may also arise due to straindeformation in the formations above the reservoir. The varia-tion of the properties of the surrounding layers can affect theLPV attribute to a greater extent than the SU measurement.This may be particularly important in regions of high-initialporosity, where stress redistribution impacts the total stressfield. This phenomenon is discussed further below.

D I S C U S S I O N

Despite the apparent success of the pore-pressure change es-timation outlined in the previous section, there are a few dis-parities between results from the LPV and SU attributes andsome mismatch with the simulation predictions. There are anumber of effects that may disrupt equation (1) used in thisanalysis and our research has shown that two major groupscan be identified as contributing to an increased error: stressredistribution and un-anticipated overburden effects. Theseare described in more detail below.

Stress re-distribution

One possible complication to the observed behaviour is stressarching, which gives rise to changes of stresses in the overbur-

den (Staples et al. 2007). This can be understood by consid-ering the effective stress tensor σe f f of the rock and its link tothe reservoir’s fluid pressure P via the relation:

σe f f = σtot − α I P, (2)

where σtot is the total external stress acting on the rock andfluid, α is the effective stress coefficient and the stress field isdefined here as a second-rank tensor such that I is a 3 × 3diagonal unit matrix (Sayers 2010). α is a number that liesbetween 0–1 and depends on the property being affected bythe stress (whether a particular wave property (for example,velocity) or a geomechanical parameter) and the boundaryconditions involved (Hofmann et al. 2005). For wave proper-ties, unconsolidated materials have α typically close to unity.For the static deformation processes of geomechanics, α isgiven by the Biot-Willis coefficient (Fjaer et al. 2008; Alam,Fabricius and Christensen 2012). From equation (2), whenpressure changes during production the consequent effectivestress change is given by:

�σe f f = −α I�P. (3)

Rock properties in the reservoir are controlled in part bythe effective stress acting on the rock frame and also by thepressure-dependent fluid properties – both, in turn, controlledby �P. Thus, in our study, both the amplitude (LPV) and time-shift (SU) attributes are assumed to be directly controlled bythe pore-pressure changes. However, if the deformation ofthe reservoir is strongly localized or influenced by structure,then the total external stress acting on the rock also changes(still in proportion to the reservoir pressure however). Theappropriate relation is now:

�σe f f = γ �P − α I�P, (4)

where γ is a matrix of ‘stress arching’ ratios induced by alarge-scale structure (Sayers 2010; HajNasser and MacBeth2010). γ is not well-known and is a function of the locationin the reservoir, it thus disrupts the relationship between theseismics and �P. As it is known that depletion gives rise toa redistribution of stresses in the whole mechanical system(Rothenburg, Bratli and Dusseault 1994), the actual situationin practice may be represented more appropriately by equa-tion (4). Depending upon the impact of the structure across thefield, γ may act to reduce the relationship between the effec-tive stress and pressure changes, thereby reducing the seismicsignal of pressure change in an uncertain way. Simulator-to-seismic modelling by Corzo (2010) using a coupled fluid flowand geomechanical simulator (Tran et al. 2004) has shownthat the variability in the layer thickness of the magnitude



observed at Valhall can also affect γ and hence alter the an-ticipated relation between the seismic and �P. High-porosityareas are found to give a larger error due to their greatercompaction and consequent perturbation of the stress field.Another source of uncertainty is the nature of the chalk de-formation – which was assumed in the above analysis to belinear elastic. This may not be the case, particularly for regionsof significant depletion. In fact for the field under study shearand plastic deformations are known to occasionally occur,these resulting in large changes in porosity and also failure(Tran et al. 2004). Finally, as an addition, it is noted that anextra complication could be the anisotropic seismic proper-ties induced by directional stress changes that are strong andwell-documented in the literature for Valhall (Hall, Kendalland Barkved 2002).

Overburden effects

When the highly porous chalk reservoir compacts due to pres-sure depletion, the reservoir’s impedance increases while theimpedance in the overburden layers decreases due to the un-loading (extensional) process. This process enhances the 4Damplitude signal whilst the SU attribute is not so sensitive anddepends on how much the overburden slow-down cancels outthe speed-up within the reservoir. This may explain the dif-ferences between the pressure estimates for the two attributesmapped around well P2. However an alternative explanationfor this difference is that the overburden impedance experi-ences a local increase due to pressure depletion propagatinginto the sideburden. Indeed, compaction in overburden shalehas been previously considered in the Valhall field (Kristiansen1998). To support this explanation, Barkved and Kristiansen(2005) showed an example using sonic logs where the ex-tensional effect in the overburden was reversed 100 m abovethe reservoir. In addition, HajNasser and MacBeth (2010)showed that pressure diffusion from a reservoir into the im-mediate shale overburden can take place over a productiontime scale and gives rise to a compaction of the surroundingshales. A large-pressure differential between the shales andthe reservoir could also cause drainage of the cap rock with asimilar effect.

CONCLUSIONS

An extension of the method of MacBeth et al. (2006) wasobtained that accurately estimates pressure depletion in thecompacting Valhall field. The proposed method is appliedto time-lapsed amplitude and time-shift attributes extracted

from six closely repeated seismic data sets shot over a periodof 18 months. Of particular focus in the development of thismethod is the strong dependence of the reservoir compactionand porosity reduction that is controlled by the initial poros-ity. Preliminary analysis suggests that most of the observedchanges in seismic data conform well with expectations i.e.,a strong signal in thick, high-porosity zones and a weak sig-nal in thin, low-porosity zones. The resultant pressure changemaps estimated from the amplitude and time-shift attributesare observed to be in close agreement with each other, aswell as with the simulation predictions – the latter agreementlending support to the accuracy of the simulation model. Itis anticipated that some errors in pressure estimation may beintroduced by the complexities of both stress redistributiondue to structure and overburden effects. The latter needs fur-ther analysis in order to completely quantify the pore-pressureeffects.

ACKNOWLEDGEMENTS

We would like to thank BP and the Valhall partnership(BP Norge AS, Amerada Hess Norge, Total E&P NorgeAS and A/S Norske Shell) for permission to publish thispaper. 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 and Taurus for their donation and advice on the useof their GeoSim software.

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