Bayesian inversion of time‐lapse seismic data for the estimation of static reservoir properties and dynamic property changes

Seismic conditioning of static reservoir model properties such as porosity and lithology has traditionally been faced as a solution of an inverse problem. Dynamic reservoir model properties have been constrained by time‐lapse seismic data. Here, we propose a methodology to jointly estimate rock properties (such as porosity) and dynamic property changes (such as pressure and saturation changes) from time‐lapse seismic data. The methodology is based on a full Bayesian approach to seismic inversion and can be divided into two steps. First we estimate the conditional probability of elastic properties and their relative changes; then we estimate the posterior probability of rock properties and dynamic property changes. We apply the proposed methodology to a synthetic reservoir study where we have created a synthetic seismic survey for a real dynamic reservoir model including pre‐production and production scenarios. The final result is a set of point‐wise probability distributions that allow us to predict the most probable reservoir models at each time step and to evaluate the associated uncertainty. Finally we also show an application to real field data from the Norwegian Sea, where we estimate changes in gas saturation and pressure from time‐lapse seismic amplitude differences. The inverted results show the hydrocarbon displacement at the times of two repeated seismic surveys.     

Analysis of time‐lapse travel‐time and amplitude changes to assess reservoir compartmentalization

Fluid depletion within a compacting reservoir can lead to significant stress and strain changes and potentially severe geomechanical issues, both inside and outside the reservoir. We extend previous research of time‐lapse seismic interpretation by incorporating synthetic near‐offset and full‐offset common‐midpoint reflection data using anisotropic ray tracing to investigate uncertainties in time‐lapse seismic observations. The time‐lapse seismic simulations use dynamic elasticity models built from hydro‐geomechanical simulation output and a stress‐dependent rock physics model. The reservoir model is a conceptual two‐fault graben reservoir, where we allow the fault fluid‐flow transmissibility to vary from high to low to simulate non‐compartmentalized and compartmentalized reservoirs, respectively. The results indicate time‐lapse seismic amplitude changes and travel‐time shifts can be used to qualitatively identify reservoir compartmentalization. Due to the high repeatability and good quality of the time‐lapse synthetic dataset, the estimated travel‐time shifts and amplitude changes for near‐offset data match the true model subsurface changes with minimal errors. A 1D velocity–strain relation was used to estimate the vertical velocity change for the reservoir bottom interface by applying zero‐offset time shifts from both the near‐offset and full‐offset measurements. For near‐offset data, the estimated P‐wave velocity changes were within 10% of the true value. However, for full‐offset data, time‐lapse attributes are quantitatively reliable using standard time‐lapse seismic methods when an updated velocity model is used rather than the baseline model.     

Sub‐sample time shift and horizontal displacement measurements using phase‐correlation method in time‐lapse seismic

Hydrocarbon production and fluid injection affect the level of subsurface stress and physical properties of the subsurface, and can cause reservoir‐related issues, such as compaction and subsidence. Monitoring of oil and gas reservoirs is therefore crucial. Time‐lapse seismic is used to monitor reservoirs and provide evidence of saturation and pressure changes within the reservoir. However, relative to background velocities and reflector depths, the time‐lapse changes in velocity and geomechanical properties are typically small between consecutive surveys. These changes can be measured by using apparent displacement between migrated images obtained from recorded data of multiple time‐lapse surveys. Apparent displacement measurements by using the classical cross‐correlation method are poorly resolved. Here, we propose the use of a phase‐correlation method, which has been developed in satellite imaging for sub‐pixel registration of the images, to overcome the limitations of cross‐correlation. Phase correlation provides both vertical and horizontal displacements with a much better resolution. After testing the method on synthetic data, we apply it to a real dataset from the Norne oil field and show that the phase‐correlation method can indeed provide better resolution.     

Time‐lapse pre‐stack seismic data registration and inversion for CO2 sequestration study at Cranfield

Pre‐stack seismic data are indicative of subsurface elastic properties within the amplitude versus offset characteristic and can be used to detect elastic rock property changes caused by injection. We perform time‐lapse pre‐stack 3‐D seismic data analysis for monitoring sequestration at Cranfield. The time‐lapse amplitude differences of Cranfield datasets are found entangled with time‐shifts. To disentangle these two characters, we apply a local‐correlation‐based warping method to register the time‐lapse pre‐stack datasets, which can effectively separate the time‐shift from the time‐lapse seismic amplitude difference without changing the original amplitudes. We demonstrate the effectiveness of our registration method by evaluating the inverted elastic properties. These inverted time‐lapse elastic properties can be reliably used for monitoring plumes.     

Stochastic inversion of pressure and saturation changes from time-lapse multi component data

Knowledge about saturation and pressure distributions in a reservoir can help in determining an optimal drainage pattern, and in deciding on optimal well designs to reduce risks of blow‐outs and damage to production equipment. By analyzing time‐lapse PP AVO or time‐lapse multicomponent seismic data, it is possible to separate the effects of production related saturation and pressure changes on seismic data. To be able to utilize information about saturation and pressure distributions in reservoir model building and simulation, information about uncertainty in the estimates is useful. In this paper we present a method to estimate changes in saturation and pressure from time‐lapse multicomponent seismic data using a Bayesian estimation technique. Results of the estimations will be probability density functions (pdfs), giving immediate information about both parameter values and uncertainties. Linearized rock physical models are linked to the changes in saturation and pressure in the prior probability distribution. The relationship between the elastic parameters and the measured seismic data is described in the likelihood model. By assuming Gaussian distributed prior uncertainties the posterior distribution of the saturation and pressure changes can be calculated analytically. Results from tests on synthetic seismic data show that this method produces more precise estimates of changes in effective pressure than a similar methodology based on only PP AVO time‐lapse seismic data. This indicates that additional information about S‐waves obtained from converted‐wave seismic data is useful for obtaining reliable information about the pressure change distribution.     

Time-lapse seismic analysis of pressure depletion in the Southern Gas Basin

In the Southern Gas Basin (SGB) of the North Sea there are many mature gas fields where time‐lapse monitoring could be very beneficial in extending production life. However, the conditions are not immediately attractive for time‐lapse seismic assessment. This is primarily because the main production effect to be assessed is a pore pressure reduction and frame stiffening because of gas production in tight sandstone reservoirs that also have no real seismic direct hydrocarbon indicators. Modelling, based on laboratory measurements, has shown that such an effect would be small and difficult to detect in seismic data. This paper makes two main contributions. Firstly, this is, to our knowledge, the first time‐lapse study in the SGB and involves a real‐data assessment of the viability for detecting production in such an environment. Secondly, the feasibility of using markedly different legacies of data in such a study is addressed, including an assessment of the factors influencing the crossmatching. From the latter, it is found that significant, spatially varying time shifts need to be, and are successfully, resolved through 3‐D warping. After the warping, the primary factors limiting the crossmatching appear to be residual local phase variations, possibly induced by the differing migration strategies, structure, reverberations and different coherencies of the volumes, caused by differences in acquisition‐structure azimuth and acquisition fold. Despite these differences, a time‐lapse amplitude signature is observed that is attributable to production. The character of the 4‐D amplitude anomalies may also indicate variations in stress sensitivity, e.g. because of zones of fracturing. Additionally, warping‐derived time attributes have been highlighted as a potential additional avenue for detection of pressure depletion in such reservoirs. Although the effects are subtle, they may indicate changes in stress/pressure in and around the reservoir because of production. However, to fully resolve the subtle time‐lapse effects in such a reservoir, the data differences need to be better addressed, which may be possible by full re‐processing and pre‐stack analysis, but more likely dedicated 4‐D acquisition would be required.     

Perturbation methods for two special cases of the time‐lapse seismic inverse problem

Scattering theory, a form of perturbation theory, is a framework from within which time‐lapse seismic reflection methods can be derived and understood. It leads to expressions relating baseline and monitoring data and Earth properties, focusing on differences between these quantities as it does so. The baseline medium is, in the language of scattering theory, the reference medium and the monitoring medium is the perturbed medium. The general scattering relationship between monitoring data, baseline data, and time‐lapse Earth property changes is likely too complex to be tractable. However, there are special cases that can be analysed for physical insight. Two of these cases coincide with recognizable areas of applied reflection seismology: amplitude versus offset modelling/inversion, and imaging. The main result of this paper is a demonstration that time‐lapse difference amplitude versus offset modelling, and time‐lapse difference data imaging, emerge from a single theoretical framework. The time‐lapse amplitude versus offset case is considered first. We constrain the general time‐lapse scattering problem to correspond with a single immobile interface that separates a static overburden from a target medium whose properties undergo time‐lapse changes. The scattering solutions contain difference‐amplitude versus offset expressions that (although presently acoustic) resemble the expressions of Landro ( 2001 ). In addition, however, they contain non‐linear corrective terms whose importance becomes significant as the contrasts across the interface grow. The difference‐amplitude versus offset case is exemplified with two parameter acoustic (bulk modulus and density) and anacoustic (P‐wave velocity and quality factor Q) examples. The time‐lapse difference data imaging case is considered next. Instead of constraining the structure of the Earth volume as in the amplitude versus offset case, we instead make a small‐contrast assumption, namely that the time‐lapse variations are small enough that we may disregard contributions from beyond first order. An initial analysis, in which the case of a single mobile boundary is examined in 1D, justifies the use of a particular imaging algorithm applied directly to difference data shot records. This algorithm, a least‐squares, shot‐profile imaging method, is additionally capable of supporting a range of regularization techniques. Synthetic examples verify the applicability of linearized imaging methods of the difference image formation under ideal conditions.     

τ-migration and velocity analysis: application to data from the Red Sea

Imaging pre‐salt reflections for data acquired from the coastal region of the Red Sea is a task that requires prestack migration velocity analysis. Conventional post‐stack time processing lacks the lateral inhomogeneity capability, necessary for such a problem. Prestack migration velocity analysis in the vertical time domain reduces the velocity–depth ambiguity that usually hampers the performance of prestack depth‐migration velocity analysis. In prestack τ‐migration velocity analysis, the interval velocity model and the output images are defined in τ (i.e. vertical time). As a result, we avoid placing reflectors at erroneous depths during the velocity analysis process and thus avoid inaccurately altering the shape of the velocity model, which in turn speeds up the convergence to the true model. Using a 1D velocity update scheme, the prestack τ‐migration velocity analysis produces good images of data from the Midyan region of the Red Sea. For the first seismic line from this region, only three prestack τ‐migration velocity analysis iterations were required to focus pre‐salt reflections in τ. However, the second line, which crosses the first line, is slightly more complicated and thus required five iterations to reach the final, reasonably focused, τ‐image. After mapping the images for the two crossing lines to depth, using the final velocity models, the placements of reflectors in the two 2D lines were consistent at their crossing point. Some errors occurred due to the influence of out‐of‐plane reflections on 2D imaging. However, such errors are identifiable and are generally small.     

Multi‐transient electromagnetic repeatability experiment over the North Sea Harding field‡

We present results of synthetic time‐lapse and real repeatability multi‐transient electromagnetic surveys over the North Sea Harding field. Using Archie's law to convert porosity and fluid saturation to resistivity we created 3D isotropic models of the reservoir resistivity at different stages of production from the initial state in 1996 through to complete hydrocarbon production by 2016 and, for each stage, we simulated an east‐west transient electromagnetic survey line across Harding. Unconstrained 1D full‐waveform Occam inversions of these synthetic data show that Harding should be detectable and its lateral extent reasonably well‐defined. Resistivity changes caused by hydrocarbon production from initial pre‐production state to production of the oil rim in 2011 are discernible as are significant changes from 2011–2016 during the modelled gas blowdown phase. The 2D repeatability surveys of 2007 and 2008 tied two wells: one on and the other off the structure. Between the two surveys the segment of the field under investigation produced 3.9 million barrels of oil – not enough to generate an observable time‐lapse electromagnetic anomaly with a signal‐to‐noise ratio of 40 dB. Processing of the 2007 and 2008 data included deconvolution for the measured source current and removal of spatially‐correlated noise, which increased the signal‐to‐noise ratio of the recovered impulse responses by about 20 dB and resulted in a normalized root‐mean‐square difference of 3.9% between the data sets. 1D full‐waveform Occam inversions of the real data showed that Harding was detectable and its lateral extent was also reasonably well‐defined. The results indicate that the multi‐transient electromagnetic method is suitable for exploration, appraisal and monitoring hydrocarbon production.     

Optimal use of PP and PS time-lapse stacks for fluid–pressure discrimination

The combined use of time‐lapse PP and PS seismic data is analysed for optimal discrimination between pressure and saturation changes. The theory is based on a combination of the well‐known Gassmann model and the geomechanical grain model derived by Hertz and Mindlin. A key parameter in the discrimination process is the opening angle between curves representing constant changes in PP and PS reflectivity plotted against pressure and saturation changes. The optimal discrimination angle in the pressure–saturation space is 90° and this is used to determine optimal offset ranges for both PP and PS data. For typical production scenarios, we find an optimal offset range corresponding to an angle of incidence of 25–30°, for both PP and PS data. For gas we find slightly different results. This means that conventional survey parameters used in marine multicomponent acquisition should be sufficient for the purpose of estimating pressure and fluid saturation changes during production.     

Estimation of pore‐pressure change in a compacting reservoir from time‐lapse seismic data

An approach is developed to estimate pore‐pressure changes in a compacting chalk reservoir directly from time‐lapse seismic attributes. It is applied to data from the south‐east flank of the Valhall field. The time‐lapse seismic signal of the reservoir in this area is complex, despite the fact that saturation changes do not have an influence. This complexity reflects a combination of pressure depletion, compaction and stress re‐distribution throughout the reservoir and into the surrounding rocks. A simple relation is found to link the time‐lapse amplitude and time‐shift attributes to variations in the key controlling parameter of initial porosity. This relation is sufficient for an accurate estimation of pore‐pressure change in the inter‐well space. Although the time‐lapse seismic estimates mostly agree with reservoir simulation, unexplained mismatches are apparent at a small number of locations with lower porosities (less than 38%). The areas of difference between the observations and predictions suggest possibilities for simulation model updating or a better understanding of the physics of the reservoir.     

Direct correlation of 4D seismic with well activity for a clarified dynamic reservoir interpretation

A method to provide an improved time‐lapse seismic attribute for dynamic interpretation is presented. This is based on the causal link between the time‐lapse seismic response and well production activity taken over time. The resultant image is obtained by computing correlation coefficients between sequences of time‐lapse seismic changes extracted over different time intervals from multiply repeated seismic and identical time sequences of cumulative fluid volumes produced or injected from the wells. Maps of these cross‐correlations show localized, spatially contiguous signals surrounding individual wells or a specific well group. These may be associated with connected regions around the selected well or well group. Application firstly to a synthetic data set reveals that hydraulic compartments may be delineated using this method. A second application to a field data set provides empirical evidence that a connected well‐centric fault block and active geobody can be detected. It is concluded that uniting well data and time‐lapse seismic using our proposed method delivers a new attribute for dynamic interpretation and potential updating of the model for the producing reservoir.     

Repeatability analysis of land time‐lapse seismic data: CO2CRC Otway pilot project case study

Time‐lapse seismics is the methodology of choice for remotely monitoring changes in oil/gas reservoir depletion, reservoir stimulation or CO₂ sequestration, due to good sensitivity and resolving power at depths up to several kilometres. This method is now routinely applied offshore, however, the use of time‐lapse methodology onshore is relatively rare. The main reason for this is the relatively high cost of commercial seismic acquisition on land. A widespread belief of a relatively poor repeatability of land seismic data prevents rapid growth in the number of land time‐lapse surveys. Considering that CO₂ sequestration on land is becoming a necessity, there is a great need to evaluate the feasibility of time‐lapse seismics for monitoring. Therefore, an understanding of the factors influencing repeatability of land seismics and evaluating limitations of the method is crucially important for its application in many CO₂ sequestration projects. We analyse several repeated 2D and 3D surveys acquired within the Otway CO₂ sequestration pilot project (operated by the Cooperative Research Centre for Greenhouse Technologies, CO2CRC) in Australia, in order to determine the principal limitations of land time‐lapse seismic repeatability and investigate the influence of the main factors affecting it. Our findings are that the intrinsic signal‐to‐noise ratio (S/N, signal to coherent and background noise levels) and the normalized‐root‐mean‐square (NRMS) difference are controlled by the source strength and source type. However, the post‐stack S/N ratio and corresponding NRMS residuals are controlled mainly by the data fold. For very high‐fold data, the source strength and source type are less critical.     

Long‐term final void salinity prediction for a post‐mining landscape in the Hunter Valley,New South Wales,Australia

Opencast mining alters surface and subsurface hydrology of a landscape both during and post‐mining. At mine closure, following opencast mining in mines with low overburden to coal ratios, a void is left in the final landform. This final void is the location of the active mine pit at closure. Voids are generally not infilled within the mines' lifetime, because of the prohibitive cost of earthwork operations, and they become post‐mining water bodies or pit lakes. Water quality is a significant issue for pit lakes. Groundwater within coal seams and associated rocks can be saline, depending on the nature of the strata and groundwater circulation patterns. This groundwater may be preferentially drawn to and collected in the final void. Surface runoff to the void will not only collect salts from rainfall and atmospheric fallout, but also from the ground surface and the weathering of fresh rock. As the void water level rises, its evaporative surface area increases, concentrating salts that are held in solution. This paper presents a study of the long term, water quality trends in a post‐mining final void in the Hunter Valley, New South Wales, Australia. This process is complex and occurs long term, and modelling offers the only method of evaluating water quality. Using available geochemical, climate and hydrogeological data as inputs into a mass‐balance model, water quality in the final void was found to increase rapidly in salinity through time (2452 to 8909 mg l⁻¹ over 500 years) as evaporation concentrates the salt in the void and regional groundwater containing high loads of salt continues to flow into the void. Copyright © 2004 John Wiley & Sons, Ltd.     

Review Paper: A semi‐empirical model of strain sensitivity for 4D seismic interpretation

We reformulate the original model of Hatchell and Bourne and Røste, Stovas and Landrø that couples fractional velocity change to subsurface strain via a fundamental constant R. The new model combines elastic compressibility of a dual‐porosity system for a sand–shale mixture with horizontal planes of inter‐granular weakness. The majority of observed R‐factor magnitudes from post‐stack 4D seismic data in both the reservoir and overburden can thus be explained. R is predicted to depend strongly on lithology and also initial strain state. The model is also extended to predict the observed angle‐dependence of time‐lapse time‐shifts from pre‐stack data. An expression for the gradient of time‐shift with incidence angle is obtained in terms of the background V_P/V_S, and also the ratio of tangential to normal compliances B_T/B_N representing loss or creation of inter‐granular coupling. If accurately estimated from data, this compliance ratio can be used as an additional parameter to assess the post‐production state of the overburden. It is concluded that whilst R remains the over‐arching parameter controlling the magnitude of time‐shifts measured from 4D seismic data, B_T/B_N is a subtler parameter that may also prove of future value.     

When 4D seismic is not applicable: Alternative monitoring scenarios for the Arab-D reservoir in the Ghawar Field

Ghawar, the largest oilfield in the world, produces oil from the Upper Jurassic Arab‐D carbonate reservoir. The high rigidity of the limestone–dolomite reservoir rock matrix and the small contrast between the elastic properties of the pore fluids, i.e. oil and water, are responsible for the weak 4D seismic effect due to oil production. A feasibility study was recently completed to quantify the 4D seismic response of reservoir saturation changes as brine replaced oil. The study consisted of analysing reservoir rock physics, petro‐acoustic data and seismic modelling. A seismic model of flow simulation using fluid substitution concluded that time‐lapse surface seismic or conventional 4D seismic is unlikely to detect the floodfront within the repeatability of surface seismic measurements. Thus, an alternative approach to 4D seismic for reservoir fluid monitoring is proposed. Permanent seismic sensors could be installed in a borehole and on the surface for passive monitoring of microseismic activity from reservoir pore‐pressure perturbations. Reservoir production and injection operations create these pressure or stress perturbations. Reservoir heterogeneities affecting the fluid flow could be mapped by recording the distribution of epicentre locations of these microseisms or small earthquakes. The permanent borehole sensors could also record repeated offset vertical seismic profiling surveys using a surface source at a fixed location to ensure repeatability. The repeated vertical seismic profiling could image the change in reservoir properties with production.     

Error in shear-wave polarization and time splitting

Shear‐wave polarization and time delay are attributes commonly used for fracture detection and characterization. In time‐lapse analysis these parameters can be used as indicators of changes in the fracture orientation and density. Indeed, changes in fracture characteristics provide key information for increased reservoir characterization and exploitation. However, relative to the data uncertainty, is the comparison of these parameters over time statistically meaningful? We present the uncertainty in shear‐wave polarization and time delay as a function of acquisition uncertainties, such as receiver and source misorientation, miscoupling and band‐limited random noise. This study is applied to a time‐lapse borehole seismic survey, recorded in Vacuum Field, New Mexico. From the estimated uncertainties for each survey, the uncertainty in the difference between the two surveys is 31° for the shear‐wave polarization angle and 4 ms for the shear‐wave time delay. Any changes in these parameters greater than these error estimates can be interpreted with confidence. This analysis can be applied to any time‐lapse measurement to provide an interval of confidence in the interpretation of shear‐wave polarization angles and time splitting.     

Application of diffracted wave analysis to time‐lapse seismic data for CO2 leakage detection

Time‐lapse seismic analysis is utilized in CO₂ geosequestration to verify the CO₂ containment within a reservoir. A major risk associated with geosequestration is a possible leakage of CO₂ from the storage formation into overlaying formations. To mitigate this risk, the deployment of carbon capture and storage projects requires fast and reliable detection of relatively small volumes of CO₂ outside the storage formation. To do this, it is necessary to predict typical seepage scenarios and improve subsurface seepage detection methods. In this work we present a technique for CO₂ monitoring based on the detection of diffracted waves in time‐lapse seismic data. In the case of CO₂ seepage, the migrating plume might form small secondary accumulations that would produce diffracted, rather than reflected waves. From time‐lapse data analysis, we are able to separate the diffracted waves from the predominant reflections in order to image the small CO₂ plumes. To explore possibilities to detect relatively small amounts of CO₂, we performed synthetic time‐lapse seismic modelling based on the Cooperative Research Centre for Greenhouse Gas Technologies (CO2CRC) Otway project data. The detection method is based on defining the CO₂ location by measuring the coherency of the signal along diffraction offset‐traveltime curves. The technique is applied to a time‐lapse stacked section using a stacking velocity to construct offset‐traveltime curves. Given the amount of noise found in the surface seismic data, the predicted minimum detectable amount of CO₂ is 1000–2000 tonnes. This method was also applied to real data obtained from a time‐lapse seismic physical model. The use of diffractions rather than reflections for monitoring small amounts of CO₂ can enhance the capability of subsurface monitoring in CO₂ geosequestration projects.     

Time‐lapse seismic modelling of CO2 fluid substitution in the Devonian Redwater Reef,Alberta, Canada

Common shot ray tracing and finite difference seismic modelling experiments were undertaken to evaluate variations in the seismic response of the Devonian Redwater reef in the Alberta Basin, Canada after replacement of native pore waters in the upper rim of the reef with CO₂. This part of the reef is being evaluated for a CO₂ storage project. The input geological model was based on well data and the interpretation of depth‐converted, reprocessed 2D seismic data in the area. Pre‐stack depth migration of the ray traced and finite difference synthetic data demonstrate similar seismic attributes for the Mannville, Nisku, Ireton, Cooking Lake, and Beaverhill Lake formations and clear terminations of the Upper Leduc and Middle Leduc events at the reef margin. Higher amplitudes at the base of Upper‐Leduc member are evident near the reef margin due to the higher porosity of the foreslope facies in the reef rim compared to the tidal flat lagoonal facies within the central region of the reef. Time‐lapse seismic analysis exhibits an amplitude difference of about 14% for Leduc reflections before and after CO₂ saturation and a travel‐time delay through the reservoir of 1.6 ms. Both the ray tracing and finite difference approaches yielded similar results but, for this particular model, the latter provided more precise imaging of the reef margin. From the numerical study we conclude that time‐lapse surface seismic surveys should be effective in monitoring the location of the CO₂ plume in the Upper Leduc Formation of the Redwater reef, although the differences in the results between the two modelling approaches are of similar order to the effects of the CO₂ fluid replacement itself.