Multi-scenario, multi-realization seismic inversion for probabilistic seismic reservoir characterization Kester Waters* and Michael Kemper, Ikon Science Ltd. Summary We propose a two tiered inversion strategy that aims to address and better explore the solution space during seismic inversion and reservoir characterization. First a range of plausible geological prior scenarios are defined in terms of layer configurations and horizon/picking uncertainty, number of facies and their corresponding abundances, and rock property trends and relationships (with associated uncertainties). Then, per scenario, stochastic Markov chain Monte Carlo sampling (McMC) is performed to create equi-probable realizations from the posterior distribution. The benefit of this approach is two-fold; first of all, no prior low frequency model is stipulated by the operator, with the low frequency content instead being derived through iterative fitting of seismic amplitude data via sampling from facies based elastic property trends. This provides a novel way of exploring uncertainty in the low frequency end of the earth spectrum. Second, it provides estimates of uncertainty from each scenario within the seismic bandwidth. Although these uncertainties are typically much lower than those of the scenario s, they are useful for analysis of thin layer connectivity and hydrocarbon in place volumetric estimates of seismically subtle hydrocarbon accumulations. Introduction Seismic inversion has seen industry wide adoption as the tool of choice for subsurface characterisation at and away from well control. The derivation of the impedance data required to perform this characterisation typically utilizes a starting background low frequency model (LFM). This LFM is required because seismic data lack the low to ultralow frequencies required to extract absolute elastic property estimates, which are a pre-requisite for quantitative subsurface characterisation. The LFM is iteratively updated over the seismic bandwidth by matching forward synthetic seismic models with seismic trace data until the misfit between the two is reduced to an acceptable level a process known as model-based inversion. The challenge with this approach is that the LFM is not updated outside the seismic frequency band; e.g. the overall compaction trends present in the starting LFM are fundamentally unchanged. In other words, there are many different LFM scenarios that will give the same or similar fits to the seismic data, because the fit is performed only within the seismic bandwidth. However, the outputs from these different LFM scenarios can give rise to dramatically different absolute rock property estimates and a wide spread in resulting petrophysical rock property estimates - there is much ambiguity. This fact is sometimes overlooked during subsurface seismic characterisation, with many practitioners preferring to utilise a single best LFM, or perhaps just a handful of simple input LFM s utilising different well calibration points in the construction of each. There is also considerable uncertainty in the inversion result over the seismic bandwidth as seismic is a noisy signal. The uncertainty over the entire frequency band needs to be understood in order to better characterise e.g. reservoir connectivity and pay thicknesses, particularly in marginal reservoirs. After all, depending on the number of (elastic) facies in the subsurface and their corresponding elastic properties there may be a large number of different plausible combinations of facies interfaces which will give rise to the observed seismic response. Theory Bayesian facies and impedance inversion is described in Kemper & Gunning, 2014. The prior information for this inversion consists of per-facies compaction trends, perfacies rock physics models, a seismic wavelet per angle stack and estimates of facies abundances within zones bounded by stratigraphic interpretations. The inversion process globally solves for maximum aposteriori probability (MAP) facies and corresponding elastic properties without the requirement for a conventional low frequency model. That is, the low frequency model is inverted for during the process of inversion (possible, as the prior information over-specifies in the low frequency range). Creating multiple scenarios can be derived by rerunning the MAP inversion with different parameterizations (readily automated). Note that certain scenarios may be discarded if seismic-synthetic residuals are too large or results geologically inconsistent. Performing McMC sampling to derive, per scenario, multiple equi-probable realizations from the posterior distribution is not straightforward, the inversion being both discrete (facies) and continuous (impedances). In this paper we employed a form of simulated annealing to achieve an optimal compromise between quality and speed. Application to a North Sea Oil Field The dataset utilized in this study covers the Echo area of the Forties field in the UKCS. The Forties field is a giant Paleocene oil field, the largest offshore UK, discovered in 1973 by BP and now under operatorship by Apache UK. Page 3146
With originally ~4.5 BBls oil in place, the field has been producing for in excess of forty years and continues to deliver significant volumes of oil to the global market. We utilize the 1988 vintage seismic data set consisting of five angle stacks, re-processed in 2010. At 1988, the Echo platform and field area had only been producing for some 6 months in total, meaning that in place oil accumulations during seismic acquisition were close to virgin conditions (i.e. oil column and contacts relatively undisturbed), providing a good test candidate in which the oil water contact (OWC) and reservoir geometry is known and calibrated by a significant number of appraisal wells. A set of elastic facies models consisting of a P-velocity (Vp) compaction trend, P-velocity to S-velocity (Vs) and P- velocity to density (Rhob) transforms were developed using ten high quality vertical appraisal wells from across the full field area. Four facies were defined; overburden shale (Sele Formation), reservoir shale (Forties formation) and brine and oil bearing reservoir (Forties sandstones). Three horizons, Sele Fm, Forties Fm, Lista Fm were selected to constrain the structural- stratigraphic model. A fluid contact was defined at 2270ms TWT in order to constrain fluid distribution to the approximate position of the original oil water contact (OOWC). The Bayesian inversion technique adopted allows the capture of a variety of sources of uncertainty. Rock physics, wavelet and structural model uncertainty were all initially set to fixed values based on the least squares regressions to well data, estimated wavelets and structural interpretation confidence levels respectively. Having fixed the uncertainties of the inputs, a range of net:gross (N:G) values were tested through the Forties interval until an adequate match was achieved through analysis of predicted N:G at available well locations. The final N:G within the Forties-Lista seismic was set at 60%. Following this calibration step, a similar process was followed for prior oil abundance above the approximate OOWC. A range of prior oil abundances from 1% through to 40% (of total rock volume) was tested, after which values of 5% and 20% were selected based on analysis of the results at wells and on vertical sections. Following assessment of the prior facies abundances, ranges of compaction trend uncertainties, seismic noise levels and structural model uncertainties were explored and selected for use in generation of final inversion parameters. A total of 14 scenarios were defined. For each scenario, five realizations were produced using simulated annealing, giving a total of 70 realizations. Post processing of the 70 realizations was performed to determine the probability of each facies, most-likely facies and the mean and standard deviations of the elastic properties. Resulting facies predictions are good to moderate, though a large degree of variability is noted. Areas of poor predictions are generally correlated with areas of significant residual move-out in the pre-stack seismic, noise and associated picking uncertainty. Figure 1 shows facies predictions at two key well locations. Note that despite only poor to moderate well tie quality, the inversion predicts facies with good confidence. Of most interest is the elastic property uncertainty, which for Vp/Vs is seen to be considerable at and around the top reservoir interface, indicating significant ambiguity in the seismic response and possible horizon mis-picking. Figure 1: Inversion results for two key wells from the Forties Echo field area. Left to right, tracks are VShale, porosity/saturation, up-scaled facies log, most likely facies from inversion, insitu acoustic impedance log, inverted acoustic impedance (mean = black, realizations = grey), insitu VpVs log, inverted VpVs (mean = black, realization s = grey), posterior facies probabilities, insitu synthetic angle gather, seismic angle gather, near stack well tie. Bold green line is the position of the TWT contact used to define oil prior proportions. Note that the inversion predicts brine above this position and is thus not overconstrained to the prior model. Results of the inversion were reviewed along sections intersecting the well locations, figure 2. The inversion performs well, predicting the overall geometry of the Page 3147
reservoir and also indicating areas where connectivity between wells may be reduced or impeded. High N:G and thick channel sand sequences are predicted with high confidence across all realizations, giving rise to very high reservoir and oil probabilities. Figure 2: Arbitrary line through 8 key appraisal and production wells over the Forties Echo field area. Most likely facies (top) and oil probability (row 2, white = high probability). Middle and bottom rows show three randomly selected facies realizations. Prior model TWT OWC shown in green. Facies colors are purple = soft shale, grey = reservoir shale, orange and green = brine and oil reservoir respectively The very high probabilities driven by strong signal to noise and prominent AVO effects at tops/bases of reservoir units. Areas with low N:G as confirmed by wells show considerable uncertainty and variability in the reservoir / oil predictions. This can be in part explained by the fact that when thinly layered, the sand / shale mixture behaves as an effective medium and thus many different thinly layered facies solutions will fit the same seismic response. It can also be explained by the fact that oil bearing sand and reservoir shale have very similar acoustic impedance and thus when thinly layered only subtle Vp/Vs ratio contrasts are produced resulting in ambiguity in seismic response. Both of these factors mean that areas of low N:G show much greater sensitivity when modifying the prior proportion profiles (varying oil proportion from 5% to 20% above the constant TWT OWC) thus allowing these areas of high uncertainty to be better captured and understood. Page 3148
Figure 3: Most likely facies (top, yellow = brine, green = oil, grey = shale), P50 oil column thickness (row 2, 0-60ms thickness), STD AI and Vp/Vs (row 3 and 4, red = high uncertainty) close to top reservoir, generated from 70 stochastic realizations of facies and impedances over the Forties Echo field area. The combination of most likely facies, elastic property uncertainty and P50 thickness map provide useful tools for well planning and probabilistic volumetric analysis. The oil probability cube was used to generate a set of column thickness maps to assess the spatial distribution of hydrocarbon at P10, P50 and P90 confidence levels. Similarly, cubes of elastic property uncertainty and most likely facies were generated and sculpted to identify areas across the structure which show good potential as infill drilling targets, figure 3. The P50 oil distribution shows an excellent conformance to structure. Areas of thick oil column that coincide with low elastic property uncertainties would present favorable infill drilling targets. Conclusions A multi-scenario, multi-realization seismic reservoir characterization workflow utilizing facies-based inversion was applied to the Forties Echo field area. Different scenarios of prior parameters were developed to account for both subsurface (proportions of different facies in the subsurface) and data (rock physics trends, seismic noise, structural) uncertainty during inversion. Inversion results provide good to moderate calibration to well data. Areas of high N:G were delineated with high confidence. Low N:G areas show considerable uncertainty, which is demonstrated by strong sensitivity to the prior proportion model parameters. The combination of facies based thickness estimates and elastic property uncertainty from multiple scenarios and realizations allows a greater understanding of the range of possible LFM s and reservoir and oil distributions and provides a powerful tool for field management. Future work will aim to better constrain the inversion by incorporation of an additional low N:G facies, utilization of a depth to time converted OWC and introduction of additional zonation from time converted depth surfaces from the geological model. Acknowledgments We would like to thank Apache UK for providing the Forties field seismic and well database to Ikon Science. Page 3149
REFERENCES Kemper, M. A. C., and J. Gunning, 2014, Joint Impedance and Facies Inversion Seismic Inversion Redefined: First Break, 32, 89 95. Page 3150