Volume 29 Issue 8 August 2011 Near Surface Geoscience Special Topic Technical Articles Anisotropy in the salt outcrop at Cardona, Catalonia implications for seismic imaging Integration of geology and geophysics through geostatistical inversion: a case study 100 4D pre-stack inversion workflow integrating reservoir model control and lithology supervised classification 95 75 EAGE News Back from the Boot Camp! 25 5 0 Workshop reports on CO2 projects, reservoir modelling and AGORA initiative
first break volume 29, August 2011 technical article Integration of geology and geophysics through geostatistical inversion: a case study Mark Sams, 1* Ian Millar, 2,3 Wawan Satriawan, 2,4 Denis Saussus 5 and Sumon Bhattacharyya 6 Abstract Geostatistical inversion of seismic data can be used to build highly detailed reservoir models with integration of information from diverse sources. A key to successful integration is the solution for facies during the inversion, provided that the facies definition is meaningful in the elastic, petrophysical, geological, and reservoir engineering domains. This case study from a field offshore Vietnam shows that the seismic data are only able to constrain the vertical distribution of facies when the beds are close to or above seismic resolution. Prior facies probability trends are required to ensure that the detailed vertical distributions of facies are consistent with geological and reservoir engineering expectations. However, even when below seismic resolution and when the probability trends are laterally invariant, the lateral variations of facies are driven by the seismic data. Introduction A state-of-the-art reservoir model is a 3D volume of the subsurface that has been subdivided into cells whose distribution and alignment has been arranged to reflect the expected continuity of flow units. The cells are populated with a range of values that, amongst other things, characterize the properties of the rock, the fluids within each cell, and the environmental conditions (e.g., temperature and pressure) at each cell s location. These properties permit the static and dynamic properties of the reservoirs within the volume to be estimated. It is often taken as a given that tighter integration of all available data and information about a reservoir will result in models that are more predictive and have a lower degree of uncertainty associated with them. In a typical case, these data come from well and seismic measurements set in the context of regional studies. The data represent geophysical, geological, reservoir engineering, petrophysical, and rock physics information. There are various issues in integrating these data, such as the problem of scale, or finding meaningful and quantitative relationships between the different types of data. In this case study, we present the geostatistical inversion approach as the means of data integration. We propose that a key to integration is the simultaneous modelling of facies and elastic properties within the inversion and ensuring that the chosen facies have relevance in the different domains that are to be integrated. We show how the final distribution of facies is controlled by both geophysical constraints (seismic) and geological/reservoir engineering considerations whilst honouring well control. The properties within each facies can be modelled to mimic the trends and relationships found from well measurements. The issue of scale is overcome by upscaling or downscaling the various data to a single scale at which the reservoir model is built. Field The study field is located in the Nam Con Son Basin, East Vietnam Sea (Figure 1). The field structure is a three-way dip closure oriented N S (Figure 2). The structural development of the field relates to the development of the Nam Con Son Basin from the Palaeogene to the Middle Miocene, and is interpreted to be a function of the relative importance of East Vietnam Sea rifting and the synchronous propagation of fault systems related to the collision of India with Eurasia (Lee et al., 2001). The stratigraphic section penetrated in the field ranges from the Pliocene Bien Dong Formation, penetrated at the seabed, to the Oligocene Cau Formation. The interval of interest is the Early Miocene where a series of sands, termed the Middle Dua Sands, were deposited (Figure 3). Four wells have penetrated the structure: two in the north and two in the south. The first well drilled, N1, in the north- 1 Fugro-Jason (M), Menara TA One, Level 27, 50250 Kuala Lumpur, Malaysia. 2 Premier Oil Vietnam Offshore 7/F, Saigon Finance Center, 9 Dinh Tien Hoang Street, Da Kao Ward, District 1, Ho Chi Minh City, Vietnam. 3 Present address: Greenways, High Street, Whitchurch on Thames, Reading, RG8 7HB, UK. 4 Present address: Premier Oil Indonesia, Indonesia Stock Exchange Building, Tower 1, 10 th Floor, Jalan Sudirman Kav 52-53 12190, Jakarta, Indonesia. 5 Fugro-Jason Netherlands, Veurse Achterweg 10, 2264 SG Leidschendam, The Netherlands. 6 Fugro-Jason (UK), Fugro House, Hithercroft Road, Wallingford, Oxfordshire, X10 9RB, UK. * Corresponding author, E-mail: msams@fugro-jason.com 2011 EAGE www.firstbreak.org 1
technical article first break volume 29, August 2011 Figure 1 Location of the study area. ern part of the structure, penetrated the Middle Dua Sands but the sands were water-bearing at this location. The field was discovered by the S1 well and was appraised by wells S2 and N2. The northern and southern wells lie approximately 7 km apart. All four wells have reasonably extensive logging suites including density, P-wave, and S-wave logs. There are seven sands in the interval of interest (MDS 0 to MDS 6) that can be identified with reasonably high confidence in all the wells. The depositional environment of these Figure 2 Time structure map of the study field (top of MDS 6). The locations of the wells are indicated. The black contour represents roughly the oil-water contact for the reservoir MDS 6. Colours represent time with blue being shallow and yellow being deep. sands has been interpreted as a sub-littoral tidally influenced shoreline or tidal delta. Hydrocarbons in economic quantities are present at four levels, but in this study only the two main accumulations are considered: those in the MDS 5 and MDS 6 sands. The MDS 6 sands lie unconformably on the Oligocene Cau Formation. The MDS 5 and MDS 6 reservoir units can be subdivided based on the quality of the reservoir (Figure 4). Reservoir Sub-unit Facies belt Facies (major) MDS 5 MDS 5a Heterolithic sands Sand Type 1 Soft Shale MDS 5b Shoreface sand complex Sand Type 2 Sand Type 3 MDS 5c Heterolithic sands Sand Type 1 MDS 6 MDS 6a Heterolithic sands Sand Type 1 Soft Shale Table 1 Reservoir units and facies belts. MDS 6b Tidal delta front complex Sand Type 2 MDS 6c Distal Delta Front Sand Type 1 2 www.firstbreak.org 2011 EAGE
first break volume 29, August 2011 technical article The MDS 5 sands can be divided into two or possibly three sub-units representing, from bottom to top, heterolithic sands, shoreface sand complex, and heterolithic sands (Table 1). The lowest unit is very thin. The MDS 6 sands can be divided into three sub-units representing, from bottom to top, distal delta front, tidal delta front complex, and heterolithic sands. The field is covered by high quality 3D seismic acquired in 2007. The data have been processed through pre-stack time migration and output as four angle stacks: 5 15, 15 25, 25 35 and 35 45. Calibration to the well data suggests that the seismic amplitudes are suitable for both structural and stratigraphic interpretation, although some parts of the data are noisier due to the effects of faulting, particularly beneath the western bounding faults. The peak frequency of the seismic data varies from about 30 Hz at the near angles to 25 Hz at the furthest angles. The mean velocity within the reservoir sands is roughly 4000 m s -1, giving dominant wavelengths of 120 160 m. A deterministic inversion of the angle stacked seismic data to P-impedance and V P /V S had previously been carried out (Figure 5). The inversion was used to interpret the top and base of the two main sands. Extractions from within the reservoirs indicated lateral variations but it was not possible to interpret the distribution of the sub-units within the reservoirs, although some indications of vertical variations were observed. This limitation to the resolution is not surprising given the Figure 3 Stratigraphic column. 2011 EAGE www.firstbreak.org 3
technical article first break volume 29, August 2011 Figure 4 Cross-section through the wells showing the distribution of facies and reservoir units. The facies log of each well is plotted at log resolution in depth aligned at the top of the MDS 5 reservoir. The sub-units of the main reservoirs are indicated. The colour code for the facies is given in Table 2. Figure 5 Cross-section through the deterministic inversion. The top and base of the MDS 5 and MDS 6 have been picked on the P-impedance and V p / V s volumes and adjusted to fit the formation tops interpreted from the well log data as shown. Here the low-cut filtered V p /V s volume from deterministic inversion is shown with overlays of the measured well log data. ratio between the dominant seismic wavelengths and the thicknesses of the reservoir units, which are roughly 25 m for MDS 5 and 50 m for MDS 6. Geostatistical inversion A geostatistical inversion project was carried out on this field to build a range of reservoir models for dynamic simulation. Geostatistical inversion was proposed so that the models would be driven by the seismic data yet honour, to some degree, the fine-scale heterogeneity observed at the wells. Geostatistical inversion also allows for the integration of various data whilst taking into account the uncertainties in those data. The workflow results in a number of models that explore the range of uncertainty afforded by the combination of all the input data. Geostatistical inversion combines the laterally dense measurements of seismic data with the fine-scale vertical detail of well logs to produce highly detailed models of the reservoir and rock properties of interest. There are a range of geostatistical inversion techniques from single-stack single trace inversions for a single elastic property (e.g., Haas and Dubrule, 1994) to multi-stack fully 3D inversions that solve for elastic properties simultaneously with facies (e.g., Merletti and Torres-Verdin, 2006) and others with varying degrees of sophistication (e.g., Sams et al., 1999; Buland and Omre, 2003; Gunning and Glinksy, 2004). The method chosen in this case study is a multi-stack fully 3D inversion solving simultaneously for facies and elastic properties through a Bayesian approach to compute a global probability density function describing all known information about the reservoir, and then applying a Markov chain Monte Carlo (MCMC) algorithm to obtain statistically fair samples from that probability density function (Merletti and Torres- Verdin, 2006). The properties are generated on a stratigraphic grid in time and then transferred to a corner point grid in depth using a process that retains the vertical and lateral heterogeneity. For this particular reservoir, the information input into the inversion process included the following: n A 3D stratigraphic grid to capture the zonal and stratigraphic variations of the reservoir. n Prior facies proportion trends to reflect geological knowledge regarding the depositional environment. n Plurigaussian representations of the facies to reflect the size and spatial continuity of the reservoir rocks. n For each facies, multi-dimensional probability density functions of the elastic properties (P-impedance, V P /V S, density) and reservoir engineering properties (effective porosity, clay volume) of interest. n For each facies, variograms of these properties to reflect the different spatial continuity patterns of the properties within different rocks. n For each facies, low frequency trends for each of the elastic properties to reflect various compaction trends caused by the overburden. n Measured data, including four pre-stack 3D seismic stacks and four wells with a standard suite of wireline logs and their petrophysical and facies interpretations. 4 www.firstbreak.org 2011 EAGE
first break volume 29, August 2011 technical article n For each seismic stack, a trace-dependent volume of estimated wavelets and an estimate of the seismic noise introduced by measurement and processing errors. The result of the geostatistical inversion process is a set of highly detailed realizations that honour all measured and inferred data regarding the reservoir. Facies Facies are important to modelling and integration, particularly in the context of using geostatistics and inversion to construct models. Geostatistics imposes a degree of spatial smoothness that can be at odds with the degree of heterogeneity of the reservoir. Facies are, by definition, groups of rocks with common specific characteristics. If facies are modelled prior to, or simultaneously, with rock properties (characteristics), the smoothness criterion of geostatistics is overcome to some degree. Modelling with facies will allow for sharp boundaries between regions of different characteristics that are at a scale smaller than the gross layer definition often adopted for reservoir modelling. Therefore, models can have levels of heterogeneity (intra-facies, inter-facies, and inter-layer variations) that cannot be achieved by geostatistical simulation of or inversion for elastic properties alone. With respect to inversion, it is important that if we want the seismic data to drive the distribution of the facies to any degree, the facies must have some degree of separation from each other in the elastic domain. Ideally, we would choose a facies definition that gives the maximum separation and define the rocks purely on the basis of their elastic characteristics to give what might be called elasto-facies. However, the seismic data cannot be the only criteria for facies definition; the facies must also be meaningful in terms of geology and reservoir engineering. A geologist might optimally define facies based on characteristics that allow for the prediction of the distribution of those facies within the context of the depositional environment; a reservoir engineer on characteristics that control fluid flow. In addition, facies should also be identifiable from wireline logs so that well data can play a full role in the model-building process. It is not a given that all these criteria are consistent, but before quantitative integration can begin a facies definition has to be made that addresses the key aspects of all these demands, and compromises must be made. In this study, geological modelling had already begun before the geostatistical inversion was initiated. The reason for using inversion was to generate a set of models that were tightly integrated with the seismic data as an alternative to those based on the sparse well data alone or wells and seismically derived trends. Facies had been defined based on all the relevant criteria save the elastic characteristics. These facies were generally identifiable from the wireline petrophysical interpretation of porosity and clay volume. Analysis of cross-plots of the key elastic properties for seismic data, P-impedance and V P /V S, indicated that a change from one mudstone and five sandstone facies applied during the geological modelling (Table 2, column 1) to two shale and three sandstone facies (Table 2, column 2) was the best compromise. The cut-off values applied to the porosity and clay volume were slightly adjusted to optimize the new definition. The cross-plot of elastic properties colour-coded by the final facies definition (Figure 6) shows that there is reasonable separation of the facies in the elastic domain. In particular, the three types of sand are well separated. The biggest overlap is between the Type 1 heterolithic sands and the hard shales. This ambiguity is mitigated to a greater extent by the expectation that there is little hard shale within the reservoir interval. A cross-plot of core porosity versus core permeability highlights the importance of the facies definition for reservoir properties (Figure 7). The three sand types are also fairly well separated in this domain, but the existence of a separate trend for the Type 3 chloritic sands is important. This separate trend is caused by the presence of chlorite on the grains that has preserved porosity during burial. However, significant amounts of chlorite within pore throats reduce permeability and result in a distinct porosity-permeability trend with only moderate permeability in the highest porosity sands. Prediction of the distribution of Type 3 sands is, therefore, imperative for the application of the appropriate Figure 6 Cross-plot of elastic properties colour coded by the facies used for the geostatistical inversion. Ellipses representing the two-standarddeviation Gaussian distribution of each facies are also shown. 2011 EAGE www.firstbreak.org 5
technical article first break volume 29, August 2011 Geological Modelling Facies Geostatistical Inversion Facies Description Colour code Mudstone Hard Shale Silty/laminated harder shale Soft Shale Less silty/laminated shale Argillaceous sandstone Sand Type 1 Heterolithic low porosity Wavy-lenticular sandstone sandstone Flaser-bedded sandstone Sand Type 2 Higher quality reservoir sands Lo-chlorite sandstone with moderate porosity Hi-chlorite sandstone Sand Type 3 Higher quality reservoir sands with high porosity due to chlorite grain coating Table 2 Comparison of facies used for geological modelling and geostatistical modelling. The colour code in the last column is used throughout the paper to identify the different facies. Figure 7 Cross-plot of core porosity versus core permeability for the sands in the MDS 5 and MDS 6 reservoir units. The sands are colour coded according to Table 2. The inset shows an image of the grains from Sand Type 3 where chlorite coats the grains and blocks the pore throats. aligned at the top of the MDS 5 reservoir. There are some points of interest. In the MDS 5 reservoir we can observe that Type 3 sand is only present in the two northern wells. The accuracy of any reservoir model that is built will depend on the ability to predict the distribution of this sand between the northern and southern wells, which are approximately 7 km apart. We also note that the reservoir units can be readily characterized into sub-units: two (possibly three) sub-units in the MDS 5 sands and three in the MDS 6 sands. These sub-units represent zones of different reservoir quality. These sub-units vary in thickness between the wells and again these thickness variations must be predicted to provide accurate reservoir models. As mentioned earlier, these sub-units are at or below the seismic resolution. The geostatistical inversion was carried out in the time domain and was set to produce models sampled at approxporosity-permeability relationship. Use of an average trend or one derived from Type 2 sands would result in assignment of over-optimistic permeability values to the chloriterich sands and an inaccurate representation of the dynamic properties of the reservoir. The abundance of chlorite is most likely controlled by the relative amount of mixing of iron-rich fresh water with marine water in this transitional environment. The circulation and mixing of the marine and fresh water can be influenced by subtle variations in coastal morphology and shelf geometry, and well control within the field does not provide sufficient data to model these controls. The facies definition can be applied to the wells to produce facies logs sampled at intervals of 0.5 ft. A comparison of the well log facies for the four wells in the field is shown in Figure 4. The data are plotted in the depth domain, but 6 www.firstbreak.org 2011 EAGE
first break volume 29, August 2011 technical article imately 1 ms in thickness (the actual time thickness at any location depends on the layer thickness, the number of stratigraphic micro-layers, and the assigned stratigraphy). The well log data were converted to time and the effective porosity, volume of clay, and the elastic property logs were upscaled to 1 ms. The final facies definition for modelling was made from the upscaled reservoir property logs. All further discussion of log data refers to these upscaled logs. Interpretation The geostatistical inversion is run within a structural and stratigraphic framework. The structure is defined through horizon and fault interpretation. The sands in this field have similar P-impedance values to the surrounding shales but strongly contrasting V P /V S values, so an interface between reservoir and shale produces a Class II AVO signature. Therefore, horizon interpretation was carried out primarily using the V P /V S results (Figure 5) from the simultaneous deterministic inversion of the same seismic angle stacks, using the methodology described by Jarvis et al. (2004). The top and base of the MDS 5 and MDS 6 sands were picked along with a number of faults, including the major bounding faults to the west. The horizons were adjusted to tie the formation tops in the wells. Another horizon was picked at about the MDS 0 level to form the top of the model, and an arbitrary horizon within the Cau Formation as the base of the model. The stratigraphy was set as conformable in all layers save for the base layer, which was set as parallel to top. Property modelling The geostatistical inversion employed here solves for the distribution of facies simultaneously with the distribution of elastic properties. The facies-dependent elastic properties (fundamentally P-velocity, S-velocity, and density), generated through the MCMC sampling algorithm previously mentioned, are used to create a reflectivity model using the Zoeppritz equations, which is then used to create synthetic seismic data through convolution with wavelets that vary with angle for comparison with the processed seismic data. Since the solution for facies and elastic properties is simultaneous, each facies can be assigned unique statistical and geostatistical properties. The statistics for each facies are required to be stationary. In fact, there are vertical variations in the means of the elastic properties as determined from analysis of the well log data. These variations can be defined in terms of absolute depth and also depth relative to the stratigraphic level. These trends were estimated and removed from the well log data to leave the higher frequency variations, which we shall term residuals. The elastic property residuals were analysed and joint probability density functions determined. Spatial correlations were set in terms of these residuals. During inversion, the simulated residuals are added to the pre-defined trends for population of the different facies. To use Zoeppritz s equations, we require trends and residuals for P-velocity, S-velocity, and density. Simulation for reservoir properties, such as porosity and clay volume, can be carried out during the inversion or after using joint probability density functions with the absolute elastic properties. However, in this paper we focus on the ability of the seismic data to control the distribution of the facies and do not analyse the results of the reservoir property simulation. The elastic properties are dependent on the fluids in the rocks, so the properties change across the oil-water contact. This change is handled in this study by assuming that the contact is known in depth, which is reasonable as we have three wells that give consistent results. The contact in depth is transformed to time using a velocity model derived from seismic stacking velocities and calibrated to the four wells. Different elastic properties (residuals) are used above and below the contact. Since the oil in these reservoirs has a low API, the effect of oil on the elastic properties is really only noticeable in the highest porosity rocks. This methodology allows for continuity of facies across the fluid contact but discontinuity in the elastic properties. The uncertainty in the depth-to-time conversion of the contact is not included in this analysis. Facies trends A prerequisite for geostatistical modelling or inversion is a prior facies probability model. This model can be simple and represent a global probability for each facies within each layer, or complex and define the probability at each point within each layer. We used the simple approach to investigate the ability of the seismic data to constrain the vertical facies variations in the output models. Then we used prior probabilities that varied vertically, in a stratigraphic sense, to introduce geological control on the vertical distribution of facies beyond seismic resolution. In the simple case, the four wells were used to find initial distributions of each facies in each layer by counting the number of samples of each facies compared with the total number of samples in that layer. The results are shown as pie charts in Figure 8. Also shown in this figure is the proportion of each facies for each stratigraphic micro-layer derived from the four wells. Since there are only four wells, the proportions can only take integer multiples of 0.25. This display shows the general vertical facies trends within each layer. The sub-units of the reservoirs can be clearly observed. In the complex case, we started with the vertical proportions averaged from the wells as prior probabilities to the geostatistical inversion these prior probabilities were laterally invariant along each stratigraphic microlayer (Figure 9). The inversion was run unconstrained to the four wells and the results were analysed. Based on the predictions of the facies at the four wells compared with the actual facies at the wells, the prior probabilities were manually adjusted. Several iterations were performed before an acceptable blind well prediction was made. 2011 EAGE www.firstbreak.org 7
technical article first break volume 29, August 2011 Figure 8 The facies distribution as determined from the well data. On the left the facies for each well is shown after upscaling to 1 ms. The data are plotted in stratigraphic depth. To the right the data are rearranged to show the proportion of each facies at each stratigraphic depth. The pie charts show the facies proportions per layer as used for the geostatistical inversion. Results Geostatistical inversion was run twice with identical settings other than the prior facies probability models as discussed above. For each run, several realizations were generated and the results analysed in terms of general facies distributions and the uncertainties. Here we analyse only a single realization chosen at random from each run. The analysis is performed on the output facies models. To analyse the vertical variations we summarized the model as a single profile. This was achieved by taking each stratigraphic micro-layer and assessing the proportion of each facies in that layer across the entire area of interest. This analysis was carried out for each stratigraphic micro-layer and the results plotted as proportion curves in Figure 10 in a similar fashion to the proportion curves of the well data, which are also plotted in this figure for comparison. The results from the realization where a simple prior facies probability was used bear some resemblance to the average of the well logs. Obviously, the major layers are well defined because the overall facies distribution is restricted for each of the major layers in addition to there being strong elastic property contrasts at the interfaces between these layers. Within the reservoir layers there are some trends in the vertical distribution of facies. For example, in the MDS 6 sands the distribution of good quality and poor quality (or non-) reservoir shows an overall similarity to the subunits defined by the wells. It should be emphasized that the only control over the vertical distribution of facies within the layers for this realization are the seismic data and the variograms applied to the facies and the properties within the facies. In the MDS 5 sands the inversion result suggests a trend of decreasing sand quality towards the top of the interval, which is also indicated by the wells, but the upper and lower units in this interval are not well defined by the inversion. In addition, in the MDS 6 sands there are shales predicted in the lower units, which are not expected from observation of the wells or the depositional setting. These details are clearly beyond the ability of the seismic to con- Figure 9 The prior probability trend for Type 3 sand is shown in the central panel, compared with the far angle seismic data to the left and a single realization of facies from a geostatistical inversion constrained to the wells and using the vertically varying probability trends. Note that the probability trend is laterally invariant along the stratigraphic layering and that the maximum probability is only 0.5. The colour code for the facies is given in Table 2. 8 www.firstbreak.org 2011 EAGE
first break volume 29, August 2011 technical article Figure 10 The average vertical facies distribution per stratigraphic micro-layer from the geostatistical inversions compared with the average facies distribution from the wells. On the left the results from a geostatistical inversion where the prior facies probabilities were set as constants per layer as indicated by the pie charts in Figure 8. On the right the result of a geostatistical inversion where the prior facies probabilities were set as laterally constant vertically varying trends within the reservoir layers. strain. Small amounts of shale in thin layers present here and there do not impact the seismic significantly and so, without further constraints, can appear anywhere. The result when vertical prior facies probability trends were used shows a much greater similarity to what is seen in the wells. The different sub-units in both the MDS 5 and MDS 6 sands are clearly identifiable. It must be emphasized that these results represent the average vertical distribution and that there are significant lateral variations, which we will discuss later. It should also be noted that the output distribution does not identically match the input prior probabilities, as can be seen in Figure 9. However, it is important to find out whether these facies trends have dominated the inversion results at the cost of the match with the seismic data. An analysis of the signal-to-noise ratio of inverted synthetic to residual for each of the four seismic sub-stacks shows that there is no difference to the overall seismic match between results generated with the different prior probabilities. That is, the two results, one using a simple and one a complex prior facies probability model, honour the seismic data to the same degree. Lateral variations The facies probability trends described above are laterally invariant within each stratigraphic micro-layer. Any lateral variations in facies are driven primarily by the seismic data in combination with the lateral variograms, whose ranges are set from geological analogues, and the wells, which have influence only within proximity of their locations. The correct distribution of Type 3 sand within the MDS 5 between the northern and southern wells was earlier highlighted as a key requirement for accurate reservoir characterization. The distribution of facies along one stratigraphic microlayer from within the MDS 5 is shown for one realization in Figure 11. The distribution is shown for three cases: the first is for global facies probabilities, the second for vertically varying facies trends, and the third where no seismic inversion has been run (that is, the result of a geostatistical simulation) but the vertical probability trends have been employed. In the first two cases, the Type 3 sand extends all the way from the north down to close to the southern wells, but is not present further to the south. The only real difference between these two cases is the presence of small amounts of shale facies in the first case which are not permitted by the vertical facies trends in the second case. In the third case, the lateral distribution is being controlled only by the wells and the statistics. Away from the wells the pattern is random. For each of these three cases other realizations show the same overall patterns as presented in this figure. This suggests that, although this Type 3 sand is below seismic resolution, the lateral distribution of this sand is being controlled by the seismic data. This may be due to the fact that although the bed is below seismic resolution, it is not below seismic detection. Discussion and conclusions Seismic data are band-limited. It is, therefore, not unexpected that the vertical distribution of facies resulting from geostatistical inversion is poorly resolved for the detail sought. Although some additional constraints on the vertical distribution can be obtained from an imposed variogram, the lack of resolution is often captured in the uncertainty obtained through generating multiple realizations. However, when building reservoir models that are to be used for static and dynamic modelling, it is important that the distribution of facies makes sense to the geologist and reservoir engineer 2011 EAGE www.firstbreak.org 9
technical article first break volume 29, August 2011 Figure 11 The facies distribution within one micro-layer of the MDS 5, as indicated on the facies proportion plot to the left, from one realization each of two geostatistical inversions and one geostatistical simulation. The result on the left is from a geostatistical inversion where the prior facies probabilities are given as constants per layer. The result in the centre is from a geostatistical inversion where the prior facies probabilities are set as laterally constant vertical trends within the reservoir layers. The result on the right is from a geostatistical simulation where the seismic is not used and the prior facies probabilities are the same as for the centre plot. for all realizations. The example in this study indicates that prior facies probabilities, which are allowed to vary vertically, can be used to ensure that the results are consistent with geological and reservoir engineering expectations. The concern is how much influence these trends have on the lateral distribution of the facies. This study also shows that even when some beds are below seismic resolution, the lateral distribution of facies is not necessarily dominated by the probability trends. In this case, laterally invariant probability trends were used within each layer and yet significant lateral variations in facies were generated that were not random and so must have been driven by the seismic data. Naturally, to achieve this, the facies distribution must be solved simultaneously with the elastic properties during inversion and there must be good separation of facies in the elastic domain. In addition, the facies definition must make sense in all the domains elastic, petrophysical, geological and reservoir engineering for the results to be acceptable for static and dynamic modelling. Often this means that compromises on facies definition must be made, as highlighted in the case study presented. Acknowledgements We thank the management of Premier Oil Vietnam Offshore and its partners, Santos, and PetroVietnam, for permission to publish this paper. References Buland, A. and Omre, H. [2003] Bayesian linearized AVO inversion. Geophysics, 68, 185 198. Gunning, J. and Glinsky, M.E. [2004] Delivery: an open-source model based Bayesian seismic inversion program. Computers and Geosciences, 30, 619 636. Haas, A. and Dubrule, O. [1994] Geostatistical inversion a sequential method of stochastic reservoir modelling constrained by seismic data. First Break, 12(11), 561 569. Jarvis, K., Folkers, A. and Mesdag, P. [2004] Reservoir characterization of the Flag Sandstone, Barrow Sub-basin, using an integrated, multiparameter seismic AVO inversion technique. The Leading Edge, 23, 798 800. Lee, G.H., Lee, K. and Watkins, J.S. [2001] Geologic evolution of the Cuu Long and Nam Con Son basins, offshore southern Vietnam, South China Sea. AAPG Bulletin, 85, 1055 1082. Merletti, G.D. and Torres-Verdín, C. [2006] Accurate detection and spatial delineation of thin-sand sedimentary sequences via joint stochastic inversion of well logs and 3D pre-stack seismic amplitude data. SPE 102444. Sams, M.S., Atkins, D., Said, N., Parwito, E. and van Riel, P. [1999] Stochastic inversion for high resolution reservoir characterisation in the central Sumatra Basin. SPE 57620. Received 4 February 2011; accepted 29 May 2011. doi: 10.3997/1365-2397.2011023 10 www.firstbreak.org 2011 EAGE