Research paperImproved lithology prediction in channelized reservoirs by integrating stratigraphic forward modelling: Towards improved model calibration in a case study of the Holocene Rhine-Meuse fluvio-deltaic system
Introduction
Reservoirs with complex sedimentary heterogeneities such as low net-to-gross channelized deposits hold significant amounts of energy resources worldwide. Despite locally good reservoir quality, the estimation of reservoir properties in these heterogeneous deposits remains highly uncertain. The inherent heterogeneities in these deposits necessitate geological reservoir models, which are typically based on stochastic geometric and interpolation methods (Deutsch, 2002). Such methods generate solutions which are locally optimal, capturing the overall setting but are not constrained by the large-scale geological setting of the reservoir (Weltje et al., 2013) nor include processes associated with sediment dispersal and deposition. Stratigraphic forward models (SFMs), that combine topographic diffusion and advective transport equations, are well suited for investigating the morphodynamic and resulting stratigraphic evolution of sediment dispersal systems over a wide range of spatial and temporal scales (Granjeon and Joseph, 1999; Paola, 2000; Meijer, 2002; Hajek and Wolinsky, 2012). Using SFM's inherent holistic approach and geological results, they provide attractive tools for incorporating basin-scale information at the reservoir scale through the conditioning of geological data in a variety of ways (Cross and Lessemger, 1999; Wijns et al., 2004; Imhof and Sharma, 2006; Charvin et al., 2009; Falivene et al., 2014).
Efficiency in matching the data is essential because it determines the applicability of SFMs in real field cases (Bertonello et al., 2013). Karssenberg et al. (2001, 2007) demonstrated the possibility of conditioning SFMs to well data using a simple 3D alluvial architecture model characterized by a single channel belt moving by avulsion over an aggrading floodplain. Sacchi et al. (2015, 2016) implemented the method proposed by Weltje et al. (2013) for conditioning the stratigraphic output derived from SimClast (Dalman and Weltje, 2008, 2012), a basin-scale advection-diffusion model of fluvio-deltaic systems, in which the channels are represented by sub-grid elements. This SFM provides a more efficient sediment transport algorithm for reproducing channelized flow as opposed to conventional linear diffusion models (Meijer, 2002; Dalman and Weltje, 2008; Falivene et al., 2014; Karamitopoulos et al., 2014; Sacchi et al., 2016).
This workflow has been shown to work in a synthetic setting. The simulated channel occurrences were: a) fitted (conditioned) to synthetic seismic and local well data and b) integrated as soft constraints in geostatistical reservoir modelling. The static reservoir models that were constrained to maintain the quantitative coherence with the synthetic large-scale geological setting improved predictive power relative to the models using local well data only.
In this case study, we conditioned SimClast (output/channel occurrences) to a data-rich real-world setting, i.e. the Holocene Rhine-Meuse fluvio-deltaic system. The calibration dataset consists of detailed lithological information obtained from GeoTOP, a high-resolution 3D voxel model that captures the distribution of channel bodies and overbank fines of the fluvial-deltaic deposits in the shallow subsurface down to 50 m below mean sea level (Stafleu et al., 2011, 2012; Van der Meulen et al., 2013; Maljers et al., 2015: Stafleu and Dubelaar, 2016; Stafleu and Busschers, 2017).
The applicability of a new workflow is demonstrated to a real-world setting through the implementation of a hierarchical optimization approach. This approach significantly differs from the one proposed by Sacchi et al. (2015, 2016), which adopted a less efficient Quasi-Monte Carlo approach with systematic sampling to explore the SFM parameter space. In fact, matching the SFM output to a real-world dataset requires a highly complex suite of parameters and calibration constraints compared to synthetic datasets. Therefore, a more efficient matching routine was required to minimize the number of runs to find the most optimal solution or solutions. Moreover, Sacchi et al. (2015) used a well calibration fitness functions based on well tops and lithological logs which turned out to be less effective for the inversion process. Therefore, in this study the well calibration function is based on the average net-to-gross values at wells to manage the scale difference between well (meter grid scale) and SFM (kilometer grid scale) information, which can be problematic when calibrating well data (Sacchi et al., 2016), This is in line with Falivene et al. (2014), who observed that the representativeness problem could be mitigated by averaging over relatively large intervals.
By using the data-rich Holocene-Rhine Meuse GeoTOP model the robustness of the workflow is illustrated and expanded where necessary. The predictive capabilities by incorporating synthetic stratigraphy created by the SFM through the sedimentary processes are shown. Lessons learned may be taken to future applications in deeper subsurface examples for accurate resource estimation. In addition to testing hypotheses on the controlling parameters of the sedimentary system in question, the matched/calibrated basin-scale model allows further use in constraining static models of channelized reservoirs.
Section snippets
Method
The proposed methodology may be summarized as follows (Fig. 1):
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Pre-processing
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Characterization of the reference case: Holocene Rhine-Meuse fluvio-deltaic system
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Definition of the constraints used for the calibration process
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Sensitivity analysis to extrapolate the range of the input parameters used for SFM
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Inversion process for SFM calibration
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Stratigraphic forward modeling using SimClast
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Application of the Neighborhood Algorithm to explore the domain of the unknown input parameters of SFM
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Result
Results
The first part of the work concentrated on the comparative analysis of the proposed 2-stage NA approach with respect to the 1-stage NA approach, (paragraph 2.4.3) evaluating their capability to sample a range of valid models that are consistent with typical calibration constraints. The optimization results were compared in terms of evolution of the fitness function with the number of models sampled during the iterative process. The error evolution is obtained by selecting the error at each
Matching optimization
The results outlined above show the possibility of matching lithological variations simulated with a basin-scale SFM to real data. In this numerical framework, accurate estimation of the SFM input parameters, especially initial topography and sediment entry points, ensured a reliable prediction of the spatial distribution of channelized deposits (Sacchi et al., 2015).
The results demonstrate that a significant improvement is obtained by implementing the novel two-step optimization approach as
Computer code availability
The related code is written in MATLAB 2018. The file name of related code is “NA_Basin”. To access the source file of the code, one can visit the repository on GitHub (https://github.com/REDD-PoliTO/Optimization).
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
We express our gratitude to Prof. Gert Jan Weltje from KU Leuven for his support during the initial conceptualization and development stages of the project.
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Cited by (0)
- 1
Built the GeoTOP model in Petrel, carried out the basin simulations, analyzed and interpreted the results, co-wrote and reviewed the manuscript.
- 2
Wrote and implemented the optimization algorithm in MATLAB, analyzed and interpreted the results, co-wrote and reviewed the manuscript.
- 3
Initiated the study, support for SimClast code, provided the necessary data, analyzed and interpreted the results, co-wrote and reviewed the manuscript.
- 4
Support for SimClast code, analyzed and interpreted the results, co-wrote and reviewed the manuscript.
- 5
Provided the necessary data, advisor and reviewed the paper.
- 6
Advisor.
- 7
Advisor and reviewed the paper.