Modeling Digital Twins of grain-based Reservoir Rocks

Exact digital replication of a rock and its pore geometry.

The key to accelerate research and production in the energy industry resides in the efficient and generally applicable determination of physical properties of reservoir rocks. Here, we present recent advancements in the generation of statistical digital twins of reservoir rocks. The presented workflow may be applied generically to any grain-based sample.

We generate digital twins of reservoir rocks as a voxel-based geometry with dimensions of 6003 voxels and larger. Our aim is to accurately replicate the rock and the pore geometry.

Recent developments in Digital Core Analysis and reservoir modeling make digital twins increasingly important. Especially because numerical simulations applied to these rocks have become progressively powerful in recent years, the digital twin can then be used for further non-destructive digital measurements, reducing costs and resource usage.

By representing the physical parameters of the original rock sample in the modeled digital twin, the digital twin may then be used for further applications in the range of digital core analysis. The approach is validated via analysis, modeling, and property prediction based on a digital rock core sample.

The Doddington sandstone is a fine- to medium-grained sandstone from the Fell Sandstone Formation in the UK with an approximate age of 343-339 million years. In addition to quartz, it contains small amounts of calcite, feldspars and clay minerals. Porosity lies within a range of 16-23 %. Permeability is in the range of 3.7-5.4 Darcy.

We determine the grain-size distribution of a Doddington sandstone and subsequently, generate a statistical 3D digital twin of the rock structure. The absolute permeability is computed and compared for both 3D geometries and validates the approach within sufficient accuracy. We thereby demonstrate the applicability of this workflow to other reservoir rocks with a high-performance approach. 

What does this mean for our customers?

Modeling digital twins of a certain type of reservoir rock is important for quality control for both industrial and academic purposes. Thus, changes in the properties in the digital twin may be used to determine the sensitivity of various structural parameters in relation to the properties of a rock.

Authors and application specialists

Dr. Arne Jacob

Application Engineer
for Digital Rock Physics

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Dr. Dominik Michel

Application Engineer

Dr. Erik Glatt

Chief Technology Officer (CTO)

Dr. Christian Hinz

Business Manager
for Digital Rock Physics

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Structure analysis

The gray scale image of a Doddington sandstone taken by micro-computed tomography (µCT) is used as the basis for the material analysis. After importing the full image stack into GeoDict, the images are filtered, cropped and segmented using the efficient tools and modules of GeoDict to obtain a representation of the 3D structure of the rock (digital twin). The Doddington sandstone is a fine- to medium-grained sandstone.

The use of digital twins is crucial to calculate the dependence of physical parameters on the size of a structure. Since these digital twins are variable in size, the size-dependent parameters can be identified and their sensitivity to sample size can be classified.

The following GeoDict modules were used

Modeling process method

In our approach, we recreate the modeling of a standard reservoir rock. It is assumed that the structure has REV size, meaning that the rock parameters are independent of the size of the studied sample and of the direction being observed. A Doddington sandstone sample scanned by µCT imaging is used for this purpose. It is rich in quartz and shows a high porosity and permeability.

A classification of the physical parameters of the reference sample is indispensable for the sufficiently accurate modeling of a digital twin. This high level of information can be accessed by calculating, for example, not only pore size distributions, but also grain size distributions and chord length distributions.

In our approach, the reference rock is modeled by approximating user-defined parameters through an iterative method. The function of the parameters necessary for the modeling can be changed, as well as the error measures set as stopping criterion. In this example, we use five different grain size distributions as function parameters, which then generate a structure within the GeoDict software. This structure is then analyzed using the same characterization of the parameters as the initial structure. If the specified accuracy is not achieved, the error measurements are used to approximate the structure in another loop using our method.

The structure generation implemented in GeoDict is used as a modeling basis, as well as a Gaussian Random Field. Both are included in the modeling in variable proportions, whereby the exact proportion is determined automatically by the algorithm of the method.

Validation of modeling results

The modeling of a digital twin of reservoir rocks is well possible in GeoDict, as shown here. Our iterative approach reveals that conventional sandstones may be sufficiently modeled by our method. The modules available in the GeoDict software can be used for validation and referencing of the rock parameters.

Permeability is calculated in GeoDict using the LIR flow solver, through which the Stokes equations are solved. The permeabilities of the reference structure and the digital twin are determined. A differential pressure of 0.02 Pa is assumed as a boundary condition. The permeability is then used to improve the modeling of the digital twin.

The results show that the flow velocity in the reference structure and in the digital twin, as well as their deviations, are in good agreement. Furthermore, by analyzing the pore throat size distributions, geometric parameters can be included to validate the results.

References

[1] Andrew, M., Bijeljic, B., and Blunt, M., "Doddington Sandstone." Digital Rocks Portal, 30 April 2020, http://www.digitalrocksportal.org/projects/290 Accessed 27 Dec. 2021.

[2] Andrew, M., Bijeljic, B., and Blunt, M.J., Pore-scale imaging of trapped supercritical carbon dioxide in sandstones and carbonates. International Journal of Greenhouse Gas Control. 2014