The challenges in acquiring quality laboratory flow measurements in very low-permeability reservoir rock samples has furthered the development of image-based rock physics simulations of multiphase transport properties.
The concept of “digital rocks” originated 50 years ago and has become more widespread recently with advances in imaging technology, computing power and robust algorithms for representing complex multiphase flow behavior at the pore scale. Simulation results based on high-resolution images have the dual role of complementing laboratory measurements on conventional reservoirs and acting as a stand-alone predictive tool for unconventional reservoirs where the very low permeability values limit what can be measured in the laboratory. Current imaging technology, particularly X-ray microscopy and focused ion beam scanning electron microscopy, has improved spatial resolution that captures much of the pore system in these fine-grained unconventional reservoirs to allow for accurate and predictive image-based rock physics simulations.
XRM, or micro-CT, senses the contrast in X-ray absorption of grains and pores in the sample, with multiple scans being reconstructed into 3-D image volumes. Image resolution is strongly affected by the diameter of the cylindrical core plug, with 1 micron resolution often requiring a plug that has a diameter of 1 to 2 millimeter. This is an order of magnitude smaller than a standard laboratory core plug, so there are always upscaling issues to resolve.
FIB-SEM achieves higher image resolution by combining an ion beam that progressively mills thin layers from the top of the sample volume and a high-resolution SEM that captures an image after each milling event. FIB-SEM provides resolution down to 0.005 to 0.010 microns that can capture much of the connected pore volume, which in turn can be the basis of an image-based simulation. The challenge is that current FIB technology severely limits the area and depth dimensions of the ion-milled volume to less than 100 microns in any direction. FIB-SEM technology is improving, so sample volumes will only get larger (figure 1).
The datasets associated with these high-resolution images quickly become very large with individual micro-CT, or FIB-SEM images of a 3-D volume exceeding several gigabytes. The processing, analysis and management of such large datasets is a familiar challenge for geophysicists. Likewise, digital rock studies also emphasize the shift toward cloud computing, fast graphical processors and parallel computing algorithms designed for large-scale images. Management of these numerous datasets, each with large file sizes, requires specialized software that organizes the raw images along with calculated results into accessible data structures.
The Supervised Machine Learning Method
The processing and analysis of these large image datasets benefit from the use of various artificial intelligence techniques, especially in the critical step of segmentation of the pore system from the surrounding rock matrix. A supervised machine-learning approach upends the standard image processing workflow that first applies a series of filters to denoise and enhance features in the single image prior to segmentation. The SML method applies these filters to create a large number of new images that provide the massive amounts of data points for each voxel that are subjected to the machine learning decision tree. A small region in the image is trained by the user to define the pore and multiple grain components. Each voxel in the training region is now represented by a series of more than 100 values that are run through the Random Forest analysis in order to generate a regression expression that can be applied to remaining untrained regions of the image. The SML training is evaluated by the probability of each voxel being assigned to the proper phase, that is, pore or grain. These probability-based images can also be used as inputs to various deep learning neural networks used to segment images that lack strong contrast amongst components, which is often the case in both XRM and FIB-SEM images of “shale.”
Pore Geometry Representation
The simulation of multiphase transport properties requires a pore system connected from one boundary to its opposite. There are two main approaches to creating this connected pore geometry; a pore-network model that interpolates pore connectivity between visible pores, or an image-based approach that uses only the image-resolved pore system. Pore network models have proven useful in situations where image resolution is insufficient to capture throats that connect the sample’s larger pores. There are a variety of image processing algorithms that add throats or connecting pathways to generate a PNM. Many studies reconstruct 3-D volumes from high-resolution 2-D SEM images, which has the advantage of greater resolution and the disadvantage of inferring pore connectivity in the third dimension. There are several DL techniques under development for the projection of 2-D images into a 3-D volume that may prove useful in the near future.
Most conventional reservoir samples are characterized by connecting pore throats that are larger than micro-CT image resolution, so it is possible to directly use the segmented image volumes. There are a number of studies of conventional reservoir rock where the captured 3-D images provide sufficient information to generate a connected pore system. The challenge with low-permeability samples is that many of the connecting throats are much smaller than the approximately 1.0-micron spatial resolution of conventional micro-CT techniques, so that any reconstruction of a connected pore system based only on micro-CT must use the PNM approach or include another imaging technique to identify those smaller throats.
The image-based simulation of these unconventional reservoir samples therefore requires the use of FIB-SEM images. After completing the segmentation of the pore system from the images and the calculation of various static properties – for example, pore size distributions, tortuosity and spatial distribution of the porosity for representative elementary volume evaluation – the simulation of capillary pressure curves provides a means to validate the extracted pore geometry from images with laboratory results. Laboratory mercury injection capillary pressure measurements provide insights on the connectivity of the pore system, its total volume and the range of pore throat sizes. Simulation of capillary pressure uses standard percolation models to determine the displacement of wetting phase by the non-wetting phase – that is, mercury displacing air/vacuum – and generates a saturation vs pressure curve (figure 3). The simulated pressure is determined by the image resolution with one voxel representing the maximum pressure. The simulation allows for an easy switch between Hg/air systems to various oil/brine/gas scenarios with their own contact angles and interfacial tension values to correlate with other laboratory measurements such as centrifuge or porous plate experiments. The simulation also generates images of the distribution of wetting and non-wetting phases in the pores that assist the visualization of the displacement process.
Simulation of relative permeability is performed by solving fluid flow equations for the connected wetting and non-wetting phases at different saturation states defined by the segmented pore system. These saturation steps are usually determined from a simulation of the capillary pressure based on the connected pore system. The capillary pressure simulation determines the distribution of wetting and non-wetting phases within the segmented pores based on the parameters used for surface tension and contact angle and some assumptions on the thickness of the wetting layer.
The permeability calculation determines fluid velocity in the pore system with an implicit pressure-explicit momentum approach for the finite volume method at each saturation step. Boundary conditions include a pressure gradient between the inlet and outlet faces, and no-flow for the other directions, along with no-slip conditions at the pore-grain interface. Darcy’s law is then used to calculate the permeability constant at each saturation step with the pressure and velocity field generated by solver. The intrinsic permeability is calculated on the extracted pore geometry with no distinction between wetting and non-wetting phases.
Figure 4 shows how information extracted from high-resolution images can be used to calculate two- and three-phase relative permeability curves. The left-most figure compares simulated relative permeability values and trends for the wetting phase (blue) and non-wetting phase (green) against single point values measured on crushed samples taken from a very low-permeability core (red). The ternary diagrams on the right are different representations of three-phase relative permeability for a very low-permeability rock that cannot be duplicated in the laboratory.
All data management, image analysis, AI segmentation, and relative permeability simulations are supported by DigiM I2S software.