DigitalROCK functions as a reservoir rock analysis technique that can provide important petrophysical properties including porosity and permeability. As with RCAL (routine core analysis lab) and SCAL (special core analysis lab) physical testing, Digital Rock uses a rock sample retrieved from the subsurface. Once a sample of interest is obtained, a series of steps comprising the workflow are carried out. Typically, a small plug is drilled out and 3D imaging is performed on this plug with a micro-CT scanner. The raw image data is enhanced with image processing algorithms to better distinguish between the pore space and the solid material of the rock. The resulting 3D image is used to perform geometrical studies, analysis of the pore space available to fluids, and finally fluid flow simulations to predict critical flow properties needed for reservoir modeling/engineering.
- Sample Plug
- 3D Imaging
- Image Processing/Segmentation
- Pore Space Analysis
- Mercury Injection Capillary Pressure (MICP)
- Flow Simulation of Single Phase Absolute Permeability (K0)
- Flow Simulation of Multi-Phase Relative Permeability (KR)
1. Sample Plug
The first step in the digital rock workflow is to obtain a small piece that is optimally sized for imaging from the rock sample. This is typically done by drilling out a small cylindrical plug, usually about 1” long and 1/5” diameter. If the rock sample is not strong enough to withstand the drilling, a polymer stabilizing process can be used, where a liquid polymer fills the pore space and then hardens.
Pore-scale imaging of the prepared plug is performed using a micro-CT scanner that generates a stack of 2D slices, usually oriented along the central axis of the cylinder. The pore space which governs fluid flow in most sandstone reservoir rocks and some carbonates consists of pores in the 1-100um size range, allowing the use of micro-CT technology for digital rock applications. When necessary, other imaging techniques (e.g. FIB-SEM) can be used to resolve sub-micron features.
Micro-CT images capture the density within the sample, resulting in grayscale images like the ones shown above. Dense materials appear as lighter shades, while lower density regions appear as darker voxels. Given that pores are filled with air (or polymer) and the rock matrix is composed of heavier solid minerals, a visual distinction between pore and rock can be achieved.
3. Image processing/segmentation
In order to use a pore-scale 3D image for computational analysis and simulation, it is necessary to determine for each location in the image whether it should be considered pore space or solid rock. Ideally it would be straightforward to segment the grayscale image into a black (pore) and white (grain) binary representation of the scan using a simple color threshold. However, even when the difference between pore and rock seems visually apparent, real images always contain noise, scanning artifacts, and other features that interfere with the accuracy of simple color thresholding. To avoid altering the pore space geometry, and thereby affecting the downstream analyses, it is necessary to include various image processing techniques as part of the image segmentation process to correct for non-physical scan noise and defects.
The above images are before/after examples of an image segmentation process in which noise has been removed and the overall pore to grain contrast has been enhanced. Image segmentation is a critical and often challenging step for any digital rock application. When a proper image segmentation has been achieved, a geometric representation of the 3D pore space can be generated, as shown in the example below.
4. Pore Space Analysis
Before running a fluid flow simulation on the 3D pore space geometry, a Pore Space Analysis (PSA) is carried out to examine several important attributes of the rock sample. These include overall porosity, connected porosity, and pore size distribution. An example whole field visualization of pore size distribution is shown for 3 different samples below.
Another important quantity generated by PSA is the critical pore throat radius (also called percolation threshold), which indicates the minimum pore size necessary to have a connected flow path through the sample. PSA is also used to estimate the representative elementary volume (REV) of the sample, which is the minimum domain size needed to have an adequate statistical representation of the pore space. Ideally, the image domain will be a few orders of magnitude bigger than the largest pores, with enough resolution to capture the entire range of pore sizes relevant to fluid flow. REV is studied by looking at subdomains of increasing size and observing the variation in quantities such as porosity. Very small domains will suffer high levels of noise; e.g. a region entirely within a solid grain will have zero porosity while one mostly inside a pore will have very high porosity. As domain size is increased to contain hundreds of pores and grains, porosity (and other quantities) will asymptote to a representative value. It is particularly important to determine REV so that subsequent fluid flow simulations are well sized; if the simulated domain is too small then the calculated fluid flow properties are not representative, while simulating larger domains than needed would result in unnecessary computational expense.
5. Mercury Injection Capillary Pressure (MICP)
MICP curves are one of the most common and basic types of core analysis data. During an MICP test, pressure is increasingly applied at a sample’s boundary while the volume of intruded pore space is measured. The resulting curve is used to characterize the rock’s pore structure and identify features such as dual porosity systems; it also provides an estimate of the fraction of total oil that is recoverable, and is often helpful for interpretation of relative permeability lab test results. The plot below shows an example Digital Rock MICP curve predicted by running an intrusion test algorithm on the digital pore space. A visual representation of the intruded pore space can be obtained for every applied pressure; two such images are shown below.
6. Flow Simulation of Single Phase Absolute Permeability (K0)
Once a PSA is carried out on a segmented 3D image, an REV has been determined, and pore connectivity has been assessed, a flow simulation can be performed to predict absolute permeability for a chosen flow direction. The Exa Digital Rock flow simulator is based on an enhanced lattice Boltzmann method (LBM) with a surface element (surfel) based boundary scheme, providing a high fidelity geometric representation of the boundary and precise control of surface fluxes. The use of surfels effectively adds sub-voxel resolution to the pore/grain boundary. To highlight the importance of the flow simulation boundary scheme for digital rocks, the figure below zooms in on a tiny portion of a 2D image slice of a Berea sandstone, comparing the stair-step boundary formed by the underlying cubic grid (left) to the surfel-based boundary (right) for a typical computational grid resolution (critical pore throat radius of less than 5 grid cells).
To alleviate stair-step boundaries, other LBM implementations commonly use point-wise interpolation schemes; however, these methods face challenges in controlling the fluxes at the wall, such as ensuring exact mass conservation. In contrast, Exa’s unique proprietary method provides precisely defined boundary locations, exact control of surface fluxes, and robust handling of extremely complex digital rock geometry.
Single phase flow simulations can be performed on domains over 10003 computational grid cells, providing the sample’s permeability, and the velocity field throughout the domain (as shown below).
The results can be used to compare samples from the same well, reservoir or field. A variety of well stimulation techniques and formation damage can also be studied.
Along with individual sample permeability values, each Exa Digital Rock k0 flow simulation also provides a porosity-permeability trend, generated by evaluating subvolumes of the simulated domain. The example below shows a plot of permeability vs porosity for subsamples obtained by dividing the original simulated domain into 8ths (blue) and 27ths (black). This type of correlation can be used, for example, to estimate the permeabilities as a function of depth based on the porosities measured from well log data.
7. Flow Simulation of Multi-phase relative permeability (KR)
In addition to the pore space geometry, relative permeability simulations require specification of initial fluid distribution, surface wetting condition, and the overall flow rate, which is held fixed during the test and can be represented in non-dimensional form as a parameter known as Capillary number. A series of steps are taken for multi-phase flow simulations to estimate a proper initial fluid distribution and wetting condition, which are essential to modeling reservoir conditions. The initial volume fraction of water is estimated from the MICP intrusion test, with small pores assumed to be water wet and large pores oil wet.
Wettability, such as water-wet, oil-wet, or neutral, is an indication of the distribution of contact angles on the surfaces of the pores. In the Exa Digital Rock technology, any contact angle (from 0-180o) can be assigned to any surface element within the simulation domain in terms of contact angles. A prescribed contact angle distribution is assigned based on a measured or estimated wettability index. Example 3D representations are shown for the initial fluid distribution, contact angle distribution, and predicted relative permeability results (linear and log plots).