Pore Architecture Models (PAMs) and the Prediction of Petrophysical (and Other) Properties
A team led by Dr. Gary D. Couples (gary.couples@pet.hw.ac.uk) of Heriot-Watt Institute of Petroleum Engineering (http://www.pet.hw.ac.uk/) is developing numerical tools that reconstruct porous rocks (or other materials), and additional tools that are used to calculate flow properties of the reconstructed media. Additional work is underway to develop techniques that will enable the team to predict other physical properties, such as rock mechanics, acoustics, and dielectrics. This article illustrates recent developments in the reconstruction effort, and also shows some of the results obtained from the work to predict petrophysical properties.
What determines the petrophysical properties of porous rocks? A first-order control is the pore network - which we can take to mean the spatial arrangement of pores and their connections. For understanding multi-phase flow properties, the characteristics of the solid components are also important (mineralogy of the grains and cements, their surface attributes, etc). It was once believed that textural descriptions of rocks (grain size, sorting, packing) would be the key to predicting the flow properties, but that hope was not realised. In more-recent times, researchers have sought to find “equivalent” pore networks whose flow properties are equivalent to laboratory measurements. The work described here represents a marriage of both approaches.
Working with the SIMBIOS Group, based at the University of Abertay Dundee (Prof. John Crawford and Prof Iain Young), the team at the Heriot-Watt Institute of Petroleum Engineering have developed a technique to create 3D reconstructions (PAMs = Pore Architecture Models) of porous media using input data derived from thin sections. The initial motivation for PAMs arose in regard to the work on soil biophysics at Abertay, but has been extended to rocks at Heriot-Watt.
Dr Kejian Wu has played a continuing role in this development, initially in Dundee and now at Heriot-Watt. The numerical method he has created differs, in detail, from similar stochastic methods developed by other research teams. Importantly, the approach does not have a fundamental scale limitation as do tomographic methods. The PAMs algorithm has been applied to a range of sample types (soils, reservoir sandstones, deformed rocks, mudstones), creating realisations that look like the original sample (Figure 1). Recent work by Dr. Wu has enhanced the algorithms to better capture sample heterogeneity.
Figure 1: Examples of 3D Cubes Generated by the PAMs Algorithm. (The top row shows thin section photomicrographs, and the bottom row shows the reconstructed porous medium, based on the thin section images. The models, from left to right, are: high-quality sandstone, slightly-deformed sandstone, sandstone with shear band, and vuggy carbonate.)
The PAMs algorithm creates a voxelated structure representing solids and voids. Such a model serves as an ideal input to flow simulation using a Lattice-Boltzmann (LB) scheme. The present LB method was developed at Abertay by Xiaoxian Zhang. For the majority of the rock samples analysed thus far (~50), the calculated flow properties agree very well with the measured permeabilities. If the input data image(s) used to construct a PAM contains directional fabrics, then the directional LB flow calculation leads to the estimation of a directional permeability tensor (Figure 2).
Figure 2: Example Showing a Directional Permeability Prediction Using a Lattice-Boltzmann Scheme. (The thin section image on the left shows a moderately-deformed sample, and the PAM in the centre captures the texture of this sample. The image on the right shows the permeability variation calculated for the central cube.)
A separate suite of numerical tools has been developed at HWU (by Dr. Kejian Wu and Zeyun Jiang, who is beginning a PhD study at Heriot-Watt, with additional contributions by Dr Jingsheng Ma jingsheng.ma@pet.hw.ac.uk) to analyse the pore systems of reconstructed porous media - such as the PAMs described above. These methods make use of the IDL6.0 toolkit (marketed by RSI - http://www.rsinc.com). After extracting the complete pore system of a model, simple geometric shapes are fitted to all of the components. Pore size distribution is readily calculated, along with several topological descriptors (Figure 3).
Figure 3: Illustration of Pore-Size Determination. (The thin section is from a reservoir sandstone. The second image shows the pore system, colour-coded by pore size. The plot on the right shows the pore-size distribution. The large variation at about 30 µm is associated with the key pores that control the critical entry pressure.)
The pore network can be used as input to more complex flow simulations. One example of this use is to calculate the response of the model to a simulated mercury injection process. It is possible to run the simulation to obtain directional mercury injection curves (Figure 4).
Figure 4: Illustration (left) Showing an Extracted (Skeletonised) Pore Network. (The plot on the right shows the simulated mercury injection results, compared with the measured data for this sample.)
Thus far, the team have considered a range of rock types, and the methods seem to work very well in most cases - with calculated properties being very close to the measured data. It appears that the approach may represent a valuable new tool to enable operators to determine (estimate) petrophysical properties. Work is underway to develop additional tools to allow the calculation of other properties - such multi-phase flow, acoustic velocity, and mechanical strength. A 2D version of the mechanical prediction method has given encouraging results.
The HWU team is now seeking to undertake a substantial trial involving a number of samples provided by sponsoring companies. For a copy of the proposal describing the trial, please contact Dr. Gary Couples Tel: +44 (0)131 451 3123