This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada
Net confining stress or NCS caused by overburden pressure on a rock-sample and the internal pore pressure can affect rock properties, such as porosity and permeability. While the mechanical stresses on a rock in the subsurface can be high and are dependent on the depth, pore pressure and local geology, laboratory testing for the above mentioned properties are often performed at rather low confining pressures. For digital rock physics applications, micro-CT images are typically obtained at ambient conditions and imaging under reservoir stress conditions can be complicated and compromise on image quality, resolution, and field of view.
To understand the variation of rock porosity and permeability as a function of NCS and to improve the accuracy of the prediction of rock properties for reservoir engineering, a digital workflow to directly simulate the compaction of an unconsolidated sand is presented. The process involves using a finite element analysis tool to apply stresses to a solid system made out of sand grains, extract the geometry, and compute permeability with a Lattice-Boltzmann solver for different stress states.
The generation of the distribution of sand grains before and after compaction is done using a finite element (FE) solver. For each sand grain, a finite element mesh is generated. Initially, all sand grains are randomly arranged within a rigid container so that the grains do not touch each other or the container – they are floating. The process of all sand grains falling into the container is directly simulated using a FE method by applying gravity to all sand grains. The initial location and orientation of the grain space is obtained when all sand grains come to a full halt. A FE model of a rigid plate is put on top of the loose sand pack. A second FE calculation is performed to simulate the compaction process by defining a step-wise displacement of the plate. The applied movement leads to relocation of sand grains, as well as to some elastic deformation of sand grains. The resulting force on the plate is measured and converted to the corresponding NCS.
The sand grains at initial and compacted conditions can be used to derive pore spaces for the evaluation of absolute permeability as a function of NCS. For the corresponding direct fluid flow simulation at pore scale, a Lattice-Boltzmann method based approach is used.
The results of the structural compaction of the sand pack are compared to reported compaction characteristics of unconsolidated sand from Pomponio Beach (Zimmer, 2003). The stress dependent porosity reduction is overall captured, but slightly under-predicted compared to Zimmer’s data. The reason for the under-prediction of porosity could lay in the absence of modelling plastic deformations which include grain crushing and grain-grain penetration (ductility).
The NCS dependent permeability curve follows the behaviour of a weakly consolidated sandstone up to 20 MPa. We see larger deviations in permeability reduction for higher stress levels where plastic deformations occur in real rocks. Another potential reason for the discrepancy is that the sand used in this computation does not contain gaps and fractures which are known to be very sensitive to NCS.
The current compaction process modelling includes grain relocation as well as elastic deformations. While the overall NCS induced porosity and permeability reduction follows published data from laboratory experiments, a slight under-prediction of the compaction effect can be seen. Additional modelling including plastic deformations should improve the results further.
To the best of the authors’ knowledge, this is the first published investigation of a workflow for digital analysis of NCS effects on porosity and permeability of three-dimensional grain and pore spaces.
|Date||18th June 2019|