Speaker
Description
Three-phase flow in porous media is encountered in several recovery and storage operations in subsurface reservoirs, including water-alternate-gas injections for improved oil recovery as well as permanent CO2 storage and seasonal gas storage in reservoirs containing residual oil. Such fluid injections are often slug-wise or cyclic, leading to multiple irreversible drainage and imbibition processes in the reservoir that must be described by three-phase capillary pressure and relative permeability as functions of saturations with hysteresis. Reservoir simulations typically describe these flow functions using correlations and hysteresis loop logic. However, this approach could be inaccurate, as three-phase correlations are often constructed based on more readily available two-phase data and saturation-weighted interpolation, and it is also a challenge to describe accurately higher-order scanning curves and trapped saturations in three-phase systems. Typically, measuring enough hysteresis-loop data from three-phase core-scale experiments is not feasible, and pore-scale simulation of these relations directly on micro-CT images is computationally demanding.
The discrete-domain model (DDM) represents an efficient, physics-based, method to describe hysteresis in three-phase systems [1]. DDM divides the porous rock into a set of compartments where, for each compartment and fluid phase, an evolution equation relates the Helmholtz energy contribution to the local phase saturation and pressure. By imposing certain saturation constraints and corresponding Lagrange multipliers that couple the equations together, DDM simulates three-phase capillary displacements with hysteresis controlled by either pressure, saturation or given saturation trajectories. The hysteresis occurs due to irreversible saturation jumps across energy barriers separating the local energy minima. The inclusion of saturation constraints leads to three-phase displacements with fluid redistribution among compartments (cooperative behavior), as well as pressure and saturation jumps.
Thus far, the DDM has only employed simple phenomenological energy functions. The objective of this work is to explore the applicability of the DDM on realistic three-phase data from rock samples. For this purpose, we use a multiphase level set (MLS) model [2, 3] to simulate three-phase capillary-controlled displacement for gas-water invasion cycles in Castlegate sandstone after a two-phase saturation history. The three-phase MLS simulations explore pressure- and saturation-controlled displacement modes with and without global preservation of the oil saturation. The generated data from saturation-controlled MLS simulations is used to calculate energy functions in the saturation space for different compartment architectures in the DDM. From the data we also explore differences in the energy functions between drainage and imbibition.
The DDM reproduces the capillary pressure curves from MLS simulations using the energy functions from the saturation-controlled case, including the pressure- and saturation-jump features. A finer compartment division of the rock sample leads to more energy minima and smoother results in the DDM. Using the same energy landscape for either drainage or imbibition on all processes (including scanning curves) leads to a slight deviation from the MLS results, whereas the case with different energy landscapes for drainage and imbibition shows excellent agreement. Hence, the DDM emerges as a suitable pore-to-core upscaling approach for hysteresis as its compartmental description is based on extensive properties.
| References | [1] Helland, J. O., Jettestuen, E., Friis, H. A. (2021). A discrete-domain approach to three-phase hysteresis in porous media. Water Resources Research 57, e2021WR029560. https://doi.org/10.1029/2021WR029560. [2] Helland, J.O., Pedersen, J., Friis, H. A., Jettestuen, E. (2019). A multiphase level set approach to motion of disconnected fluid ganglia during capillary-dominated three-phase flow in porous media: Numerical validation and applications, Chemical Engineering Science 203, 138-162. https://doi.org/10.1016/j.ces.2019.03.060. [3] Jettestuen, E., Friis, H. A., Helland, J. O. (2021). A locally conservative multiphase level set method for capillary-controlled displacements in porous media, Journal of Computational Physics 428, 109965. https://doi.org/10.1016/j.jcp.2020.109965. |
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| Country | Norway |
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