A Permeability Estimation Method Based on Elliptical Pore Approximation

Digital rock images may capture more detailed pore structure than the traditional laboratory methods. No explicit function can correlate permeability accurately for flow within the pore space. This has motivated researchers to predict permeability through the application of numerical techniques, e.g., using the finite difference method (FDM). However, in order to get better permeability calculation results, the grid refinement was needed for the traditional FDM and the accuracy of the traditional method decreased in pores with elongated cross sections. The goal of this study is to develop an improved FDM (IFDM) to calculate the permeabilities of digital rock images with complex pore space. An elliptical pore approximation method is invoked to describe the complex pore space. The permeabilities of four types of idealized porous media are calculated by IFDM. The calculated results are in sound agreement with the analytical solutions or semi-empirical solutions. What’s more, the permeabilities of the digital rock images after grid coarsening are calculated by IFDM in three orthogonal directions. These results are compared with the previously validated lattice-Boltzmann method (LBM), which indicates that the predicted permeabilities calculated by IFDM usually agree with permeabilities calculated by LBM. We conclude that the presented IFDM is suitable for complex pore space.

Numerical Simulations of Surfactant Flooding in Carbonate Reservoirs: The Impact of Geological Heterogeneities Across Scales

We demonstrate how geological heterogeneity impacts the effectiveness of surfactant-based enhanced oil recovery (EOR) at larger (inter-well and sector) scales when upscaling small (core) scale heterogeneity and physicochemical processes. We used two experimental datasets of surfactant-based EOR where spontaneous imbibition and viscous displacement, respectively dominate recovery. We built 3D core-scale simulation models to match the data and parameterize surfactant models. The results were deployed in high-resolution models that preserve the complexity and heterogeneity of carbonate formations in the inter-well and sector scale. These larger-scale models were based on two outcrop analogues from France and Morroco, respectively, which capture the reservoir architectures inherent to the productive carbonate reservoir systems in the Middle East. We then assessed and quantified the error in production forecast that arises due to upscaling, upgridding, and simplification of geological heterogeneity. Simulation results showed a broad range of recovery predictions. The variability arises from the choice of surfactant model parameterization (i.e., spontaneous imbibition vs viscous displacement) and the way the heterogeneity in the inter-well and sector models was upscaled and simplified. We found that the parameterization of surfactant models has a significant impact on recovery predictions. Oil recovery at the larger scale was observed to be higher when using the parametrization derived from viscous displacement experiments compared to parameterization from spontaneous imbibition experiments. This observation clearly demonstrated how core-scale processes impact recovery predictions at the larger scales. Also, the variability in recovery prediction due to the choice of surfactant model was as large as the variability arising from upscaling and upgridding. Upscaled and upgridded models overestimated recovery because of the simplified geology. Grid coarsening exacerbated this effect because of the increased numerical dispersion. These results emphasize the need to use correctly configured surfactant models, appropriate grid resolution that minimizes numerical dispersion, and properly upscaled reservoir models to accurately forecast surfactant floods. Our findings present new insights into how the uncertainty in production forecasts during surfactant flooding depends on the way surfactant models are parameterized, how the reservoir geology is upscaled, and how numerical dispersion is impacted by grid coarsening.

Toward a large-scale particle-based parallel simulator of Aeolian sand transport, including a model for mobile sand availability

We develop a numerical tool for particle-based simulations of Aeolian sand transport. Our model combines a Discrete-Element-Method for the sand particles with an efficient hydrodynamic description of the average turbulent horizontal wind velocity field over the granular bed, which has been developed in previous work and accounts for the two-way coupling of the granular and fluid phases. However, here we implement our model within the open source library LAMMPS for granular massively parallel simulations and incorporate a new grid coarsening scheme for the wind model. We show that our model quantitatively reproduces observed values of the steady-state (saturated) sand flux under various flow conditions. Furthermore, we model different conditions of mobile sand availability and find a strong dependence of the sand flux on this availability.

Long term hydrologic simulations for the meso-scale catchments Rur and Bode in Germany by TSMP

<p>Integrated terrestrial systems modeling is important for the comprehensive investigation of the coupled terrestrial water, energy and biogeochemical cycles. In this work, we applied the Terrestrial Systems Modeling Platform (TSMP) to the two meso-scale catchments in Germany (Rur and Bode) to conduct a long time hydrologic simulation with a focus on variables such as soil moisture, evapotranspiration (ET) and groundwater recharge. Simulations for the Rur and Bode catchments were performed at three different spatial horizontal model resolutions (1000, 500, and 200m) with CLM and CLM-PF in TSMP. Each of the three resolution models was run for 24 years (1995-2018) with transient atmospheric forcings derived from COSMO-REA6 data. The long term simulation results show that the summer of 2018 resulted in the lowest soil moisture content over the time series that is around 0.20, lower than the dry summers of 1995 and 2003. ET was more reduced in July-August 2018 due to the decrease of soil moisture content during this period. Nevertheless, actual evapotranspiration was even in the summer of 2018 often not limited by soil moisture content. For these catchments ET is most of the time energy limited. In addition, the vegetation evaporation (resulting from interception) accounts for the smallest percentage of the ET (ca. 20%), whereas the vegetation transpiration and soil evaporation account for almost the same percentage of the total ET (each 40% approximately). Both the CLM and CLM-PF simulation results indicate that grid coarsening (lower model resolution) leads to larger ET and soil moisture content, which is related to the decreasing slope gradient with grid coarsening. The analysis of groundwater recharge is underway.</p>

Development and Validation of a Hybrid RANS-LES Approach Based on Temporal Filtering

To address the challenge of controlling the energy partition in hybrid RANS-LES methods, the use of a consistent operator based on temporal filtering is desirable. This formalism leads to the development of a consistent continuous hybrid RANS-LES approach called Hybrid Temporal LES (HTLES). In this paper, an upgraded version of HTLES is presented, focusing on improving the model for wall-bounded flows. Notably, a shielding function is integrated in the model to impose the RANS behavior in the near-wall regions. The calibration and validation of the hybrid method applied to the standard k-ω-SST model is then carried out on several test cases: decaying isotropic turbulence, channel flow and periodic-hill flow. The new version of the model fulfills the specifications: the correct subfilter dissipation; the correct migration from RANS to LES in the boundary layer; the robustness of the results to grid coarsening; the accuracy of the predictions at a reasonable computational cost.

Aquifer Acceleration in Parallel Implicit Field-Scale Reservoir Simulation

Summary Grid coarsening outside of the areas of interest is a common method to reduce computational cost in reservoir simulation. Aquifer regions are candidates for grid coarsening. In this situation, upscaling is applied to the fine grid to generate coarse-grid flow properties. The efficacy of the approach can be judged easily by comparing the simulation results between the coarse-grid model and the fine-grid model. For many reservoirs in the Middle East bordered by active aquifers, transient water influx is an important recovery mechanism that needs to be modeled correctly. Our experience has shown that the standard grid coarsening and upscaling method do not produce correct results in this situation. Therefore, the objective of this work is to build a method that retains the fine-scale heterogeneities to accurately represent the water movement, but to significantly reduce the computational cost of the aquifer grids in the model. The new method can be viewed as a modified two-level multigrid (MTL-MG) or a specialized adaptation of the multiscale method. It makes use of the vertical-equilibrium (VE) concept in the fine-scale pressure reconstruction in which it is applicable. The method differs from the standard grid coarsening and upscaling method in which the coarse-grid properties are computed a priori. Instead, the fine-scale information is restricted to the coarse grid during Newton's iteration to represent the fine-scale flow behavior. Within the aquifer regions, each column of fine cells is coarsened vertically based on fine-scale z-transmissibility. A coarsened column may consist of a single amalgamated aquifer cell or multiple vertically disconnected aquifer cells separated by flow barriers. The pore volume (PV), compressibility, and lateral flow terms of the coarse cell are restricted from the fine-grid cells. The lateral connectivity within the aquifer regions and the one between the aquifer and the reservoir are honored, inclusive of the fine-scale description of faults, pinchouts, and null cells. Reservoir regions are not coarsened. Two alternatives exist for the fine-scale pressure reconstruction from the coarse-grid solution. The first method uses the VE concept. When VE applies, pressure variation can be analytically computed in the solution update step. Otherwise, the second method is to apply a 1D z-line solve for the fine-scale aquifer pressure from the coarse-grid solution. Simulation results for several examples are included to demonstrate the efficacy and efficiency of the method. We have applied the method to several Saudi Arabian complex full-field simulation models in which the transient aquifer water influx has been identified as a key factor. These models include dual-porosity/dual-permeability (DPDP) models, as well as models with faults and pinchouts in corner-point-geometry grids, for both history match and prediction period. The method is flexible and allows for the optional selection of aquifer regions to be coarsened, either only peripheral aquifers or both the peripheral and bottom aquifers. The new method gives nearly identical results compared with the original runs without coarsening, but with significant reduction in computer time or hardware cost. These results will be detailed in the paper.

An adaptive multiscale algorithm for efficient extended waveform inversion

Subsurface-offset extended full-waveform inversion (FWI) may converge to kinematically accurate velocity models without the low-frequency data accuracy required for standard data-domain FWI. However, this robust alternative approach to waveform inversion suffers from a very high computational cost resulting from its use of nonlocal wave physics: The computation of strain from stress involves an integral over the subsurface offset axis, which must be performed at every space-time grid point. We found that a combination of data-fit driven offset limits, grid coarsening, and low-pass data filtering can reduce the cost of extended inversion by one to two orders of magnitude.

Balancing aggregation and smoothing errors in inverse models

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.