High-resolution climate simulations are increasingly in demand and require tremendous computing resources. In the Community Earth System Model (CESM), the Parallel Ocean Model (POP) is computationally expensive for high-resolution grids (e.g., 0.1 •) and is frequently the least scalable component of CESM for certain production simulations. In particular, the modified Preconditioned Conjugate Gradient (PCG), used to solve the elliptic system of equations in the barotropic mode, scales poorly at the high core counts, which is problematic for high-resolution simulations. In this work, we demonstrate that the communication costs in the barotropic solver occupy an increasing portion of the total POP execution time as core counts are increased. To mitigate this problem, we implement a preconditioned Chebyshev-type iterative method in POP (called P-CSI), which requires far fewer global reductions than PCG. We also develop an effective block preconditioner based on the Error Vector Propagation Method to attain a competitive convergence rate for P-CSI. We demonstrate that the improved scalability of P-CSI results in a 5.2x speedup of the barotropic mode in high-resolution POP on 16,875 cores, which yields a 1.7x speedup of the overall POP simulation. Further, we ensure that the new solver produces an ocean climate consistent with the original one via an ensemble-based statistical method.

the understanding of water adsorption and desorption behavior in the shale rocks is of great significance in the reserve estimation, wellbore stability and hydrocarbon extraction in the shale gas reservoirs. However, the water sorption behavior in the shales remains unclear. In this study, water vapor adsorption/desorption isotherms of the Longmaxi shale in the Sichuan Basin, china were conducted at various temperatures (30 °C, 60 °C) and a relative pressure up to 0.97 to understand the water sorption behavior. Then the effects of temperature and shale properties were analyzed, and the water adsorption, hysteresis, saturation and capillary pressure were discussed. The results indicate that water adsorption isotherms of the Longmaxi shale exhibit the type II characteristics. The water molecules initially adsorb on the shale particle/pore surfaces at low relative pressure while the capillary condensation dominates at high relative pressure. Temperature favors the water sorption in the shales at high relative pressure, and the GAB isotherm model is found to be suitable for describe the water adsorption/desorption behavior. The high organic carbon and full bedding are beneficial to water adsorption in the shales while the calcite inhibits the behavior. There exists the hysteresis between water adsorption and desorption at the whole relative pressure, which suggests that the depletion of condensed water from smaller capillary pores is more difficult than that from larger pores, and the chemical interaction contributes to the hysteresis loop for water sorption. The capillary pressure in the shales can be up to the order of several hundreds of Mpa, and thus the desorption of water from the shales may not be as easy as the water adsorption due to the high capillary pressure, which results in water retention behavior in the shale gas reservoirs. these results can provide insights into a better understanding of water sorption behavior in the shale so as to optimize extraction conditions and predict gas productivity in the shale gas reservoirs.

Efficiently and accurately understanding the fluid flow behavior in ultra-deep natural gas reservoirs is very challenging due to the complex geological environment and the intricate gas properties at high pressure. In this study, a fully coupled fluid flow and geomechanical model was developed to simulate complex production phenomena in ultra-deep natural gas reservoirs. Stress-dependent porosity and permeability models were applied, and then the governing equations of the model were incorporated into COMSOL Multiphysics. Furthermore, the model was verified by the reservoir depletion from the Keshen gas field in China, and the effects of reservoir properties and geomechanics on gas production were discussed. The results showed that the reservoir pressure and water saturation exhibited a significant funnel-shaped decline during the reservoir depletion. The higher relative permeability of the gas phase results in more methane gas production, thereby reducing the average pore pressure and gas saturation near the wellhead. When considering geomechanical effects, the production behavior significantly changes. The predictive value of gas production was higher when the reservoir rock deformation was ignored. The gas production exhibited strong positive correlations with reservoir porosity, fracture permeability, elastic modulus, and Poisson's ratio. Larger porosity, elastic modulus, and Poisson's ratio resulted in smaller deformation, while a smaller fracture permeability leads to larger deformation in ultra-deep natural gas reservoirs.

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Abstract. In the Community Earth System Model (CESM), the ocean model is computationally expensive for highresolution grids and is often the least scalable component for high-resolution production experiments. The major bottleneck is that the barotropic solver scales poorly at high core counts. We design a new barotropic solver to accelerate the high-resolution ocean simulation. The novel solver adopts a Chebyshev-type iterative method to reduce the global communication cost in conjunction with an effective block preconditioner to further reduce the iterations. The algorithm and its computational complexity are theoretically analyzed and compared with other existing methods. We confirm the significant reduction of the global communication time with a competitive convergence rate using a series of idealized tests. Numerical experiments using the CESM 0.1 • global ocean model show that the proposed approach results in a factor of 1.7 speed-up over the original method with no loss of accuracy, achieving 10.5 simulated years per wall-clock day on 16 875 cores.

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We show that every sum of squares in the three-variable Laurent series field R( (x, y, z) ) is a sum of 4 squares, as was conjectured in a paper of Choi, Dai, Lam and Reznick in the 1980's. We obtain this result by proving that every sum of squares in a finite extension of R( (x, y) ) is a sum of 3 squares. It was already shown in Choi, Dai, Lam and Reznick's paper that every sum of squares in R( (x, y) ) itself is a sum of two squares. We give a generalization of this result where R is replaced by an arbitrary real field. Our methods yield similar results about the u-invariant of fields of the same type.

Gas content and flow characteristics are closely related to shale lithofacies, and significant differences exist in the pore structure and fractal characteristics among lithofacies. In this study, X-ray diffractometer (XRD), field-emission scanning electron microscopy (FE-SEM), gas adsorption (N 2 and CO 2 ), and fractal theory were employed to systematically characterize the pore attributes of the marine Wufeng−Longmaxi formation shales. The information of various pores and microfractures among lithofacies was extracted and quantified via high-resolution FE-SEM image stitching technology. Shales were classified into four types based on mineral compositions, and siliceous shales possess the largest SEM-based surface porosity (2.84%) and the largest pore volume (PV) (average 0.0243 cm 3 /g) as well as specific surface area (SSA) (average 28.06 m 2 / g). The effect of lithofacies variation on the PV of shale is minor. In contrast, the lithofacies variation has a significant impact on the SSA, and the SSA of siliceous shale is 39.11% higher than that of argillaceous shale. PV and SSA show strong positive correlation with the total organic carbon (TOC) content but negative correlation with clay minerals. Siliceous shales have the greatest fractal dimension D1 (pore surface roughness) (average 2.6821), which is contributed by abundant organic matter pores with more complicated boundaries. The largest fractal dimension D2 (pore structure complexity) (average 2.8263) is found in mixed shales, which is attributed to well-developed intraparticle (intraP) pores associated with carbonate mineral dissolution. This indicates that siliceous shales have the highest methane adsorption capacity and that shale gas desorption, diffusion, and seepage are more difficult in mixed shales.