Finite-difference algorithm with local time-space grid refinement for simulation of waves

This paper presents a new approach to a local time-space grid refinement for a staggered-grid finite-difference simulation of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used, the finite-difference scheme preserves second order of convergence. We have proved that this approach is low-reflecting, the artificial reflections are about 10^− 4 of an incident wave. We have also shown that if a successive refinement is applied, i.e. temporal and spatial steps are refined at different interfaces, this approach is stable.     

SAGD开发中突破夹层技术对策研究

开发实践表明,稠油油藏内部发育的夹层影响蒸汽辅助重力泄油(SAGD)开发效果。实际SAGD开发应当充分考虑夹层对SAGD生产效果的影响,寻找突破夹层的有效对策,以期提高SAGD产量。以国内某超稠油油藏地质特征为基础,结合夹层岩石力学参数测试结果,利用耦合岩石力学数值模拟技术确定了不同参数(岩石力学参数、物性参数、操作参数)对岩石变形量、SAGD产量的敏感性。研究结果表明,夹层的渗透率和SAGD注汽压力是影响SAGD产量的主要因素。进一步地,针对夹层特征,结合实际操作可行性,提出了提高注汽压力和直井辅助两种突破夹层技术对策,并给出了相应的技术界限及突破效果,该研究结果可用于指导稠油油藏双水平井SAGD经济高效开发     

Spatial grid correction for short-term numerical simulation results of carbon dioxide dissolution in saline aquifers

Numerical simulation is an essential component of many studies of geological storage of carbon dioxide, but care must be taken to ensure the accuracy of the results. Unlike several other possible sources of simulation errors, which have previously been considered in detail and have well-understood techniques for mitigating their effects, comparatively little discussion of the spatial grid dependence of the dissolution rate of carbon dioxide into the formation water has appeared in the literature, despite its importance to simulation studies of geological storage of carbon dioxide in saline aquifers. In many instances, sufficient refinement of the computational grid can be a practical solution. However, this approach is not always feasible, especially for large-scale simulations in three dimensions requiring multiple realisations, which commonly feature a coarse grid due to constraints on available computational capabilities. A measure of the error in the amount of dissolved carbon dioxide introduced by the use of a finite grid is therefore of great interest. In this study, the use of finite-sized grid blocks is shown to overestimate the amount of dissolved carbon dioxide in short-term results by a factor of 1?+?V _f/V _p, where V _f is the grid block volume at the saturation front and V _p is the total grid block volume of the plume. This result can be used in a number of ways to correct the calculated short-term dissolution in coarse-scale simulations so that the amount dissolved agrees better with that obtained from fine-scale simulations.     

A review of SAGD technology development and its possible application potential on thin-layer super-heavy oil reservoirs

Super-heavy oil is a significant unconventional energy source, and more than 30 years of research have shown that steam-assisted gravity drainage (SAGD) technology is suitable for thick super-heavy oil reservoirs. Recently, more and more thin-layer super-heavy oil reservoirs have been discovered in China, while their deep buried depth and serous heterogeneity make the existing SAGD technology difficult to apply, so it is urgent to improve the existing SAGD technology for the thin-layer super-heavy oil. To this end, this paper focuses on the enlightenment of field application in SAGD technology. Firstly, based on typical SAGD field projects, the development history of SAGD technology in the world was reviewed, and the influence of reservoir physical properties on the application of SAGD technology in thin-layer super-heavy oil reservoirs was analyzed. Secondly, the well pattern, wellbore structure, pre-heating, artificial lift, and monitor technique of SAGD were detailed described, and their adjustment direction was expounded for the development of thin-layer super-heavy oil reservoirs. Lastly, the gas- and solvent-assistant SAGD were comprehensively evaluated, and their application potential in thin-layer super-heavy oil reservoirs was studied. The research results can provide theoretical guidance for the application of SAGD technology in thin-layer super-heavy oil reservoirs.     

Efficient multiphysics modelling with adaptive grid refinement using a MPFA method

A sequential solution procedure is used to simulate compositional two-phase flow in porous media. We employ a multiphysics concept that adapts the numerical complexity locally according to the underlying processes to increase efficiency. The framework is supplemented by a local refinement of the simulation grid. To calculate the fluxes on such grids, we employ a combination of the standard two-point flux approximation and a multipoint flux approximation where the grid is refined. This is then used to simulate a large-scale example related to underground CO₂ storage.     

Vertical equilibrium with sub-scale analytical methods for geological CO2 sequestration

Large-scale implementation of geological CO₂ sequestration requires quantification of risk and leakage potential. One potentially important leakage pathway for the injected CO₂ involves existing oil and gas wells. Wells are particularly important in North America, where more than a century of drilling has created millions of oil and gas wells. Models of CO₂ injection and leakage will involve large uncertainties in parameters associated with wells, and therefore a probabilistic framework is required. These models must be able to capture both the large-scale CO₂ plume associated with the injection and the small-scale leakage problem associated with localized flow along wells. Within a typical simulation domain, many hundreds of wells may exist. One effective modeling strategy combines both numerical and analytical models with a specific set of simplifying assumptions to produce an efficient numerical–analytical hybrid model. The model solves a set of governing equations derived by vertical averaging with assumptions of a macroscopic sharp interface and vertical equilibrium. These equations are solved numerically on a relatively coarse grid, with an analytical model embedded to solve for wellbore flow occurring at the sub-gridblock scale. This vertical equilibrium with sub-scale analytical method (VESA) combines the flexibility of a numerical method, allowing for heterogeneous and geologically complex systems, with the efficiency and accuracy of an analytical method, thereby eliminating expensive grid refinement for sub-scale features. Through a series of benchmark problems, we show that VESA compares well with traditional numerical simulations and to a semi-analytical model which applies to appropriately simple systems. We believe that the VESA model provides the necessary accuracy and efficiency for applications of risk analysis in many CO₂ sequestration problems.     

FV-MHMM method for reservoir modeling

The present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing defining accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called multiscale hybrid-mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach (Harder et al. 2013). We extend here the MH-mixed method to a finite volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively w.r.t. a posteriori error estimators. The method is applied to single phase (well-testing) and multiphase flow in heterogeneous porous media.     

超稠油油藏溶剂辅助蒸汽重力泄油室内实验研究

以国内某超稠油油藏为基础,应用二维物理模拟装置开展了蒸汽辅助重力泄油(SAGD)对比实验,研究了溶剂辅助SAGD技术对SAGD蒸汽腔发育特征、原油产量以及采收率的影响。研究结果表明,溶剂辅助SAGD中,溶剂以液相和气相共同存于油藏中,溶剂浓度越高,气相组分含量越高;溶剂中的气相组分在油藏中可以减少蒸汽在上覆岩层的热损失,提高蒸汽腔垂向扩展均匀性;合理溶剂浓度下,溶剂辅助SAGD可以显著提高峰值产量;低浓度溶剂辅助SAGD的单位原油产量的能耗明显低于纯蒸汽SAGD。实验结果表明,低浓度溶剂辅助SAGD对于开采超稠油油藏具有较大的应用潜力。     

Structure refinement of a nonstoichiometric pyroxene synthesized under ambient pressure

Structure refinement was carried out on a nonstoichiometric clinopyroxene grown under the ambient pressure from a glass with composition of 23%(mol)Di+53%Es+24%An. The degree of nonstoichiometry in this crystal is significantly larger than those of clinopyroxenes reported previously, which were found in high pressure products. The refinement gave the empirical chemical formula (Ca_0.742Fe_0.087)(Mg_0.016Al_0.888Fe_0.075)(Al_0.500Si_1.500)O₆ for the crystal and showed that vacancies are located mainly at M2 sites. Despite replacement of Si by Al, the crystal has a smaller cell volume than diopside primarily owing to a significant amount of Mg at M1 being replaced by Al. Received: 25 June 1997 / Revised, accepted: 6 September 1997     

泥质薄夹层不同参数对油砂SAGD 开发效果的影响

泥质夹层对油砂SAGD的开发效果具有一定影响。以加拿大麦凯河某区块为研究对象,利用数值模拟手段,对位于注入井上方和注采井间的泥质薄夹层进行表征,模拟对比了泥质薄夹层的位置、延展长度、渗透率、厚度以及条数对SAGD开发效果的影响,得到了油砂SAGD开发的泥质薄夹层的临界参数。研究表明,泥质薄夹层位于注入井上方时对SAGD开发效果影响较小,位于注采井间时有不利影响,且越靠近生产井,蒸汽腔发育越晚,累产油量越低。注采井间泥质薄夹层超过7条、延展长度超过20 m时蒸汽腔几乎不发育,而渗透率与厚度对SAGD开发效果影响不明显。因此油砂SAGD布井时注采井间应尽量避开泥质薄夹层,从而有效降低泥质薄夹层对SAGD的影响。该研究结果,对于指导油砂SAGD部署、规避地质风险、实现SAGD高效开发具有重要指导意义。     

Investigating CO<Subscript>2</Subscript>-enhanced oil recovery potential for a mature oil field: a case study based on Ankleshwar oil field,Cambay Basin,India

CO₂-enhanced oil recovery (EOR) is an upcoming technology in India. At present, no Indian field is under CO₂-EOR and implementation of this technique to a mature oil field needs a rigorous study. In the present work, we made an attempt to investigate the CO₂-EOR potential of a mature oil field, situated in Cambay Basin, India. The field was put on production in 1961, and it has produced approximately 65.36 MMt oil during massive water flooding, leading to residual oil reserves of 6.49 MMt. The operator of the field is interested in incremental oil recovery from this field by injecting CO₂. This requires estimation of incremental oil recovery potential of the field by carrying out systematic study. We, therefore, developed a conceptual model inspired by Ankleshwar oil field of Cambay Basin using available information provided by the field operator and carried out systematic studies to establish an optimized strategy for CO₂ injection. To achieve this goal, we investigated the effect of various operational parameters on oil recovery efficiency of our conceptual model and selected optimum parameters for reservoir simulations. Simulation results clearly indicate that the field can be a good candidate for CO₂-EOR, and an additional oil recovery of 10.4% of hydrocarbon pore volume is feasible. Major outcome of the study is an optimized black-oil simulation model, which is in good agreement with the fine grid compositional model of high accuracy. The proposed black-oil model can easily be implemented and updated compared with compute intensive finer compositional simulation model.     

自适应网格在复杂地形浅水方程求解中的应用

计算域内地形的概化精度对模拟结果有较大影响,针对实际地形中同时存在狭长河谷与广阔泛洪区的问题,在层次自适应网格模型的基础上,研究了网格快速加密与合并的步骤,并以水位梯度与局部弗劳德数为基础设计了网格自适应准则,当水流运动情势变化时网格密度自动调整,实现计算精度与效率的平衡。在此网格模型基础上,采用有限体积法求解二维浅水方程,利用梯度限制器技术及龙格-库塔法提高模型的空间、时间计算精度。算例表明,层次自适应网格模型既能实现随水流运动动态变化并捕获水位计算敏感区,也能对局部区域进行静态固定加密,自适应性良好,具有较好的推广应用价值。     

A stable space-time FE method for the shallow water equations

We consider the finite element (FE) approximation of the two dimensional shallow water equations (SWE) by considering discretizations in which both space and time are established using a stable FE method. Particularly, we consider the automatic variationally stable FE (AVS-FE) method, a type of discontinuous Petrov-Galerkin (DPG) method. The philosophy of the DPG method allows us to establish stable FE approximations as well as accurate a posteriori error estimators upon solution of a saddle point system of equations. The resulting error indicators allow us to employ mesh adaptive strategies and perform space-time mesh refinements, i.e., local time stepping. We establish a priori error estimates for the AVS-FE method and linearized SWE and perform numerical verifications to confirm corresponding asymptotic convergence behavior. In an effort to keep the computational cost low, we consider an alternative space-time approach in which the space-time domain is partitioned into finite sized space-time slices. Hence, we can perform adaptive mesh refinements on each individual slice to preset error tolerances as needed for a particular application. Numerical verifications comparing the two alternatives indicate the space-time slices are superior for simulations over long times, whereas the solutions are indistinguishable for short times. Multiple numerical verifications show the adaptive mesh refinement capabilities of the AVS-FE method, as well the application of the method to some commonly applied benchmarks for the SWE.

     

A method for quantitative pyrite abundance in mine rock piles by powder X-ray diffraction and Rietveld refinement

The abundance of pyrite and other sulfide minerals in mine rock piles is a potentially significant if not a determinative factor in terms of the geochemical and geomechanical evolution of the dumps as oxidation produces acid solutions that drive hydrolysis reactions. A technique is presented here that supports the quantitative determination of pyrite abundance in mine rock dumps by heavy liquid mineral separation to concentrate pyrite for powder X-ray diffraction and then Rietveld method refinement of the diffraction data on a large number of samples using commonly available laboratory equipment. In order to improve and constrain the accuracy of XRD results, binary (pyrite-quartz) and 6-part mineral mixtures (pyrite and rock-forming andesite minerals) spanning a wide range of pyrite concentrations were prepared gravimetrically and run as standards. These standards were then used to minimize errors in pyrite abundance data by constraining key input parameters in the Rietveld refinement. A new polynomial relationship was derived between diffracting crystallite size and the Brindley microabsorption correction input size. This method provides a means to determine uncertainties in pyrite abundance, whereas conventional Rietveld refinement techniques done without the use of standards yield only statistical measures of the least-squares fit, rather than absolute uncertainties in mineral constituent weight percentages. The technique was applied to a number of mine rock pile samples and the uncertainty in the results determined by applying the relationship derived from the 6-part gravimetric standards to the results of the Brindley corrected Rietveld refinements. Uncertainties determined by this method are found to be on the order of ±10% for samples with pyrite content greater than 10 wt% and ±30% for samples with pyrite content less than 10 wt%. In order to evaluate the technique’s improvement upon traditional visual mineral abundance estimation the quantitative results are compared to manual volumetric estimates.     

Modeling atmospheric chemistry and transport with dynamic adaptive resolution

We discuss an adaptive resolution system for modeling regional air pollution based on the chemical transport model STEM. The grid adaptivity is implemented using the generic adaptive mesh refinement tool Paramesh, which enables the grid management operations while harnessing the power of parallel computers. The computational algorithm is based on a decomposition of the domain, with the solution in different subdomains being computed with different spatial resolutions. Various refinement criteria that adaptively control the fine grid placement are analyzed to maximize the solution accuracy while maintaining an acceptable computational cost. Numerical experiments in a large-scale parallel setting (~0.5 billion variables) confirm that adaptive resolution, based on a well-chosen refinement criterion, leads to the decrease in spatial error with an acceptable increase in computational time. Fully dynamic grid adaptivity for air quality models is relatively new. We extend previous work on chemical and transport modeling by using dynamically adaptive grid resolution. Advantages and shortcomings of the present approach are also discussed.     

Modeling of shear failure in fractured reservoirs with a porous matrix

A finite volume-based numerical modeling framework using a hierarchical fracture representation (HFR) has been developed to compute flow-induced shear failure. To accurately capture the mechanics near fracture manifolds, discontinuous basis functions are employed which ensure continuity of the displacement gradient across fractures. With these special basis functions, traction and compressive forces on the fracture segment can be calculated without any additional constraints, which is extremely useful for estimating the irreversible displacement along the fracture (slip) based on a constitutive friction law. The method is further extended to include slip-dependent hydraulic aperture change and grid convergent results are obtained. Further, the change in hydraulic aperture is modeled using an asymptotic representation which respects the experimentally observed behavior of pore volume dilation due to shear slip. The model allows the initial rapid increase in hydraulic aperture due to shear slip and asymptotically approaches a finite value after repeated shearing of a fracture segment. This aperture increase is the only feedback for mechanics into the fluid flow for a linear elastic mechanics problem. The same model is also extended to include poroelastic relations between flow and mechanics solver. The grid convergence result in the case of poroelastic flow-mechanics coupling for flow-induced shear failure is also obtained. This proves the robustness of the numerical and analytical modeling of fracture and friction in the extended finite volume method (XFVM) set-up. Finally, a grid convergent result for seismic moment magnitude for single fracture and fracture network with random initial hydraulic and friction properties is also obtained. The b-value, which represents the slope of seismic moment occurrence frequency decay vs seismic moment magnitude, which is approximately constant in a semi-logarithmic plot, is estimated. The numerical method leads to converged b-values for both single fracture and fracture network simulations, as grid and time resolutions are increased. For the resulting linear system, a sequential approach is used, that is, first, the flow and then the mechanics problems are solved. The new modeling framework is very useful to predict seismicity, permeability, and flow evolution in geological reservoirs. This is demonstrated with numerical simulations of enhancing a geothermal system.     

The role of iron in tetrahedrite and tennantite determined by Rietveld refinement of neutron powder diffraction data

Rietveld refinement of neutron powder diffraction data on four samples of synthetic, iron-bearing tetrahedrite (Cu_12?xFe_xSb₄S₁₃) with x = 0.28, 0.69, 0.91, 2.19 and four samples of synthetic tennantite (Cu_12?xFe_xAs₄S₁₃) with x = 0.33, 0.38, 0.86, 1.5 indicate unambiguously that iron is incorporated into tetrahedral M1 (12d) sites and not into triangular M2 (12e) sites in the cubic crystal structure (space group I $ \ifmmode\expandafter\bar\else\expandafter\=\fi{4} Rietveld refinement of neutron powder diffraction data on four samples of synthetic, iron-bearing tetrahedrite (Cu_12−xFe_xSb₄S₁₃) with x = 0.28, 0.69, 0.91, 2.19 and four samples of synthetic tennantite (Cu_12−xFe_xAs₄S₁₃) with x = 0.33, 0.38, 0.86, 1.5 indicate unambiguously that iron is incorporated into tetrahedral M1 (12d) sites and not into triangular M2 (12e) sites in the cubic crystal structure (space group I 3 m). The refinement results also confirm that M2 is a split (24g), flat-pyramidal site situated statistically on both sides of the S1−S1–S2 triangle. In tetrahedrite, this split is about 0.6 ?, in tennantite about 0.7 ?. Trends in bond lengths and magnitude of the M2 split were evaluated by means of linear regression with Fe concentration as the independent variable.     

Nested gridding and streamline-based simulation for fast reservoir performance prediction

Detailed reservoir models routinely contain 10⁶–10⁸ grid blocks. These models often cannot be used directly in a reservoir simulation because of the time and memory required for solving the pressure grid on the fine grid. We propose a nested gridding technique that efficiently obtains an approximate solution for the pressure field. The domain is divided into a series of coarse blocks, each containing several fine cells. Effective mobilities are computed for each coarse grid block and the pressure is then found on the coarse scale. The pressure field within each coarse block is computed using flux boundary conditions obtained from the coarse pressure solution. Streamline-based simulation is used to move saturations forward in time. We test the method for a series of example waterflood problems and demonstrate that the method can give accurate estimates of oil production for large 3D models significantly faster than direct simulation using streamlines on the fine grid, making the method overall approximately up to 1,000 times faster than direct conventional simulation.