Streamline Tracing and Applications in Dual Porosity Dual Permeability Models

Streamline-based methods have proven to be effective for various subsurface flow and transport modeling problems. However, the applications are limited in dual-porosity and dual-permeability (DPDK) system due to the difficulty in describing interactions between matrix and fracture during streamline tracing. In this work, we present a robust streamline tracing algorithm for DPDK models and apply the new algorithm to rate allocation optimization in a waterflood reservoir. In the proposed method, streamlines are traced in both fracture and matrix domains. The inter-fluxes between fracture and matrix are described by switching streamlines from one domain to another using a probability computed based on the inter-fluxes. The approach is fundamentally similar to the existing streamline tracing technique and can be utilized in streamline-assisted applications, such as flow diagnostics, history matching, and production optimization. The proposed method is benchmarked with a finite-volume based approach where grid-based time-of-flight was obtained by solving the stationary transport equation. We first validated our method using simple examples. Visual time-of-flight comparisons as well as tracer concentration and allocation factors at wells show good agreement. Next, we applied the proposed method to field scale models to demonstrate the robustness. The results show that our method offers reduced numerical artifacts and better represents reservoir heterogeneity and well connectivity with sub-grid resolutions. The proposed method is then used for rate allocation optimization in DPDK models. A streamline-based gradient free algorithm is used to optimize net present value by adjusting both injection and production well rates under operational constraints. The results show that the optimized schedule offers significant improvement in recovery factor, net present value, and sweep efficiency compared to the base scenario using equal rate injection and production. The optimization algorithm is computationally efficient as it requires only a few forward reservoir simulations.

Three-Dimensional Streamline Tracing Method over Tetrahedral Domains

Getting a clear understanding of the fluid velocity field in underground porous media is critical to various engineering applications, such as oil/gas reservoirs, CO2 sequestration, groundwater, etc. As an effective visualization tool and efficient transport behaviors solution algorithm, the streamline-based method was improved significantly by numerous studies conducted in the last couple of decades. However, the implementation of streamline simulation is still challenging while working with Finite Element Method (FEM) over 3D tetrahedral domains, where the mass conservation is not guaranteed. Considering the increased computational cost to enforce mass conservation in FEM and additional complexity, a new three-dimensional streamline tracing algorithm is presented that only relies on the velocity vector of a flow field on each vertex of a tetrahedron in a 3D unstructured mesh system. Owning to the shape functions and transformation equations between the master element and actual element, the exit coordinate leaving a tetrahedral element can be determined effectively. As a result, Time of Flight (TOF), the coordinate variable along each streamline, can be calculated accurately and efficiently because that the analytical solution depicting the trajectory in Master Element is deduced. The presented streamline-based method is tested under FEniCS, a programming framework for FEM, which eases the implementation and further development of the presented method.

A Vector Field Texture Generation Method without Convolution Calculation

In the LIC algorithm process, symmetrical streamline tracing is used to symmetrically convolve the original values of all the primitive values that pass by to obtain the resulting texture. In this process, streamline tracking and convolution consume a lot of computing resources. To generate more expressive textures for vector fields with less time consumption, a novel method named random increment streamline (RIS) is put forward, which can generate streamline textures without convolution calculations. First, the mesh unit filling preprocessing (MUFP) method is presented to transform an undressed irregular grid into a special kind of regular grid named a “texture pixel”, and the point location and interpolation processes of all sampling points in the texture pixels are calculated before streamline tracking. Second, the random increment streamline method is used to generate line integral convolution style textures without any convolution calculations, thus greatly reducing the algorithm’s time consumption. Third, the vector directions at each point in the static vector field are clearly expressed using the periodic cyclic animation method. Finally, several simplifications of the RIS algorithm are discussed, which help to achieve a better visual effect with faster speed. The programming results show that the method is faster and more applicable than the traditional LIC method and provides clearer expression of the vector field.

Application of Flow Diagnostics to Rapid Production Data Integration in Complex Grids and Dual-Permeability Models

Summary Streamline-based methods, as repeatedly demonstrated in multiple applications, offer a robust and elegant framework for reconciling high-resolution geologic models with observed field responses. However, significant challenges persist with the application of streamline-based methods in complex grids and dual-permeability media due to the difficulty with streamline tracing in these systems. In this work, we propose a novel and efficient framework that circumvents these challenges by avoiding explicit tracing of streamlines but exploits the inherent desirable features of streamline-based production data integration in high-resolution geologic models. Our approach features the application of flow diagnostics to inverse problems involving the integration of multiphase production data in reservoir models. Here, time-of-flight as well as numerical tracer concentrations for each well, on the basis of a defined flux field, are computed on the native finite-volume grid. The information embedded in these metrics are used in the dynamic definition of stream-bundles and, eventually, in the computation of analytical water arrival-time sensitivities with respect to model properties. This calculation mimics the streamline-derived analytical sensitivity computation used in the well-established generalized travel-time inversion (GTTI) technique but precludes explicit streamline tracing. The reservoir model property field is updated iteratively by solving the LSQR (sparse least-squares with QR factorization) system composed of the computed analytical sensitivity and the optimal water travel-time shift, augmented with regularization and smoothness constraints. The power and efficacy of our approach are demonstrated using synthetic model and field applications. We first validate our approach by benchmarking with the streamline-based GTTI algorithm involving a single-permeability medium. The flow-diagnostics-derived analytical sensitivities were observed to show good agreement with the streamline-derived sensitivities in terms of correctly capturing relevant spatiotemporal trends. Furthermore, the desirable quasilinear behavior characteristic of the traditional streamline-based GTTI technique was preserved. The flow-diagnostics-based inversion technique is then applied to a field-scale problem involving the integration of multiphase production data into a dual-permeability model of a large naturally fractured reservoir. The results clearly demonstrate the effectiveness of the proposed approach in overcoming the limitations of classical streamline-based methods with dual-permeability systems. By construction, this approach finds direct application in single/multicontinuum models with generic grid designs, both in structured and fully unstructured formats, thereby aiding well-level history matching and high-resolution updates of modern geologic models. This work presents, for the first time, an application of the GTTI to dual-permeability models of naturally fractured reservoirs. This is facilitated by a simplified, yet effective approach to travel-time sensitivity computations directly on finite-volume grids. The proposed approach can be easily applied to subsurface models at levels of complexity identified as challenging for classical streamline-based methods.

An airframe/inlet integrated full-waverider vehicle design using as upgraded aerodynamic method

ABSTRACTWith the aims of overcoming the limitations of the existing basic flow model derived from an axisymmetric generating body and extending the aerodynamic design method of the airframe/inlet integrated waverider vehicle, this study develops an upgraded basic flow model derived from an axisymmetric shock wave. It then upgrades the design method for airframe/inlet integration of an air-breathing hypersonic waverider vehicle, which is termed the ‘full-waverider vehicle’ in this study. In this paper, first, the design principle and method for the upgraded full-waverider vehicle derived from an axisymmetric basic shock wave are described in detail. Second, an upgraded basic flow model that accounts for both internal and external flows is derived from an axisymmetric basic shock wave by use of both the streamline tracing method and the method of characteristics (MOC). Third, the upgraded full-waverider vehicle is developed from the upgraded basic flow model by the streamline tracing method. Fourth, the design theories and methodologies of both the upgraded basic flow model and the upgraded full-waverider vehicle are validated by a numerical computation method. Finally, the aerodynamic performances and viscous effects of both the upgraded basic flow model and the upgraded full-waverider vehicle are analysed by numerical computation. The obtained results show that the upgraded basic flow model and aerodynamic design method are effective for the design of the airframe/inlet integration of an air-breathing hypersonic waverider vehicle.