Well Index in Reservoir Simulation for Slanted and Slightly Curved Wells in 3D Grids

Abstract

A new, accurate method for computing the well index (WI) for a well that is oriented in an arbitrary direction in a 3D grid is presented. The method is simple and seminumerical and takes well direction and neighboring gridblocks into account. It is assumed that the medium is homogeneous. The method can be applied for any grid or discretization. However, only Cartesian grids with a seven-point stencil are used here. Properties of the seminumerical WI are investigated for both synthetic and field examples. The investigated properties are convergence rate and dependency on well direction, well location, grid geometry, and anisotropy. The new method shows the importance of taking the neighboring gridblocks into account. Seminumerical Well IndexThe problem of finding the WI is one of finding a relation between the well pressure, the well rate and the discrete pressure value from a numerical simulation for the entire gridblock. A typical well radius is about 10 cm, while one numerical pressure value for a gridblock typically represents a volume of 100×100×1 m 3 . The well represents a sink (or source) for the pressure distribution. This means that in the wellblock there will be a huge variation in the real pressure. An illustration is given in Fig.

Small-stencil 3D schemes for diffusive flows in porous media

“…The medium is homogeneous, but anisotropic. An analytical solution of this problem is described in [2] for a diagonal diffusion tensor in the xyz-coordinate system. Diagonal elements are denoted as Λ x , Λ y and Λ z .…”

Mathematical modeling of operating modes of underground gas storage facilities

“…Existing approaches have not yet been brought to the simulation of these systems as a single hydraulic system, taking into account all the features of its operation. The main problems that arise in the development of settlement procedures are the complexity of models and incompleteness of their information support [3][4][5][6][7][8][9][10][11]. There are significant difficulties in adapting models under conditions of existing uncertainty of parameters, especially reservoir systems.…”

“…Equally important are the requirements for the accounting of regulatory operating documents, as well as for ensuring ease of implementation, operation and provision of simulation modes for various modifications of UGS facilities. Some studies [5][6][7][8][9] take into account the integrated approach to the calculation of the operating regimes of the «reservoir-pipeline» chain.…”

“…The mathematical model of UGS [5][6][7][8][9] is formed on the basis of object models, which are combined into a single hydraulic model according to the technological scheme. The heterogeneity of mathematical models of objects makes it difficult to develop iterative procedures for reconciling the parameters of gas flow within neighboring objects.…”

3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on General Grids

“…The exact solution u 4 (x, y, z) is detailed in [1]: once a stretching of the axes has been performed so as to obtain an isotropic problem, we seek an exact solution that is constant on the well boundary. The solution simulates the pressure field that would be obtained for the same infinite slanted circular well in an infinite domain for a given constant flow rate q across any section of the well.…”