TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractFormation Testing (FT) can collect high-resolution data sufficient to capture small variations in fluid and formation properties.Unfortunately, conventional interpretation techniques are rarely capable of processing the data from complex tool configurations and formation properties. Studies have shown that numerical simulation can replicate the complex physics of multiphase fluid flow but often not at the level of detail needed for high-resolution data interpretation.In this paper, we propose a general three-dimensional and multiphase numerical model to incorporate various wellbore and/or tool factors. Unlike the analytical source representation of a well commonly used in reservoir simulation, the proposed model establishes the internal boundary of a well, generally involving the pressure and flow rate at the sandface, where the size of the wellbore or tool configuration is equivalent to or smaller than that of the grid cells. This fully coupled and fully implicit model at a fine spatial and temporal scale is advantageous in revealing further potentially useful information and realizing the synergy across a spectrum of FT applications. As a result, wellbore and/or tool factors, particularly the tool storage effect, can be integrated at a level of detail not previously possible in the absence of a comprehensive wellbore model.The mathematical formulations and numerical schemes are presented. Simulation studies include the primary FT applications in the field, i.e., pressure transient testing and fluid sampling for both oil-based and water-based mud filtrate. These examples show that the proposed near-wellbore highresolution modeling approach with non-negligible wellbore and/or tool factors permits new insights into fluid flow in FT applications.
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractDomain decomposition methods provide major advantages to large-scale and high-resolution reservoir simulation studies in terms of computer resource requirements. In this paper, a directional, intergrid mapping technique is introduced together with a nonlinear domain decomposition algorithm -the Fast Adaptive Composite Grid (FAC). Domain decomposition techniques have often been applied to solve the linear system of equations resulting from reservoir numerical models. However, a stronger, more efficient approach is to apply the domain decomposition techniques directly to the nonlinear problem. As a result, mapping dynamic reservoir properties from one grid scale to another one, a process also known as intergrid mapping, becomes a key operation in dealing with composite grid systems.Normally, upscaling and downscaling techniques focus on geological structures and formation properties. The proposed intergrid mapping operations in the FAC method honor the static reservoir properties while preserving the properties of fluid flow dynamics between grids with different scales. Most importantly, the intergrid mapping operator in FAC can accurately represent local phenomena in much coarser domains, so that the composite grid residual, which can be viewed as the relative overall solution error, can be effectively minimized. Application of the FAC method brings significant reduction in CPU time and memory requirements when compared with simulations having the same level of global grid and timestep refinement, making it possible to attain large simulation scales and resolution with limited computer resources.In this paper, the approximation of the differential conservation equations is based on the control volume approach and uses cell-centered finite difference methods. The composite grid solution is obtained through a defect-correction process of refinements. Unlike many domain decomposition algorithms, the proposed method provides full approximation storage (FAS) by computing and storing the whole coarse grid solution, including the grids for which a refinement exists.Computational results from a model featuring local spacetime refinements are presented to illustrate that a rigorous intergrid mapping operation can significantly improve the efficiency of nonlinear domain decomposition algorithms, especially in cases of multiphase flow with irregular local timestepping. The presented numerical examples demonstrate the applicability of the proposed numerical method. t J J IJ c t J rJ J J J J = − ∇Φ , represents the superficial flow associated with phase J, where the potential gradient is given by J J J , , c c c X Y Z ∆ ∆ ∆ , over which certain cells are further divided into subdomains with local grid cells, fc Ω , fc = 1, 2… N fc , of dimension ( ) p c N J J I J J
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