افزايش اندازه‌ي سلول‌هاي مدل زمين‌شناسي نفوذپذيري مطلق با استفاده از روش تجزيه‌ي چهاردرختي

Upgridding Of Absolute Permeability Geological Models Using The Quadtree Decomposition Method

در اين نوشتار، روشي جديد براي افزايش مقياس1 مدل‌هاي زمين‌شناسي نفوذپذيري ارايه مي‌شود. اين روش برمبناي تجزيه‌ي چهاردرختي2، يك مدل افزايش مقياس داده شده با سلول‌هاي3 غيرساخت‌يافته4 توليد مي‌كند كه در ناحيه‌هايي از مدل زمين‌شناسي كه تغييرات نفوذپذيري شديد است، سلول‌ها كوچك باقي مي‌مانند اما در ساير نقاط مخزن سلول‌ها بزرگ مي‌شوند. اين عمل موجب مي‌شود كه تعداد سلول‌هاي مدل مورد نظر به تعداد قابل توجهي كم شود و لذا زمان و حافظه‌ي لازم براي انجام شبيه‌سازي جريان در مخزن شديداً كاهش يابد. در اين روش سلول‌هايي توليد مي‌شود كه در هر سمت ممكن است با چندين سلول با چيدمان‌هاي مختلف همسايه باشند، و همين موجب دشواري حل معادلات شبيه‌سازي جريان مي‌شود. براي رفع اين مشكل روش جديدي پيشنهاد مي‌شود كه در هر سمت، تعداد همسايه‌هاي يك سلول را به حداكثر 2 سلول كاهش مي‌دهد و موجب تسهيل فرايند گسسته‌سازي معادلات جريان مي‌شود.

The process of upscaling is an active area of research, due to the advances made in geostatistical techniques, which allows reservoir properties, such as absolute permeability, to be described by more and more fine models. However, these detailed reservoir models cannot be used directly for numerical simulation because they require high amounts of time and memory storage capacity. As a consequence, it is necessary to coarsen detailed geological models to a scale more appropriate for reservoir simulation. The first step in upscaling is the upgridding of the original geological model. Once upgridding is completed, the reservoir properties are reassigned to the simulation grid using various property upscaling methods. An important issue in upscaling is that the upscaled model must maintain the essential heterogeneity details of the original geological model. Moreover, the flow characteristics of the upscaled and geological models must be the same. In this study, a new and simple method for the upscaling of absolute permeability geological models is presented. This method, based on quadtree decomposition, upscales the geological model such that the grids of the upscaled model are unstructured. In other words, in the regions of the geological model where permeability variation is high, the grids of the upscaled model remain small, but, in regions where permeability is almost uniform, the grids of the upscaled model become large. So, this method reduces the total number of grids, and results in large savings of the time and memory required for flow simulations in the reservoir. The grids of the upscaled model have different sizes and each grid may be adjacent to several grids with several arrangements. Simulation of flow through such complex upscaled models is very hard. To solve this problem, we present a new method, in which, each side of all grids reduces the number of neighbors to a maximum of 2, and facilitates discretization of the flow equations.