شبيه‌سازي تركيبي جريان در مخازن نفتي با استفاده از يك روش تقريب مركزي با دقت بالا

A HIGH-RESOLUTION CENTRAL SCHEME FOR COMPOSITIONAL FLOW SIMULATIONS IN HYDROCARBON RESERVOIRS

در اين تحقيق، به‌كارگيري يك روش تقريب مركزي با دقت بالا در مدل تركيبي براي سيالات هيدروكربني مورد مطالعه قرار گرفته است. معادلات حاكم عبارت‌اند از يك معادله‌ي سهموي براي تغييرات فشار و يك دستگاه معادلات هذلولوي انتقال اجزا . براي حل معادله‌ي فشار سهموي از روش تفاضل محدود ضمني استفاده شده است، و براي حل صريح معادلات انتقال اجزا از يك روش مركزي دقت بالاي مستقل از عدد كورانت مبتني بر كار «كورگانُف و تادمُر» استفاده شده است. دو ويژگي بارزِ اين نوع جديد از روش‌هاي مركزي، عدم نياز به تعيين و تجزيه‌ي بردارهاي ويژه و نيز مستقل‌بودن جمله‌ي پخش مصنوعي از عدد كورانت است. در انتها، با ارايه‌ي چند مسيله‌ي نمونه‌ي يك‌بُعدي ــ كه نتايج آنها در مقالات معتبر علمي موجود است ــ دقت و هزينه‌ي محاسباتي روش ارزيابي مي‌‌شود.

The compositional model is the most complete model used in hydrocarbon reservoir simulation. The model provides a three-phase, multi-component representation of the fluid flow problem, in which several components, such as; methane, propane and decane, may coexist in three phases (liquid, vapor and aqua). In this model, water only appears in the aqua phase, while the other components can be present in both the liquid and vapor phases. Here, a variation of this model proposed by Trangenstein and Bell is used. The final governing equations include an elliptic pressure equation and a set of parabolic convection-dominated transport equations. Numerical simulation of the pressure equation is usually a straightforward matter. Solving the component mass conservation equations, however, can be challenging. In recent years, most of the numerical methods used for this purpose have been based on the, so-called, Godunov method, which needs information about the eigen-structure of the governing equations. This makes the numerical algorithms complex and highly time consuming. In this paper, a high-resolution central scheme, proposed by Kurganov and Tadmor, is extended to solve compositional flow equations. This is a numerical scheme, which is computationally efficient and its accuracy is independent of time step size. The computational algorithm is implemented within the context of the finite volume method. The paper briefly presents the governing equations and elaborates the computational algorithm used here along with full details on the implementation of the high-resolution scheme. To assess the performance of the proposed numerical algorithm, a number of one-dimensional benchmark problems are solved. Numerical results are compared with available data in the literature.