شبيه‌سازي تركيبي و صريح ـ ضمني مخازن هيدروكربني به‌كمك پارامتري‌كردن تطبيقي فضاي تركيب

Explicit-implicit compositional hydrocarbon reservoir simulation using adaptive compositional space parameterization

مدل‏‌سازي تركيبي يكي از پركاربردترين روش‌ها براي شبيه‌سازي مخازن نفتي و فرايندهاي ازدياد برداشت است. در شبيه‌سازهاي تركيبي براي محاسبه‌ي تركيب اجزا در فازهاي مختلف معمولاً از معادله‌ي حالت استفاده مي‌شود كه البته باعث صرف زمان محاسباتي زيادي مي‌‌شود. در اين مقاله براي كاهش تعداد معادلات حالت مورد نياز، فضاي تركيب به‌كمك پارامترهاي خطوط رابط بيان مي‌شود و خواص ترموديناميكي سيستم به‌كمك اين پارامترها به‌دست مي‌آيد. براي اين كار تعداد كمي خطوط رابط اصلي مورد نياز است كه در طول حل به‌دست مي‌آيد. فضا با استفاده از اين خطوط رابط اصلي و مثلث‌بندي دلوني گسسته‌سازي مي‌شود و با ميان‌يابي خطي در اين فضاي گسسته‌شده خواص ترموديناميكي به ‌دست مي‌آيد. اين روش در يك شبيه‌ساز فشار ضمني درجه‌ي اشباع صريح پياده‌سازي شده ‌است. در پايان چند مسيله‌ي جابه‌جايي امتزاج‌پذير و امتزاج‌ناپذير نفت در يك مخزن يك‌بعدي شبيه‌سازي شده‌ است.

In recent decades, there have been great efforts to simulate flow in hydrocarbon reservoirs and oil recovery processes. Compositional model is one of the most advanced models for this purpose. In this model, nonlinear mass conservation equations for multicomponent flow have to be solved along with thermodynamic equilibrium constraints. In most compositional simulators, an equation of state is used to determine phase behavior of hydrocarbon mixtures. In this article, an efficient two-phase compositional model for both immiscible and miscible fluid flows in porous media is presented. In this model, the mass conservation equations are discretized using a cell-centered control volume method. The solution algorithm employs the so-called Implicit Pressure Explicit Saturation (IMPES) method. To determine the thermodynamic state of the mixture, the equation of state must be solved at each time step for each computational cell. These computations consume considerable time in a compositional simulation. Compositional space is parameterized with tie-line variables, and this parameterized space is used to reduce the number of times the equation of state must be solved. To parameterize compositional space, a few supporting tie-lines are needed, which were obtained adaptively during simulation process. The tie-line space is discretized using these supporting tie-lines and a Delaunay triangulation procedure. In the rest of discretized tie-line space, thermodynamic properties are calculated using linear interpolation. It is important to note that the equation of state is solved only at the supporting points used to discretize the tie-line space. Since tie-lines do not exist in the super-critical region, the space is represented based on overall compositions and equation of state. In this work, the used method keeps continuity of tie-line variables and overall compositions with respect to the change of the mixture state from sub-critical to super-critical space, and vice versa. The performance of the proposed approach is assessed using a number of homogeneous one-dimensional multi-component problems. Numerical results show‎ that the proposed method has acceptable accuracy and significantly reduces the total number of flash calculations needed in a compositional simulator.