Matris–Çatlak Etkileşimlerinin MINC Modellerinde Çözümlemesi: Hacim Fraksiyonu Dağılımlarının ve Ölçeklenmiş MINC Parametrelerinin Rolü

Öz

Çatlaklı rezervuarlarda, gözenekli matris ile çatlak ağı arasındaki yüksek geçirgenlik farkı karmaşık akış davranışlarına neden olur. Bu sistemlerin sayısal modellenmesinde yaygın olarak Sürekli Çatlak Modeller (CFM) ve Ayrık Çatlak Modeller (DFM) kullanılır. DFM, çatlakları ayrıntılı olarak temsil ettiği için yüksek hesaplama maliyeti gerektirir. CFM yaklaşımlarından biri olan Çoklu Etkileşimli Süreklilikler (MINC) yöntemi, matris–çatlak etkileşimini iç içe geçmiş süreklilikler aracılığıyla temsil ederek daha verimli bir alternatif sunar. Bu çalışmada, yüksek çözünürlüklü DFM modeli referans alınmış ve MINC modellerinin oluşturulması için matris ve çatlak parametreleri ölçek büyütme yöntemiyle elde edilmiştir. Eşit Hacim, Eşit Mesafe, Logaritmik Mesafe ve Üstel Mesafe olmak üzere dört farklı MINC yöntemi karşılaştırılmıştır. Ayrıca, matris–çatlak ara yüzey alanlarını ve hacimler arası mesafeleri tanımlayan yeni analitik formüller geliştirilmiştir. Sonuçlar, MINC modelinin doğruluğunu belirleyen temel unsurun ölçeklenerek büyütülmüş matris geçirgenliği olduğunu, hacim kesri dağılımının etkisinin ise sınırlı kaldığını göstermektedir. Uygulamaları kolaylaştırmak amacıyla, DFM ara yüzey alanlarından doğrudan MINC matris geçirgenliğini tahmin eden basitleştirilmiş bir analitik ifade önerilmiş ve bu yaklaşımın geçerliliği sayısal optimizasyonla doğrulanmıştır.

Anahtar Kelimeler

• MINC
• DFM
• hacim fraksiyonu
• matris geçirgenliği
• optimizasyon
• ölçek büyütme

Resolving Matrix–Fracture Interactions in MINC Models: Role of Volume Fraction Distributions and Upscaled MINC Parameters

Öz

Fractured reservoirs exhibit complex fluid flow behavior due to the strong permeability contrast between the porous matrix and fracture network systems. Numerical simulation of these systems is generally performed using two main approaches, Continuum Fracture Models (CFM) and Discrete Fracture Models (DFM). The explicit fracture details of DFM lead to a high computational burden. The Multiple Interacting Continua (MINC) method, one of CFM, provides a viable compromise by representing matrix fracture interaction through nested continua. Since a high-resolution DFM is utilized as the reference benchmark in this study, fracture and matrix parameters are upscaled to construct MINC models. This study compares four different MINC models based on varying volume fraction schemes, including Equal Volume, Equal Distance, Logarithmic Distance, and Exponential Distance methods, utilizing newly derived analytical formulations to characterize matrix fracture interface areas and nodal distances. The results demonstrate that the upscaled matrix permeability is the dominant factor governing MINC accuracy, while the influence of the specific volume fraction distribution is relatively minor. For practical application, a simplified analytical expression is derived in this study to estimate MINC matrix permeability directly from the DFM interface areas. The validity of this expression is confirmed through numerical optimization.

Anahtar Kelimeler

• MINC
• DFM
• volume Fraction
• matrix permeability
• optimization
• upscaling

Etik Beyan

No ethical issues are associated with the publication of this article.

Teşekkür

This article is derived from Ebru Berna Demir's Master's Thesis entitled "Comparison and optimization of multiple interacting continua (MINC) model parameters," supervised by Mehmet Onur Doğan (Thesis No: 833630).

Kaynakça

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