İhsan Murat GÖK, Mustafa ONUR

Düşey girişimli basınç testlerinin modellenmesi ve parametre tahmini

Bu çalışmada, düşey yöndeki geçirgenlik değerlerinin belirlenmesine de olanak tanıdığı için endüstride yaygın kullanım alanı bulan bir kuyunun farklı noktalarında yerel olarak yapılabilen düşey girişimli basınç-zaman seti verilerinden (örneğin çoklu-prob ve paker-prob testleri) kayaç özelliklerinin belirlenmesi problemi üzerinde durulmuştur. Yatay ve düşey yöndeki heterojenlikten etkilendiği bilinen düşey girişim testi basınç verilerinin yatay ve düşey yöndeki heterojenliğin çözümlenmesinde ne derece etkili olduğu bu çalışmada araştırılmıştır. Bunun için, düşey girişim testleri bu çalışmada geliştirilen üç boyutlu (3-B) r-$theta$-z tek-fazlı sayısal akış simülatörü ile modellenmiştir. Bu sayısal simülatöre ters problem metodolojisi üzerine kurulu doğrusal olmayan parametre tahmin yöntemi entegre edilmiştir. Doğrusal olmayan parametre tahmini, gradyent temelli Levenberg-Marquardt algoritması kullanılarak gerçekleştirilmiştir. Bu çalışmada geliştirilen model kullanılarak, sentetik olarak tasarlanmış bir paker problu ve bir çoklu problu düşey girişim testinin analizi sunulmuştur.

The modeling of the vertical interference test and parameter estimation

In this study, determining heterogeneity in rock properties from vertical (multi- probe and packer-probe formation test) interference pressure data sets, which has a widespread usage in the industry for allowing particularly the determination of vertical permeabilities along the wellbore, was investigated. It is known that spatial pressure data sets of the vertical interference test contain information about heterogeneity in rock properties in both lateral and vertical directions. Thus, it was examined to what degree the heterogeneity in lateral and vertical directions can be resolved from vertical interference tests. Therefore, vertical interference tests were modeled with a three dimensional (r-0-z) single-phase flow simulator developed in this study. The simulator was extensively verified by comparing its results with analytical solutions given in the literature and with the results of commercial simulator ECLIPSE 100, for a variety of cases. Non-linear parameter estimation capability based on this inverse problem theory has been integrated into this 3-D simulator to solve non-linear parameter estimation problem. Non-linear parameter estimation is achieved by using the well-known gradient-based Levenberg-Marquardt algorithm. The use of three different methods (finite difference, gradient simulator, and adjoint) for efficiently computing sensitivities coefficients required in the Levenberg-Marquardt algorithm has been investigated. Synthetic examples of multi-probe and packer-probe vertical interference lest were shown by using model developed in this study.

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