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On a Class of Integrals Useful to Solve Well‐Type Flows in Heterogeneous Porous Formations
Author(s) -
Severino Gerardo,
Cuomo Salvatore
Publication year - 2019
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2019wr025062
Subject(s) - type (biology) , class (philosophy) , mathematics , perturbation (astronomy) , porous medium , hydraulic conductivity , flow (mathematics) , variance (accounting) , statistical physics , porosity , mathematical analysis , physics , geology , geotechnical engineering , computer science , geometry , soil science , paleontology , artificial intelligence , accounting , quantum mechanics , business , soil water
Abstract We provide analytical (closed form) expression for a class of integrals that frequently arise into modeling well‐type flows through heterogeneous porous formations. In particular, these integrals are encountered when ensemble (second‐order) moments of the flow variables are computed by means of a perturbation approach that regards the variance σ Y 2of the random field Y ≡ ln K (being K the hydraulic conductivity) as a small parameter.