Matching Items (2)
Description
A new method of adaptive mesh generation for the computation of fluid flows is investigated. The method utilizes gradients of the flow solution to adapt the size and stretching of elements or volumes in the computational mesh as is commonly done in the conventional Hessian approach. However, in the new method, higher-order gradients are used in place of the Hessian. The method is applied to the finite element solution of the incompressible Navier-Stokes equations on model problems. Results indicate that a significant efficiency benefit is realized.
ContributorsShortridge, Randall (Author) / Chen, Kang Ping (Thesis advisor) / Herrmann, Marcus (Thesis advisor) / Wells, Valana (Committee member) / Huang, Huei-Ping (Committee member) / Mittelmann, Hans (Committee member) / Arizona State University (Publisher)
Created2011
Description
Pseudo-steady state (PSS) flow is an important time-dependent flow regime that
quickly follows the initial transient flow regime in the constant-rate production of
a closed boundary hydrocarbon reservoir. The characterization of the PSS flow
regime is of importance in describing the reservoir pressure distribution as well as the
productivity index (PI) of the flow regime. The PI describes the production potential
of the well and is often used in fracture optimization and production-rate decline
analysis. In 2016, Chen determined the exact analytical solution for PSS flow of a
fully penetrated vertically fractured well with finite fracture conductivity for reservoirs
of elliptical shape. The present work aimed to expand Chen’s exact analytical solution
to commonly encountered reservoirs geometries including rectangular, rhomboid,
and triangular by introducing respective shape factors generated from extensive
computational modeling studies based on an identical drainage area assumption. The
aforementioned shape factors were generated and characterized as functions for use
in spreadsheet calculations as well as graphical format for simplistic in-field look-up
use. Demonstrative use of the shape factors for over 20 additional simulations showed
high fidelity of the shape factor to accurately predict (mean average percentage error
remained under 1.5 %) the true PSS constant by modulating Chen’s solution for
elliptical reservoirs. The methodology of the shape factor generation lays the ground
work for more extensive and specific shape factors to be generated for cases such as
non-concentric wells and other geometries not studied.
quickly follows the initial transient flow regime in the constant-rate production of
a closed boundary hydrocarbon reservoir. The characterization of the PSS flow
regime is of importance in describing the reservoir pressure distribution as well as the
productivity index (PI) of the flow regime. The PI describes the production potential
of the well and is often used in fracture optimization and production-rate decline
analysis. In 2016, Chen determined the exact analytical solution for PSS flow of a
fully penetrated vertically fractured well with finite fracture conductivity for reservoirs
of elliptical shape. The present work aimed to expand Chen’s exact analytical solution
to commonly encountered reservoirs geometries including rectangular, rhomboid,
and triangular by introducing respective shape factors generated from extensive
computational modeling studies based on an identical drainage area assumption. The
aforementioned shape factors were generated and characterized as functions for use
in spreadsheet calculations as well as graphical format for simplistic in-field look-up
use. Demonstrative use of the shape factors for over 20 additional simulations showed
high fidelity of the shape factor to accurately predict (mean average percentage error
remained under 1.5 %) the true PSS constant by modulating Chen’s solution for
elliptical reservoirs. The methodology of the shape factor generation lays the ground
work for more extensive and specific shape factors to be generated for cases such as
non-concentric wells and other geometries not studied.
ContributorsSharma, Ankush, M.S (Author) / Chen, Kang Ping (Thesis advisor) / Green, Matthew D (Thesis advisor) / Emady, Heather (Committee member) / Arizona State University (Publisher)
Created2017