Quasilinear stationary problems with a quadratic gradient term having singularities

2012 ◽  
Vol 86 (2) ◽  
pp. 585-606 ◽  
Author(s):  
Daniela Giachetti ◽  
Sergio Segura de León
Keyword(s):  
Gradient Term ◽  
Stationary Problems ◽  
Quadratic Gradient

scholarly journals Elliptic equations having a singular quadratic gradient term and a changing sign datum

2012 ◽  
Vol 11 (5) ◽  
pp. 1875-1895 ◽  
Author(s):  
Daniela Giachetti ◽  
Francesco Petitta ◽  
Sergio Segura de León
Keyword(s):  
Elliptic Equations ◽  
Gradient Term ◽  
Quadratic Gradient

scholarly journals A Modified Blasingame Production Analysis Method for Vertical Wells Considering the Quadratic Gradient Term

Energies ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 2092
Author(s):  
Junjie Ren ◽  
Qiao Zheng ◽  
Chunlan Zhao
Keyword(s):  
Governing Equation ◽  
Material Balance ◽  
Gradient Term ◽  
Analysis Method ◽  
Vertical Wells ◽  
Reservoir Properties ◽  
Step Procedure ◽  
Rate Functions ◽  
Original Oil In Place ◽  
Quadratic Gradient

Fluid flow in actual oil reservoirs is consistent with material balance, which should be described by the nonlinear governing equation, including the quadratic gradient term (QGT). Nonetheless, the widely-used Blasingame production decline analysis (BPDA) is established based on the conventional governing equation neglecting the QGT, which leads to some errors in the interpretation of production data under some conditions, such as wells producing at a large drawdown pressure. This work extends BPDA to incorporate the effect of the QGT by modifying material balance time and normalized rate functions. The step-by-step procedure for the proposed production decline analysis (PPDA) is presented and compared with that for BPDA. The simulated cases for various production scenarios are used to validate PPDA. A field case is employed to show the applicability of PPDA in practice. Comparisons between the results obtained by BPDA and PPDA are analyzed in detail. It is found that BPDA overestimates the permeability and original oil-in-place, while PPDA works well. Compared with BPDA, PPDA can be employed to obtain more accurate original oil-in-place and reservoir properties, especially when wells produce at a large drawdown pressure.

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