Lagrangian formulation for penny-shaped and Perkins-Kern geometry models
- Halliburton Services, Duncan, OK (USA)
This paper discusses basic theories for vertical penny-shaped and Perkins-Kern (PK) geometry models developed with a Lagrangian formulation combined with a virtual-work analysis. The Lagrangian formulation yields a pair of nonlinear equations in R/sub f/ or L/sub f/ and b/sub f/, the fracture radius or length and half-width. By introduction of a virtual-work analysis, a simple equation is obtained that can be solved numerically. This equation is written in a form that can be used to determine fracture geometry when the fluid-loss coefficient of the fracturing fluid is known. Also, this equation, coupled with a material-balance equation after shut-in, can be used to analyze pressure-decline data after shut-in to determine the effective fluid-loss coefficient and fracture geometry.
- OSTI ID:
- 5455999
- Journal Information:
- SPE (Society of Petroleum Engineers) Formation Evaluation; (USA), Vol. 4:3; ISSN 0885-923X
- Country of Publication:
- United States
- Language:
- English
Similar Records
A new analysis of pressure decline for acid fracturing
Mini-frac analysis based on ellipsoidal geometry
Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
CRACK PROPAGATION
GEOMETRY
OIL WELLS
HYDRAULIC FRACTURING
DESIGN
FRACTURING FLUIDS
GEOLOGIC MODELS
LAGRANGE EQUATIONS
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PRESSURE DROP
RESERVOIR ENGINEERING
RESERVOIR PRESSURE
COMMINUTION
DIFFERENTIAL EQUATIONS
ENGINEERING
EQUATIONS
FLUIDS
FRACTURING
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
WELLS
020200* - Petroleum- Reserves
Geology
& Exploration
020300 - Petroleum- Drilling & Production
990230 - Mathematics & Mathematical Models- (1987-1989)