New block sparse direct solution technique - application to hydrocarbon reservoir simulation

Thesis/Dissertation · Thu Jan 01 04:00:00 EST 1987

OSTI ID:6719753

Harouaka, A

A three-phase, three-dimensional black oil simulator coupled with a multilayer completion well model is developed to test and apply the solution algorithm to actual reservoir engineering problems. The fully implicit finite difference equations are linearized using a generalized Newton-Raphson procedure. The resulting linear systems of equations are solved with a new block sparse direct solution technique. The solution scheme can handle irregular geometries, including the presence of faults, as well as any type of coordinates. The wells may be completed in some or all penetrated layers. They can operate under various constraints: (1) constant rate, oil, water, free gas, total liquids or total fluids (2) constant flowing bottomhole pressure. The well model carries the same number of primary unknowns as the simulator. In the case of a three-phase model, where the primary unknowns for a cell are average pressure and two fluid saturations, the primary unknowns for a well are taken as the flowing bottomhole pressure and two fluid wellbore saturations. This approach allows modeling of crossflow, wellbore storage and a fully implicit treatment of the source and/or sink terms. The performances of this block sparse solver are compared to those of a band algorithm, a block band algorithm and an iterative solution technique, namely block line successive overrelaxation (LSOR). Among the direct solution techniques, the block sparse approach seems to be superior to the others from almost any perspective they want to look at it. Under similar convergence criteria, LSOR and the direct solution techniques do not converge to the same values. All direct solvers, on the other hand, converge exactly to the same values. The accuracy of block LSOR improves with smaller convergence criteria.

• Research Organization: Pennsylvania State Univ., University Park (USA)
• OSTI ID: 6719753
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
ALGORITHMS
ANALOG SYSTEMS
ASSOCIATED GAS
CALCULATION METHODS
ENERGY SOURCES
ENGINEERING
ENHANCED RECOVERY
FINITE DIFFERENCE METHOD
FLUID FLOW
FLUIDS
FOSSIL FUELS
FUELS
FUNCTIONAL MODELS
GASES
GEOLOGIC DEPOSITS
GEOLOGIC FAULTS
GEOLOGIC FRACTURES
GEOLOGIC STRUCTURES
ITERATIVE METHODS
LAYERS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MINERAL RESOURCES
MULTIPHASE FLOW
NUMERICAL SOLUTION
OIL FIELDS
OIL SATURATION
OIL WELLS
PETROLEUM
PETROLEUM DEPOSITS
PRIMARY RECOVERY
RECOVERY
RESERVOIR ENGINEERING
RESERVOIR PRESSURE
RESOURCES
SATURATION
SIMULATORS
THREE-DIMENSIONAL CALCULATIONS
WATER SATURATION
WELL COMPLETION
WELLS