Front tracking in two dimensions without a grid

Journal Article · Fri Feb 01 04:00:00 EST 1985 · Soc. Pet. Eng. AIME, Pap.; (United States)

DOI:https://doi.org/10.2118/13506-MS· OSTI ID:5459075

Karp, A H; Greenstadt, J

The authors present a method for handling non-linear partial differential equations having solutions that develop steep fronts. Traditional methods for solving such problems (the finite difference and finite element methods) implicitly assume a simple form for the solution over a limited domain. Instead of using a simple basis set and many small spatial elements, they use a complex basis set and no spatial discretization. The method produces accurate results because they are able to include in the basis set a non-rational function that can represent a step. They have chosen to use the Buckley-Leverett equations to model the quarter 5-spot problem of oil reservoir modeling in two dimensions. The problem is a coupled system of partial differential equations - the flow equation which is nearly hyperbolic, and the pressure equation which is elliptic. In this paper we discuss the solution of the flow equation; the solution of the elliptic equation is discussed elsewhere. The test problem is two dimensional and restricted to the unit square. Extensions to three dimensions and more general geometries will be discussed.

• Research Organization: IBM Scientific ctr
• OSTI ID: 5459075
• Journal Information: Soc. Pet. Eng. AIME, Pap.; (United States), Journal Name: Soc. Pet. Eng. AIME, Pap.; (United States) Vol. SPE13506; ISSN SEAPA
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
020300* -- Petroleum-- Drilling & Production
CALCULATION METHODS
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
ENGINEERING
EQUATIONS
OIL WELLS
PARTIAL DIFFERENTIAL EQUATIONS
RESERVOIR ENGINEERING
SIMULATION
TWO-DIMENSIONAL CALCULATIONS
WELLS