Patent Document ID: 20160348489
Application ID: 14912848
Patent Flag: 0

Claim One:
1. A computer-implemented method for higher order simulation of hydrocarbon flows of hydraulic fracture treatments, the method comprising: generating a discretized hydrocarbon flow along a 1-dimensional flow grid in a hydraulic fracture treatment of a well system, the hydrocarbon flow defined by a first governing equation for conservation of mass and a second governing equation for conservation of momentum, wherein the first governing equation and the second governing equation are continuous equations, further comprising: approximating a spatial first derivative of an advection term of the second governing equation using a piecewise 1-dimensional solution, wherein the spatial first derivative of the advection term is approximated using a second order accurate n-point stencil; for boundary nodes of the flow grid for which the n-point stencil exceeds the flow grid, re-normalizing the spatial first derivative of the advection term as a one-sided Taylor series in terms of a spatial second derivative of the advection term; and approximating the spatial second derivative of the advection term based on the second governing equation; and based on the discretized hydrocarbon flow, determining a production activity for extracting hydrocarbons from the well system.