Modeling fluid displacement in a well system environment

摘要

In some aspects, a one-dimensional flow model is generated. The one-dimensional flow model can represent flow of a first fluid and a second fluid in a flow path in a well system environment. The one-dimensional flow model comprises an effective diffusion coefficient model for a composite fluid volume comprising the first and second fluids. The effective diffusion coefficient model calculates an effective diffusion coefficient for the composite fluid volume based on a difference between the respective densities and viscosities of the first fluid and the second fluid.

主权项

1. A flow modeling method comprising:
receiving, from a data acquisition system, properties of a flow path in a well system environment and properties of a first fluid and a second fluid in the flow path; generating a one-dimensional flow model that models flow of the first fluid and the second fluid in the flow path in the well system environment by integrating governing flow equations over a cross-section of the flow path in a two or more dimensions based on the properties of the flow path and the properties of the first fluid and the second fluid in the flow path, the governing flow equations based on Navier-Stokes equations that account for spatial and temporal variations of the properties of the first fluid and the second fluid, the one-dimensional flow model comprising an effective diffusion coefficient model for a composite fluid volume comprising the first and second fluids, the effective diffusion coefficient model based on a difference between respective densities of the first fluid and the second fluid, the one-dimensional flow model further comprising a retarding convective factor that accounts for friction-like effects of interaction between the first fluid and the second fluids and sidewalls of the flow path; wherein the one-dimensional flow model models fluid flow in a subterranean region during an injection treatment applied to the subterranean region, the first fluid comprising an injection fluid, and the second fluid comprising a native fluid that resides in the subterranean region; on a computer system, operating the one-dimensional flow model based on a cross-section averaged fluid velocity, a cross-section averaged fluid concentration, the effective diffusion coefficient model, and a Reynolds number calculated based on the first fluid's viscosity, the second fluid's viscosity, the first fluid's density, the second fluid's density, the first fluid's average velocity, and a width of the flow path; wherein the first and second fluids comprise immiscible fluids, and operating the effective diffusion coefficient model comprising calculating an effective diffusion coefficient De for the composite fluid volume based on the equation:De=Ds+(Dd+Dμ⁢μ2-μ1μ2+μ1+Dρ⁢ρ2-ρ1ρ2+ρ1)⁢UW,where Ds represents surface diffusivity, Dd represents dispersion, Dμrepresents a viscosity difference factor, Dρrepresents a density difference factor, μ1 represents the first fluid's viscosity, μ2 represents the second fluid's viscosity, ρ1 represents the first fluid's density, ρ2 represents the second fluid's density, U represents the first fluid's average velocity, and W represents a width of the flow path; and
controlling the injection treatment based on results of operating the one-dimensional flow model during the injection treatment.