INFLOW CONTROL APPARATUS, METHODS, AND SYSTEMS

摘要

In some embodiments, a simulation apparatus may comprise a processor and a memory to store a set of instructions, which when executed by the processor, forms a machine programmed to generate an analytical solution to simulate multiple scenarios for a total fluid flow rate in order to find one of the scenarios that meets a desired total flow rate for a fluid flow entering a portion of a screen to pass through one or more orifices in a base conduit covered by the screen. Additional apparatus, systems, and methods are described.

主权项

1. A simulation apparatus, comprising:
a processor; and a memory to store a set of instructions, which when executed by the processor, forms a machine programmed to generate an analytical solution to simulate multiple scenarios for a total flow rate J in order to find one of the scenarios that meets a desired total flow rate for a fluid flow entering a portion of a screen to pass through at least one orifice in a base conduit covered by the screen, wherein the total flow rate J is provided byJ=2πkf(pB-pin)μrsln(rBrs)λ1λ2(f1+f2)f1=λ2{sinh(λ1zm)-A1[1-cosh(λ1zm)]}f2=λ1{sinh[λ2(L-zm)]+A2[1-cosh(λ2(L-zm)]]}where pB is a boundary pressure associated with a surrounding formation, pin is a pressure associated with an inlet gap between the screen and the base conduit, μ is a viscosity of the fluid, rs is a radius of a sand-formation interface surrounding the conduit, rB is a drainage radius associated with a well defining the sand-formation interface, λ1 isΩ1+ωL,λ2 isΩL,zm is a length of the screen that is exposed to the fluid, A1 isλ2F1cosh[λ2(L-zm)]-F2sinh[λ2(L-zm)]λ2sinh(λ1zm)cosh[λ2(L-zm)]+λ1cosh(λ1zm)sinh[λ2(L-zm)],A2 isF1-A1sinh(λ1zm)sinh[λ2(L-zm)],F1 is cosh[λ2(L−zm)]−cosh(λ1zm), F2 is λ1 sinh(λ1zm)+λ2 sinh[λ2(L−zm)], L is a length of the base conduit, Ω is2kfL2ks(rs2-r02)ln(rBrs),ω ish36ksr0(rs2-r02),kf is a permeability of the formation in the sand-formation interface, ks is a permeability of the sand in the sand-formation interface, and r0 is a radius of the conduit.