3-D numerical simulation of horizontal well gravel pack.

Abstract

The modeling equations consist of five partial differential equations with five dependent variables, all of which were solved simultaneously. The system of partial differential equations was approximated using the central-difference finite-difference approximations method. The resulting system of non-linear algebraic equations was then solved using the Newton's method of solving nonlinear simultaneous equations. A solution algorithm was developed and implemented using a computer program. HGPSIM, a horizontal well gravel pack simulator was developed to implement the solution algorithm. The usefulness and validity of the model was also illustrated by simulating some horizontal gravel pack jobs reported in the literature and performing sensitivity study using the developed simulator.

The model was developed based on the fundamental laws of physics by solving for an overall conservation of forces during the placement of the gravel in the horizontal well bore. The equations of continuity, motion, and deposition are simultaneously solved to give a 3-D solution of the gravel pack process. The settling effect of slurry using the type of fluid, proppant and flow conditions existing in gravel pack operations in horizontal wells were also included in the model.

The chief technical contributions of this study are: (1) A 3-D numerical simulation model is developed that offers a significant improvement over the currently available empirical, 1-D, 2-D and pseudo 3-D horizontal well gravel pack models. (2) The model is a true 3-D model and can be used to simulate special situations in which significant leakage into the formation occur during gravel packing. (3) The developed horizontal well gravel pack model can be used for simulating the gravel pack process and determining the effectiveness, total pack efficiency and average pressure throughout the well bore during the gravel pack job. (4) The simulator is useful for designing jobs where there is a slim margin between reservoir fracture pressure, equipment failure pressure, and surface injection pressure by predicting the expected surface injection pressure before committing expensive assets to the job.

A 3-D numerical simulation model for horizontal well gravel packing is developed. The model is used for simulating the gravel pack process and determining the effectiveness and pack efficiency of the gravel pack job. This model, being a true 3-D model can be used to simulate special situations in which significant leakage into the formation occurs during gravel packing. It can also be used to model recent horizontal well gravel pack techniques like Alternative Path(c) technology in which significant radial flow occur at different points in space and time during the process. The simulation model is particularly suitable for deep horizontal wells because the hindered settling effect prevalent in the long vertical section of deep horizontal wells is accounted for in the modeling equations.