Session: 11-02-01 Well Drilling Fluids and Hydraulics-1

Submission Number: 176602

Multi-Component, Multi-Phase, Transient Hydraulic Model Based on the Method of Characteristics 

Hydraulic junction points between the drillstring interior and the annulus—such as at under-reamers, circulation subs, or leaks between the stator and rotor of a downhole motor—require the drilling hydraulic system to be modeled as a hydraulic network. Additional pumping in the marine riser to boost flow and aid cuttings transport further extends this network. A transient hydraulic model for drilling must therefore handle multiple hydraulic branches and junctions. In civil engineering, the method of characteristics (MOC) has long been used to solve transient flow in water distribution networks. This study investigates whether the MOC can be adapted effectively to drilling hydraulics.

The MOC transforms hyperbolic partial differential equations into ordinary differential equations (ODEs), offering an efficient alternative to finite difference or finite element methods, which require solving large linear systems. The drilling context, however, is more complex than water distribution networks: drilling fluids are non-Newtonian, slightly compressible, temperature-dependent, and multi-component/multi-phase. Some components may also settle temporarily in the annulus, changing its geometry. To apply the MOC properly, we begin with the governing equations of continuity and momentum conservation, verifying their hyperbolic nature under these assumptions. From these, the characteristic lines and associated Riemann invariants are derived, yielding the equivalent ODEs. The model also addresses the conditions at junctions between hydraulic branches.

The formulation reduces the problem to solving a system of ODEs with a Runge–Kutta scheme, avoiding iterative methods at each time step. The time step is governed by the Courant–Friedrichs–Lewy (CFL) condition. The solver is embedded within a broader thermo-hydro-mechanical model that accounts for coupled heat transfer, fluid flow, and mechanical interactions, all solved via the MOC. Implemented as a microservice, the solver enables simulations of complex scenarios, where boundary conditions evolve to represent operational sequences.

The full source code and microservice are released as open source, with a reference implementation available online. This provides the drilling community with a transparent and openly accessible simulator, supporting both research and benchmarking of other simulation tools.

Presenting Author: Eric Cayeux NORCE Norwegian Research Centre

Presenting Author Biography: Eric Cayeux is chief scientist for the Energy modelling and automation group at NORCE. After an 18 years career in the industry working with the development of expert system solutions for directional drilling and multi-disciplinary (geophysics, geology, reservoir engineering and drilling) well planning applications, he joined NORCE in 2004, where he worked with drilling automation, real-time drilling diagnostic and drilling simulators. The last decade, he has more focused on basic research and mathematical modelling of the drilling process. Cayeux holds an M.Sc. degree in civil engineering from Ecole Nationale des Travaux Publics de l’Etat, Lyon, France, an M.Sc. degree in software engineering from the University of Nice, France, and a Dr. Philos. degree in petroleum engineering from the University of Stavanger, Norway.

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