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VA – GP - OA: Numerical Multiphase PTA
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Numerical Multiphase PTA
Vincent Artus - Gérard Pellissier - Olivier Allain
1.
Introduction
In 2004-2005, KAPPA developed a multiphase option in Saphir NL. This option allowed 2-phase
flow without exchange between the phases (eg water injection in dead oil, or gas) and complex
3-phase flow with phase exchanges, for black-oil or condensate. In all those situations, it was
soon realized that multiphase simulations could exhibit large oscillations on the loglog
derivative. In the case of water injection, we were able to damp these oscillations through the
use of pseudo-kr corrections, but no ‘easy’ solution was found for black-oil or condensate. As a
consequence, a complete 3-phase option was not released, and Saphir NL was limited to two-
phase PVT including water.
With the sector model option of Rubis v4.12, 3-phase simulations can
de facto
be run in Saphir
NL, albeit through a tortuous path. It was thus decided to make the full multiphase option
directly accessible in Saphir NL during the course of the v4.20 upgrades, after a detailed
investigation of the nature of the oscillations, and the possible solutions to damp them. This
document summarizes the work undertaken; its reading is highly recommended before running
any multiphase Saphir NL cases. It is important to note that the problems described here go
unnoticed in numerical simulation, while they are exemplified in PTA by the use of the pressure
derivative, and the focus on short time scale.
Approximately a hundred numerical simulations have been run for this study, covering various
multiphase contexts across a wide range of depletion levels. Although no generic description is
possible because visible effects are strongly dependent on the simulation context (PVT, KrPc,
etc…), most of the possible situations are covered by the examples in this document.
Four main cases are presented:
Case 1 (section 2.1): water injection in an oil reservoir. Illustration of the development
of oscillations while flooding; the origin of oscillations is explained in section 2.2.
Case 2 (section 2.4): complex history of water injection into an oil reservoir. Validation
of the numerical model against the analytical results.
Case 3 (section 3.1): depletion into a black-oil reservoir. The origin of oscillations is
analyzed in section 3.2; section 3.3 is dedicated to the interpretation of the results.
Case 4 (section 4.1): depletion of a condensate gas reservoir.
The results are interpreted in section 4.2.
Yellow sections of this document are not strictly required for a global comprehension of the
origin of oscillations with multiphase transient simulations. However, they provide interesting
material for a deeper analysis of the complexity of the various physical mechanisms involved
with multiphase processes.