Water Injectivity Tests on Multilayered Oil Reservoirs

Abstract

Completion of water injection wells directly into production oil zone has become a common practice on offshore development projects. Hence, injectivity tests started to play an important role for reservoir management of these fields. In an injectivity test a single phase (water) is injected continuously for a certain period of time in an oil saturated zone followed by a falloff period. Though single-phase flow of a slightly compressible fluid analysis methods are well documented in literature, transient two-phase solutions and analysis techniques need further development. Analytical solutions that model pressure behavior during a single layer injectivity test were recently presented in literature. This paper presents a new analytical solution for a vertical water injection well completed in a layered oil reservoir of infinite extent. To the best authors’ knowledge, the proposed solution was not presented before. Two phase immiscible displacement of oil by water in a multilayer reservoir is modeled by a system of partial differential equations. This system is weakly non-linear and can be decoupled by assuming steady-state conditions in the two-phase region. The solution is then obtained by the method of characteristics on the two-phase region coupled with the infinite acting single phase radial flow solution valid for the oil region. The solution derived in this work can be used to compute the wellbore pressure, injection rates and the water front for each individual layer without resorting of a numerical flow simulator. Parameter estimation from field data can be obtained from the proposed solution if a production logging rate profile is available. Two synthetic examples are used to verify the solution derived in this work. The first example considers the behavior of a two-layer reservoir whereas in the second case a reservoir with seven layers is analyzed. The wellbore pressure is compared to a finite difference simulator. An excellent agreement is obtained for both examples.

Modeling Falloff Tests in Multilayered Reservoirs

“…To the author's best knowledge, the first work regarding injectivity tests in multilayer reservoirs was presented by Barreto et al (25). They applied Darcy's law to one given layer, so that an expression for the pressure change in this layer during the injection period is obtained.…”

“…As disclosed in this overview, existing analytical models lack to describe falloff period in multilayer systems. Using the formulation developed by Barreto et al (25) as basis, this work will attempt to extend the analytical model for falloff period in single-layer reservoirs (24) to multilayer systems as well.…”

“…In this chapter, the formulation for single-layer reservoirs during the injection period, developed by Banerjee et al (20) and Peres et al (22), will be presented. This model will be extended to multilayer systems, as proposed by Barreto et al (25). All calculations assume that a consistent unit set is used.…”

“…The starting point in order to compute the pressure variation in the reservoir during an injectivity test is Darcy's law (20,21,25), that models flow through porous media. It states that flow-rate of a given fluid is calculated as:…”

“…From now on, this term will be referred to as ∆P o (t). Besides that, the term multiplying the layer flow-rate will be denoted as a weight variable A j (t) (25):…”