The reinjection of produced water is an important prerequisite for maintaining pressure and for flooding reservoirs. Thirty years ago Barkman and Davidson introduced the first comprehensive theory for predicting the behaviour of injection wells. This theory was employed and tested for many years in actual injection projects at ‘Preussag-Energie’, including the development of a special-purpose instrument. In the present article, a survey of operational experience is given, and necessary extensions of the model are delineated. Furthermore, the article highlights some important aspects which should be considered in laboratory investigations.


Water is injected into porous layers for pressure maintenance in oil reservoirs, in geothermal projects and more recently for the disposal of brine from the salt caven leaching process.

This may lead to several severe problems. One particular source of danger are the solids which are suspended in the water. If they are deposited above the sandface (cake filtration) or within the formation (deep bed filtration), the injectivity may be reduced dramatically. This leads to increasing injection pressures and consequently to costly stimulations or even to irreversible wellbore damage.

The first comprehensive and apparently most often quoted publication which deals with the requirements for the quality of injection water and which presents models to predict injectivity, was presented by Barkman and Davidson some 30 years ago [1]. Although many articles have been published on this topic since then, the present state of its predictive power is rather poor. It is a frequent experience that predicted lifetimes or half-lives of injection wells are orders of magnitude below the actually observed values [2, 3]. The authors' recommendation to determine the model parameters by membrane filtrations has often been considered to be the cause of these false predictions [4]. An alternative strategy would be to employ core samples for measuring and predicting injectivity behaviour. Because of the lack of documented success with this approach, the validity and accuracy of the proposed models is not ascertained. Some reviews on models and experiences can be found in Vetter et al. [4] and Todd et al. [5].

For many years, the models and methods of Barkman and Davidson have been applied systematically at ‘Preussag Energie’ to the planning and interpretation of reinjection projects. In view of the aforementioned problems and the authors' own experiences, the theory of Barkman and Davidson was critically analysed and advanced. For this purpose we adopted a pragmatic approach analysed the behaviour of individual injections in detail and compared them to model predictions. The present article summarizes these developments, provides hints for application and indicates unresolved problems. Other approaches to the further development of injection predictability and the model of Barkman and Davidson may be found e.g. in [6] and [7].

Barkman and Davidson: A short review

Barkman and Davidson [1] assume that solids suspended in the water will be deposited as a filter cake above the sandface or other filter media. They consider this process, known as ‘cake filtration’, at constant injection pressure (p = const). Then, the temporal development of injectivity is given by the deterioration of the injection rate Q(t). The authors normalize this development by the initial rate Q0 and introduce the dimensionless decline parameter:

Equation 1

As a simple indicator for the injection behaviour they introduce the half-life t1/2, at which the rate Q has declined to one-half of its initial value Q0: a(t1/2) = 1/2. Figure 1 shows an example for the decline curve aa(t) and the half-life.

For injections, four different scenarios are considered:

  • Wellbore narrowing: The filter cake is deposited above the sandface of an open hole and thus reduces the effective wellbore radius.

  • Perforation plugging: The filter cake is deposited at the tip of perforations and thus reduces their effective lengths.

  • Invasion: The filter cake builds up inside the formation at an unpredictable ‘radius of invasion’ and grows towards the sandface

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