Injectivity decline is a chronicle disaster during produced water re-injection (PWRI); the phenomenon has been widely reported in the literature for North Sea, Gulf of Mexico and Campos Basin fields. The damage happens due to solid and liquid particles in the re-injected water. The injectivity decline prediction is important for planning and design of PWRI, of injected water treatment and of well stimulation procedures. The reliable prediction should be based on mathematical modelling using well injectivity index history and laboratory data.

The mathematical models for deep bed filtration of particles and for external filter cake formation have been developed and adjusted to coreflood and well data by numerous authors (Sharma, Khatib, Wennberg et. al.). Here we add modelling of external cake erosion during well closing by the growing cake and filling the well by the erosion particles and develop a comprehensive model.

The comprehensive model predicts very peculiar injectivity index (II) curve: initial II increase due to displacement of oil by less viscous water, slow II decline due to deep bed filtration, fast II decrease during external filter cake formation, II stabilization due to cake erosion during the rat hole filling by the eroded particles and further II decrease during well column filling by erosion products.

The model is implemented in Excel; the software SPIN Simulates and Predicts the INjectivity.

We present in details the history matching for three injectors (field X, Campos Basin, Brazil), showing good agreement between modelling and well data. The obtained values of injectivity damage parameters lay in the same rage intervals as those calculated from laboratory corefloods.


Drastic decline of injectivity is a wide spread disaster in offshore and onshore waterflood projects and during produced water re-injection (PWRI) in oil reservoirs 1,2. The reason for injectivity decline is the formation of internal and external cakes by solid and liquid particles containing in the injected aqueous suspension.

The mathematical models for deep bed filtration of suspended particles with internal cake formation and for development of the external filter cake are well established 3–6. The models are used for injectivity index decline forecast 4–7.

The reliable prediction of injectivity decline from well injectivity index history would allow planning of injected water treatment and well stimulation procedures. The reliable prediction should be based on mathematical modelling using parameters, which are to be well known for specific well/field.

The injectivity damage system during deep bed filtration and external filter cake formation is characterised by four parameters: filtration and formation damage coefficients, critical porosity fraction and filter cake permeability 4–6. Nevertheless, just three constants can be extracted from well injectivity decline curve: the impedance slope during deep bed filtration, the transition time and the impedance slope during external cake formation. The three measured constants are functions of the four injectivity damage parameters, i.e. the values of three constants form a system of three equations for four unknowns. So, one equation is missing.

In order to close the system of equations, one can assume the aposteriori known value of critical porosity fraction 4,6,7. Another way around the problem is to use the correlation between the critical porosity fraction and the formation damage coefficient, observed in the work 8, as an additional equation.

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