Pressure depletion during oil production results in increase of overburden effective stress in a porous matrix. This stress in turn causes rock compaction with deformation and consequential permeability and porosity reduction. Production rate decline during oil production due to rock compressibility has been observed in several reservoirs.

The rate decline during pressure depletion is particularly significant for totally unconsolidated or slightly consolidated sandstones, which are typical for Campos Basin reservoirs (Brazil).

Compaction with porosity reduction can improve production by squeezing oil from rock into wellbore. However, compaction can also impair permeability and reduce production. Understanding the interplay of these effects is essential for optimising well placement, for predicting of production rates and for reservoir management.

The collective effects of compaction phenomena on oil production and reservoir behaviour can be understood by means of mathematical experiments using synthetic, laboratory and field data. Mathematical modelling can do reliable prediction of oil production.

A mathematical model for radial oil flow towards wells in a deformable porous media is derived, and the boundary problem for the quasi steady state depletion processes is formulated. The solution is expressed by explicit analytical formulae. The model was applied to the reservoir R (Basin C, Brazil) and results were compared with laboratory data.


The deepwater Campos Basin is now a major area of activity for Brazilian oil industry1. The high cost of development in the environment of Campos Basin makes it essential that the reservoir behaviour is well understood before large-scale production commences. This is particularly true for rock deformation and compaction, which can highly affect the production in loose sand and poorly consolidated formations. In the latter case reservoir rock deformation due to pressure depletion during oil production can cause several physics consequences that highly affect reservoir development2–5.

Pore space deformation during reservoir pressure decrease has been observed in several reservoirs, where the production is accompanied by permeability and porosity decrease4,5. This phenomenon has been detected by observing production rate decline during production. Well tests show that permeability and porosity decrease with time2,3.

The weight of the saturated rock column above the reservoir is supported by the effective stress and by pore pressure in the reservoir rock. The phenomenon of rock deformation has been attributed to by the increase of effective stress during pore pressure decrease. Laboratory tests performed by Terzsagy8 show that permeability and porosity are function of effective rock stress. These dependencies should be taken into account in calculations for well and reservoir behaviour predictions.

Compressibility of grains in sandstones is very small; it cannot explain permeability and porosity decrease during the production period in real fields. Mainly, rock deformation is due to change of pore space geometry in the course of grain recompaction2.

The routine procedures for management of production from deformable reservoirs are:

  1. Determination of permeability and porosity variation as rock stress increases in laboratory loading-flow tests;

  2. Modelling oil flow towards the producing well in a deformable rock;

  3. Interpretation of production and well test data using mathematical modelling;

  4. Comparison of field and laboratory data;

  5. Prediction of production rate during oil production using the mathematical model.

A mathematical model should allow 1-D linear and radial formulations that correspond to laboratory tests and to flows around the well.

In the present work, a simple analytical model for oil reservoir depletion accounting for rock deformation is developed. It allows determining from well data the pressure dependence of absolute permeability.

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