To predict correctly injectivity for Produced Water Re-Injection (PWRI), a good description of the formation damage by oil and solid particles have to be introduced in simulators for both fractured and non fractured flows. It is well known that the complex mechanisms of the formation of an external filter cake and of a deep internal damage should be better understood. In a previous published work 1 we attempted to quantify the petro-physical external filter cake properties. In this paper, results from core flood experiments (CFE) aimed to quantify the internal damage are presented. In recent published works, CFE were performed to examine, along rock samples, the deposition profile of only solid particles. The present work focuses on the oil droplets deposition profile. The mechanisms and laws governing the internal damage with oil are different from those concerning solid particles. Like solid particles, oil tends to deposit preferentially at the core entrance but quickly a moving front of oil droplet is generated. According to our experimental results a simple method for modeling the evolution of the internal damaged permeability is presented and finally an attempt is made to extrapolate these results to the well scale for both matrix and fractured flows.
Models to reproduce injection injectivity of water solid suspension in wells are available 2,3,4. In these models, the physical formulation of internal damage is based on the classical deep bed filtration concept which needs to be calibrated with two parameters: The filtration coefficient ? and the formation damage coefficient ß. The filtration coefficient was extensively studied experimentally and a wide range of values of this parameter for a variety of solid particles was published 5. In our knowledge, no values of this parameter are available for oil and sSolid particle suspensions flow. The ß coefficient was for a long time difficult to determine experimentally for solid suspensions and from our knowledge no values of this coefficient are available in the literature for oily or oil and solid particle suspensions. A new method was recently proposed 6 to quantify parameters ? and ß from laboratory pressure measurements using the called 3 point pressure method. Other models 7,8 dedicated to simulate produced water re-injection under fracturing conditions, the depth of the internal damage is simply calculated from the injected volume of oil assuming an oil saturation and a fixed damaged permeability in the invaded zone. For other works 9 the concept of Barkman and Davidson is still used to simulate produced water injectivity decline.
Towards this persevering difficulty to measure correctly the bed filtration coefficients especially when oil is involved, an alternative approach was chosen. It consists to quantify directly the permeability decline with an empirical law. Once the law is calibrated on core flood data, the law parameters are then extrapolated to the well scale. Empirical laws were already proposed for solid suspensions in the literature 10,11 which enables to correlate permeability decline with the fluid-rock system. Recently, an empirical law for internal formation damage was coupled 12 with reservoir flow and geo-mechanics to reproduce Pwri fractured well behavior. In the present paper a quite similar concept has been used just to compute the damaged reservoir permeability in matrix flow and then extended to fractured flow.
The empirical law reproduces damaged permeability evolution for oil and solid particle emulsions. This law has the particularity to stabilize the permeability decline after a certain injection duration. Indeed, from the set of core flood experiments presented here after, oil, like solid particles, tends to deposit preferentially at the core entrance but far from the core entrance it generates a stabilized internal damage and permeability decline. This stabilization was also already observed in other works 13,14.