Porous Media Deposition Damage from Injection of Water with Particles

Friday, January 11, 2002 - 9:30am - 10:30am
Keller 3-180
Dan Marchesin (Instituto de Matematica Pura e Aplicada)
Severe fall of injectivity in porous rock occurs from the practice in offshore fields of injecting sea water containing organic and mineral inclusions. In general, injection of poor quality water in a well curtails its injectivity. The loss of injectivity is assumed to be due to particle deposition in the porous rock; cake formation is disregarded in this work.

We model porous rock formation damage due to deep filtration during injection of water containing solid particles in a linear core. The model contains two empirical functions which govern loss of injectivity - filtration coefficient versus deposited particle concentration, and permeability formation damage versus deposited particle concentration.

Potentially, empirical models such as this one may be very useful at predicting formation damage. However, the main difficulty in the usage of empirical models is to measure the value of empirical parameters and functions.

We show how to solve the inverse problem for determining the filtration coefficient function based on effluent particle concentration measurements in coreflood experiments. We show that both the direct and inverse problems relating filtration coefficient and effluent particle concentration history have a unique solution, and that both are well posed. We discuss their numerical implementation and show results.

Once the filtration coefficient function is known, we show how to utilize the pressure drop history to find the second empirical function, the permeability damage function.

The first inverse problem is solved by an iterative procedure to solve a functional equation originating from the boundary value problem for the transport equation of the particles in the water with deposition.

The second inverse problem is solved by Tichonov regularization of an ill posed integral equation.

Thus the solution of the full inverse problem on the core is completed, and full data for predicting injectivity loss in wells is generated based on laboratory experiments.

This work was conducted together with: G. Hime (IMPA), P. Bedrikovetsky (UENF), J. R. Rodrigues, F. S. Shecaira, and A. L. S. Souza (PETROBRAS).