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 injectivity loss is assumed to be due to particle retention in the porous rock.

A model for porous rock damage due to retention in deep filtration during injection of water containing solid particles is formulated. The model contains two empirical functions that affect loss of injectivity - filtration coefficient and damage coefficient versus deposited particle concentration.

We show how to solve the inverse problem for determining the first function based on effluent particle concentration measurements in coreflood tests.

The second inverse problem is the determination of the formation damage coefficient from the pressure drop history on a core. These two methods allow determining from laboratory tests the information necessary for prediction of well impairment.


Injectivity reduction due to the injection of water containing solid particles takes place in most waterflood projects to some degree.

In designing a waterflood project, the level of water treatment necessary to minimize formation damage must be assessed, so it is important to know the performance of an injector as a function of injection water quality1. Therefore, substantial efforts have been devoted to model the injectivity decline due to injection of water with solid particles.

The basic mathematical model for deep filtration with particle retention consists of a particle mass balance equation and a kinetic equation for clogging2–4. An analytical model for diffusion-free flow was developed in paper2 under the assumptions that accumulation of suspended particles can be ignored and that the suspended concentration distribution is in steady state.

In order to predict injectivity decline in wells, the mathematical model for radial flow requires two empirical functions - filtration coefficient and permeability versus deposited concentration. The problem of determining these functions from laboratory deep bed filtration requires solving two inverse problems.

Methods for determining constant filtration and formation damage coefficients from outlet particle concentration were presented in the literature4,5. However, the general inverse problems for determining filtration coefficient and permeability damage versus deposited concentration from deep bed filtration laboratory tests have not been investigated.

In the current paper we derive an exact analytical solution for 1-D linear problem for diffusive-free particle flow accounting for particle capture, without other limitations. The explicit solution of the direct problem is the basis for finding unique, stable solution of the inverse problems.

A well-posed and stable sequence of two procedures for determining the filtration and formation damage functions from outlet particle concentration and pressure drop measurements is formulated. Closed equations are derived. The solution of the two inverse problems allows complete tuning of the model from laboratory test data enabling prediction of well injectivity behaviour.

The assumptions in the model are the following. The water and particles are incompressible. The volume of the entrapped particles is negligible compared to the effective porosity (s<<f'). The kinetics of particle capture is linear, and diffusion is negligible.

Analytical model for flow of water with suspended particles

The model describes the laboratory test on injection of water with suspended particles in core initially saturated by particle free water (Fig. 1). The suspended concentration at the core outlet (breakthrough curve) and pressure drop on the core are measured during the test.

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