Two common measures of heterogeneity can be obtained from the (F Ф)- plot: the Lorentz coefficient (Lc) and the Dykstra Parsons coefficient (VDP) [32]:

(45)

•

Lc varies between 0 and 1, with 0 representing a homogeneous flow field.

• F is the derivative of (F, Ф). It is evaluated at the mean (0.5) and at one standard deviation below the mean (0.841).

IV. 2.1.5. Volumetric fluid sweep efficiency

Volumetric fluid sweep efficiency is a measure of efficiency for use of the injected fluid. It expresses that fraction of the injected water which is actively contributing to pushing the original fluids in the reservoir. Using the concept of streamlines and the definition of ‘F above, it is possible to estimate sweep efficiency directly from a tracer test.

The F(t) term can be interpreted as the fraction of streamlines that have ‘broken through’ and have started to produce injected fluid. These streamlines are not contributing further to sweeping of the reservoir. In the opposite sense, at the beginning, all the injected water is active and the sweep efficiency must be at a maximum. Hence, sweep efficiency can be expressed in terms of fractional tracer recovered and injection rates:

Sweep efficiency is typically reported as a function of dimensionless time or time normalized by the total pore volume:

„ qinj m t tD — t —

D V Mnj t *

IV. 2.1.6. Limitations of the method

• Conservative tracer travelling jointly with the water bulk flow is required.

• Steady state flow is necessary.

• The necessity for extrapolation of the tracer records (tracer production curve). Sampling for tracer is frequently terminated long before the tracer concentration falls to zero. Because the first moment is a time weighted average, failure to include late time data leads to the underestimation of
both mean residence time and pore volume. A decline pattern composed of exponential terms is most commonly observed.

• The difficulty of distinguishing between the imposed flow geometric effects (resulting from the injection pattern) and heterogeneity effects.

• The estimations can be erroneous if the tracer does not move with the ‘bulk flow’. This happens, for example, in double porosity rocks with diffusion in the secondary porosity.