Permeability is a property of a porous material and a measure of its capacity to transmit a fluid. Permeability is largely dependent on the size and shape of the pores in the substance and, in granular materials such as sedimentary rocks, on the size, shape and packing arrangement of the grains.

In general, permeability is evaluated in the laboratory by analysing samples taken from the oilfield, but the results obtained by this technique are subject to considerable uncertainty. Firstly, the core samples are small and limited to sectors around the wells. There is always a question about the representativeness of the sample for the reservoir. However, the use of interwell tracers allows average values of the permeability in the swept volume between wells to be derived.

On the basis of Darcy’s law and many simplifications, a simple formula for permeability evaluation can be developed:

к-тіг(->(7) (l3)

where

K is the permeability;

ф is the porosity;

Sw is the water saturation;

m is the viscosity;

r is the the radius of the production well;

d is the the distance between the injection well and the production well;

AP is the differential pressure between wells; t is the mean residence time.

Although this expression supposes a number of simplifications, it constitutes an acceptable approach from the experimental point of view. The main use is to derive comparative values related to the permeability of different layers in the same pattern or of several stratifications in a unique layer.

2.4.2. Interpretation

Interpretation of the response curves obtained in production wells is the final objective of an interwell study. The tracer method gives correct and comprehensive information about the reservoir’s hydrodynamic parameters, allowing the reservoir engineers to understand better the phenomena and probably to increase the recovery. Four levels of complexity are generally accepted:

(1) Qualitative: Important information can be obtained just by looking at the response curves or by means of simple calculations. Breakthrough and mean residence times, distribution of injected water, recovered tracer mass or activity and swept volume are among these parameters.

(2) Basic models and software: Decomposition of complex curves into simple ones easy to approximate by elemental functions, moment determination and evaluation of statistical parameters, simple calculations and the fitting of experimental data. Anduril software (developed by Argentina) fulfils these operations and is used for simple analysis of tracer response curves.

(3) Streamline models: The volume under study is divided into a quasi-two­dimensional grid in small cells. Assigning to each one certain properties (pressure, permeability, porosity), streamline pictures are generated by solving the pressure equations. By this method it is possible to fit the experimental data in order to obtain structural information from the reservoir.

(4) Reservoir simulators: Generally, these comprise commercial and expensive software with capabilities to simulate reservoir behaviour under different conditions. Some of them have a rather basic ‘tracer’ option to evaluate the application of water tracers.

Analysis of the response curves consists of several steps:

(1) The simpler interpretation is the qualitative one. Just by observing the curves, the following pattern characteristics can be derived: injection water arrival time (breakthrough); high permeability channels, barriers and fractures between both wells; communications between different layers; stratifications in the same layer and preferential flow directions in the reservoir. This interpretation level is completed by means of some simple calculations from the numerical response, firstly, the determination of the mean residence time. The cumulative response can be obtained by integration of the concentration versus time curve, assuming the production flow rate is known. From this new curve, the fraction of injection water reaching each producer is easily calculated. A standard spreadsheet is the best way to make all these calculations.

(2) A second level involves the use of basic mathematical models to fit simple response curves by means of theoretical expressions and to decompose complex responses in several simpler functions. In this way partial residence times, as well as other parameters, can be determined for each function. Mathematical models also allow the evaluation of some important parameters such as permeability and make it possible to predict the behaviour of unknown patterns.

(3) Finally, it is possible to make use of complex mathematical models such as numerical simulators in order to achieve a more rigorous analysis. Such tracer simulators may be coupled to full field reservoir simulators where the current reservoir model is used as input (geology, stratification, etc.). This is especially useful when the well pattern is complex, the reservoir heavily faulted and there is a complex production strategy.

(4) Reservoir simulators with a tracer option are powerful tools for determining the parameters of systems under study, for planning infill well drilling and for future tracer examinations. Well-known reservoir simulators such as ECLIPSE and VIP both have relatively simple tracer options which may be used for passive water tracers, while it is probable that the simulators from Computer Modelling Group in Calgary, Canada, represented by STARS, have the most advanced tracer simulator included. This can also be used for reversibly sorbing and phase partitioning tracers.