No abstract

Analytical models to describe tracer transport in reservoirs commonly set conditions either on the tracer concentration or the tracer flow at the injection border. Here a different formulation based on tracer sources is presented. This approach avoids some of the physical inconsistencies that can be found when setting conditions on the tracer concentration. The case of a tracer injected as a finite-step in an infinite one-dimensional homogeneous reservoir with a uniform flow is considered. The solution is analytically obtained. The results are confronted against the two common boundary cases. The new approach predicts slightly delayed and broader pulses. The tracer breakthrough curves differences can be large for small Peclet numbers. These differences weakly reduce by increasing the injection period. The new approach contains tracer injection elements that can make it suitable to describe real conditions found in reservoir tracer tests.

No abstract

Tracer tests are fundamental in characterizing fluid flow in underground formations. However, the setting of appropriate boundary conditions in even simple analytical models has historically been controversial, mainly due to the lack of sufficient physical evidence. Determining the relevance of boundary conditions on tracer test analysis becomes therefore a topic of renewed interest. The subject has been previously disscused by studying the tracer breakthrough curve sensitivity to diverse model parameter values. In our present work we examine the issue from a new practical reservoir characterization perspective. Two well-known equivalent elementary tracer transport models having different boundary conditions are matched to the same tracer test data. The resulting model parameter difference quantifies the effect of boundary conditions on reservoir property determination. In our case a tracer pulse injected in a homogeneous one-dimensional porous medium and moving at constant speed dominated by advection and dispersion is considered. The tracer transport models to be used yield conditions (i) on the tracer concentration, and (ii) on the tracer flux. Three data sets from tracer tests performed in different oil reservoirs are used to fit the models and determine the parameter values. We found that boundary conditionsbecome more important as Peclet number gets smaller. The cases analyzed have Peclet numbers 25.0, 5.4 and 3.7. The largest parameter difference obtained in each case is 5%, 18% and 37% respectively. These differences are large for laboratory experiments, but less relevant for tracer tests in oil fields, where data variability is frequently high. Nevertheless, attention should be paid when small Peclet numbers are present.

En la interpretación de pruebas de trazadores entre pozos en yacimientos petroleros, geotérmicos y en acuíferos se emplean diversos métodos de regresión no lineal para determinar algunas de las propiedades físicas promedio del sistema roca fluido. Con este propósito se ajustan modelos analíticos a los datos de campo de surgencia del trazador y se determinan los parámetros libres del modelo. La no linealidad inherente al problema puede en ocasiones dar lugar a soluciones múltiples, las cuales corresponden a distintos mínimos locales. En la metodología de interpretación tradicional se hace uso de un solo método de optimización, y se considera diversos valores iniciales de los parámetros para analizar la existencia de varias soluciones. En general, este procedimiento resulta complicado y requiere de largos tiempos de cómputo. Además, para obtener resultados confiables es necesario proponer valores iniciales cercanos al óptimo global, los cuales en muchos de los casos de campo se desconocen. El empleo de distintos métodos de búsqueda para obtener el óptimo global resulta entonces una herramienta de gran utilidad. En este trabajo presentamos una nueva metodología que consiste en el uso simultáneo de varios métodos de optimización y de tan sólo pocos valores iniciales. De esta manera se pueden encontrar soluciones al problema inverso de forma relativamente simple y confiable.