Investigación

On the boundary conditions in tracer transport models for fractured porous underground formations

M. Coronado, J. Ramírez–Sabag, and O. Valdiviezo–Mijangos

Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, 07730 México D.F., México, e–mail: mcoronad@imp.mx, jrsabag@imp.mx, ovaldivi@imp.mx

Recibido el 24 de octubre de 2006
Aceptado el 7 de junio de 2007

Abstract

A boundary condition traditionally used in analytical models for tracer or contaminant pulse transport in porous underground formations gives the tracer concentration at the injection border as a discontinuous function in time. It has recently been shown that this condition leads to a physically improper pulse behavior. Models using sounder boundary conditions are already available for non–fractured porous media, but not for fractured media, where the traditional condition is commonly employed which can potentially lead to errors. We develop two new formulations to describe tracer tests in fractured media. They set conditions (i) on the total amount of injected tracer and (ii) on the tracer flow. The new formulations are compared against the traditional debatable model by examining tracer breakthrough curve differences. It has been found that they are important at small Peclet numbers. Differences are analyzed in two ways, by (a) employing typical model parameter values, and (b) fitting the three models to the same field tracer data set, and comparing the resulting model parameter values. In the first case the breakthrough curve difference has been quantified at 25%, and in the field tests considered in the second case it was from 1% to 10%. In general these discrepancies are small, but could become significant in some cases.

Keywords: Boundary conditions; tracer transport; porous media; fractured reservoirs.

Resumen

Una condición de frontera usada tradicionalmente en modelos analíticos de transporte de un pulso de trazador o de contaminante en formaciones porosas subterraneas, establece la concentración de trazador en la frontera de inyección como una función discontinua en el tiempo. Recientemente se mostró que esta condición da lugar a comportamientos físicamente inadecuados del pulso. Modelos con condiciones de frontera mas sólidas existen para formaciones no–fracturadas pero no para fracturadas, para las cuales se emplea comúnmente el modelo tradicional, lo cual puede llevar a conclusiones erroneas. En este trabajo se presentan dos formulaciones para medios fracturados que están basadas en condiciones de frontera sólidas que especifican (i) la cantidad total de trazador inyectado, y (ii) el flujo de trazador en la frontera. Las nuevas formulaciones son comparadas con el modelo tradicional en terminos de las diferencias en la curva de surgencia del trazador. Las discrepancias son importantes a números Peclet pequeños. Ellas son cuantificadas empleando (a) valores típicos para los parámetros involucrados en los modelos, y (b) ajustando los tres modelos al mismo conjunto de datos de pruebas de trazadores y comparando el valor de los parametros obtenidos. En el primer caso la diferencia encontrada es 25% y en el segundo de 1% a 10%. En general estas discrepancias son pequeñas, pero podrían ser significativas en algunos casos.

Descriptores: Condiciones de frontera; transporte de trazador; medios porosos; yacimientos fracturados.

PACS: 05.60.Cd

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