Simple model representations of transport in a complex fracture and their effects on long‐term predictions

Abstract

A complex fracture model for fluid flow and tracer transport that incorporates many of the important physical effects of a realistic fracture, including advection through a heterogeneous fracture plane, partitioning of flow into multiple subfractures in the third dimension, and diffusion and sorption into fracture‐filling gouge, small altered rock matrix blocks within the fracture zone, and the unaltered semi‐infinite rock matrix on both sides of the fracture zone, was previously developed. It is common, however, to represent the complex fracture by much simpler models consisting of a single fracture, with a uniform or heterogeneous transmissivity distribution over its plane and bounded on both sides by a homogeneous semi‐infinite matrix. Simple‐model properties are often inferred from the analysis of short‐term (one to a few days) site characterization (SC) tracer test data. The question addressed in this paper is: How reliable is the temporal upscaling of these simplified models? Are they adequate for long‐term calculations that cover thousands of years? In this study, a particle‐tracking approach is used to calculate tracer test breakthrough curves (BTCs) in a complex fracture model, incorporating all the features described above, for both a short‐term SC tracer test and a 10,000‐year calculation. The results are considered the “real world”. Next, two simple fracture models, one uniform and the other heterogeneous, are introduced. Properties for these simple models are taken either from laboratory data or found by calibration to the short‐term SC tracer test BTCs obtained with the complex fracture model. Then the simple models are used to simulate tracer transport at the long‐term timescale. Results show that for the short‐term SC tracer test, the BTCs calculated using simple models with laboratory‐measured parameters differ significantly from the BTCs obtained with the complex fracture model. By adjusting model properties, the simple models can be calibrated to reproduce the peak arrival time and height of the complex fracture model BTCs, but the overall match remains quite poor. Using simple models with short‐term SC‐calibrated parameters for long‐term calculations yields BTCs with order‐of‐magnitude errors: peak arrival time is 10 to 100 times too late, and peak height is 50 to 300 times too small. On the other hand, using simple models with laboratory‐measured properties of unfractured rock samples for 10,000‐year calculations yields BTCs with peak arrivals and heights up to a factor of 50 too early and large, respectively. The actual magnitudes of the errors made by using the simple models depend on the parameter values assumed for the complex fracture model, but in general, simple models are not expected to provide reliable long‐term predictions. The paper concludes with some suggestions on how to improve long‐term prediction calculations.