Interwell simulation model for the advection dispersion equation

Abstract

We propose an interwell simulation model for the advection dispersion equation (ISADE) to predict the concentration of contaminant observed at the pumping well. This method comprises of two main steps. Initially, the model divides the aquifer or reservoir into a series of 1D injector-producer pairs and uses the historical contaminant observation data to estimate five major unknowns in each of these control volumes: the interwell connectivity, the pore volume, the volumetric flowrate at the grid face, the dispersion coefficient, and the number of grid cells in each control volume. Finally, once the history matching process is complete, the estimated variables are used to predict the concentration of contaminant observed at the wells. One main advantage of modeling contaminant production using the ISADE model is that it is computationally cheaper than the full physics model as it uses a series of one-dimensional connections between each producer-injector pair with all pairs connected to each other by interconnectivity factors. The advection diffusion equations is then solved for each of these pairs independently. Three examples were presented to test the effectiveness of the ISADE model. Each of the three examples involves flow of fluid in a synthetic heterogeneous aquifer with different well configurations and varying concentrations of the contaminant released into the aquifers at some injection locations. In Examples 1 and 3, non-reactive contaminants were introduced into the respective aquifers through injection wells, while in Example 2, nonreactive contaminant was introduced into the aquifer from a from a node on one of its boundary. All the examples studied show that the results obtained from ISADE closely match those from the full-scale simulation model. Furthermore, the model can easily handle changes in input parameters such as the concentration of contaminants released in the aquifer, and the injection and production rates.