How does the van Everdingen-Hurst method typically apply to geothermal reservoir simulation when dealing with a limited aquifer?

The van Everdingen-Hurst method, also known as the radial composite model, is used in geothermal reservoir simulation to model the water influx from an aquifer (a water-bearing underground layer of rock or sediment) into a geothermal reservoir. It's especially relevant when the aquifer is limited, meaning its size and ability to supply water are not infinite. In this scenario, the aquifer's pressure declines as it provides water to the geothermal reservoir due to production. The method represents the aquifer as a series of concentric rings or regions with different properties. The innermost region is adjacent to the geothermal reservoir, and the outer regions represent the rest of the aquifer. When applied to a limited aquifer, the van Everdingen-Hurst method accounts for the decline in aquifer pressure as water is withdrawn. This is done by calculating a dimensionless time function and a water influx function that depends on the pressure difference between the initial aquifer pressure and the pressure at the boundary between the reservoir and the aquifer. Because the aquifer is limited, the pressure at its outer boundary will also decline over time, affecting the overall water influx into the reservoir. The model then uses superposition, a technique to account for variable production rates over time. This involves summing up the effects of each pressure drop increment at different times on the water influx. This is essential for accurately predicting the long-term behavior of the geothermal reservoir when connected to a finite aquifer. The method's mathematical formulation ensures that the total water influx is proportional to the cumulative pressure drop in the aquifer over time, but also considers the aquifer's limited capacity to recharge, making it critical to predicting the reservoir's pressure maintenance and long-term productivity.