Effects of aquifer geometry on seawater intrusion in annulus segment island aquifers

Seawater intrusion in island aquifers was considered analytically, specifically for annulus segment aquifers (ASAs), i.e., aquifers that (in plan) have the shape of an annulus segment. Based on the Ghijben–Herzberg and hillslope-storage Boussinesq equations, analytical solutions were derived for steady-state seawater intrusion in ASAs, with a focus on the freshwater–seawater interface and its corresponding watertable elevation. Predictions of the analytical solutions compared well with experimental data, and so they were employed to investigate the effects of aquifer geometry on seawater intrusion in island aquifers. Three different ASA geometries were compared: convergent (smaller side is facing the lagoon, larger side is the internal no-flow boundary and flow converges towards the lagoon), rectangular and divergent (smaller side is the internal no-flow boundary, larger side is facing the sea and flow diverges towards the sea). Depending on the aquifer geometry, seawater intrusion was found to vary greatly, such that the assumption of a rectangular aquifer to model an ASA can lead to poor estimates of seawater intrusion. Other factors being equal, compared with rectangular aquifers, seawater intrusion is more extensive, and watertable elevation is lower in divergent aquifers, with the opposite tendency in convergent aquifers. Sensitivity analysis further indicated that the effects of aquifer geometry on seawater intrusion and watertable elevation vary with aquifer width and distance from the circle center to the inner arc (the lagoon boundary for convergent aquifers or the internal no-flow boundary for divergent aquifers). A larger aquifer width and distance from the circle center to the inner arc weaken the effects of aquifer geometry, and hence differences in predictions for the three geometries become less pronounced.

Physics Inspired Machine Learning for Solving Fluid Flow in Porous Media: A Novel Computational Algorithm for Reservoir Simulation

The Physics Inspired Machine Learning (PIML) is emerging as a viable numerical method to solve partial differential equations (PDEs). Recently, the method has been successfully tested and validated to find solutions to both linear and non-linear PDEs. To our knowledge, no prior studies have examined the PIML method in terms of their reliability and capability to handle reservoir engineering boundary conditions, fractures, source and sink terms. Here we explored the potential of PIML for modelling 2D single phase, incompressible, and steady state fluid flow in porous media. The main idea of PIML approaches is to encode the underlying physical law (governing equations, boundary, source and sink constraints) into the deep neural network as prior information. The capability of the PIML method in handling reservoir engineering boundary including no-flow, constant pressure, and mixed reservoir boundary conditions is investigated. The results show that the PIML performs well, giving good results comparable to analytical solution. Further, we examined the potential of PIML approach in handling fluxes (sink and source terms). Our results demonstrate that the PIML fail to provide acceptable prediction for no-flow boundary conditions. However, it provides acceptable predictions for constant pressure boundary conditions. We also assessed the capability of the PIML method in handling fractures. The results indicate that the PIML can provide accurate predictions for parallel fractures subjected to no-flow boundary. However, in complex fractures scenario its accuracy is limited to constant pressure boundary conditions. We also found that mixed and adaptive activation functions improve the performance of PIML for modeling complex fractures and fluxes.

A New Method of Pressure Analysis of Well-Test Data from a Well in a Multi-well Reservoir with no Flow Boundary Condition & New Diagnostic Plots to Differentiate Between the Boundary and Interference Effects

If the interference effect is not considered for well test interpretation, it could lead to wrong analyses especially in boundary identification. In addition, there are some case where interference effects might be hidden where it may not be obvious due to data uncertainty. Therefore, special diagnostics of the multi well interference models will be required to differentiate between the boundary and interference effects. In addition, there is no analytical method for a well in a multi-well reservoir with no flow boundary condition. In this paper a new method was developed to model Pressure Analysis of Well-Test Data from a Well in a Multi-well reservoir with no flow boundary condition. It covers; Derivation of the analytical model, based on the superposition principle, with and without "no flow" boundary condition; Modeling of various combination of testing & interfering well cases (i.e. testing well is on production or shut-in while interfering well is on production or shut-in) Modeling of various combinations of testing & interfering well rate cases (i.e. production or injection, rate variations) Modeling of various number of interfering well cases (i.e. location and well count) Investigation deeply on how to differentiate between the boundary and interference effects (or vice versa) and developing the special diagnostics to able to detect interference effect directly. Results are shown that 1) the multi-well interference effect with and without no flow boundary condition has huge impact on the well test interpretation and this effect might be interpreted as a boundary effect if interference is not considered. 2) Build-up (BU) behavior of testing well is depending on whether interfering well is shut-in or producing. If interfering well is producing, pressure derivative of BU curve is concave down and If the interfering wells are shutting in, pressure derivative of BU curve is concave up 3) the interfering well rate is affecting magnitude of impact on pressure derivative and the higher the rates, the bigger the response 4) the interfering well distance is affecting the timing of deviation on pressure derivative and the closer the distance, the quicker the response Study also concluded that there are 3 special characteristics, which only exists in interference cases, and which does not exist in boundary cases. Therefore, those characteristics can be used to differentiate between the interference and boundary effects. Those are 1) Pressure decrease or rise at the beginning of well testing 2) the drawn-down (DD) and BU pressure derivatives in Log-Log plot are different (i.e. when BU is concave up, DD is concave down or vice versa) in case of interfering well is on continuous production 3) The consecutive BU's (or DD's) pressure derivatives on Log-Log plot are different and changing over time

Effects of aquifer geometry on seawater intrusion in annulus segment island aquifers

Seawater intrusion in island aquifers is considered analytically, specifically for annulus segment aquifers (ASAs), i.e., aquifers that (in plan) have the shape of an annulus segment. Based on the Ghijben-Herzberg and hillslope-storage Boussinesq equations, analytical solutions are derived for steady-state seawater intrusion for ASAs, with a focus on the freshwater-seawater interface and its corresponding watertable elevation. These analytical solutions, after comparing their predictions with experimental data, are employed to investigate the effects of aquifer geometry on seawater intrusion in island aquifers. Three different geometries of ASA are compared: convergent (smaller side facing the lagoon), rectangular and divergent (larger side facing the sea). The results show that the predictions from the analytical solutions are in well agreement with the experimental data for both recharge events. In addition, seawater intrusion is most extensive in divergent aquifers, and conversely for convergent aquifers. Accordingly, the watertable elevation is lowest in divergent aquifers and highest in convergent aquifers. Moreover, the effects of aquifer geometry on the freshwater-seawater interface and watertable elevation vary with aquifer width and distance to the no-flow boundary. Both a larger aquifer width and distance to the no-flow boundary weaken the effects of aquifer geometry and hence lead to a smaller deviation of seawater intrusion between the three geometries.