Electrochemical deionization devices are crucial for meeting global freshwater demands. One such is capacitive deionization (CDI), which is an emerging technology especially suited for brackish water desalination. In this work, we extend an electrolytic capacitor (ELC) model that exploits the similarities between CDI systems and supercapacitor/battery systems. Compared to the previous work, we introduce new implementational strategies for enhanced stability, a more detailed method of describing charge efficiency, layered integration of leakage reactions, and theory extensions to new material and operational conditions. Thanks to the stability and flexibility the approach brings, the current work can present the first fully coupled and spatiotemporal three-dimensional (3D) CDI model. We hope that this can pave the way toward generalized and full-scale modeling of CDI units under varying conditions. A 3D model can be beneficial for investigating asymmetric CDI device structures, and the work investigates a flow-through device structure with inlet and outlet pipes at the center and corners, respectively. The results show that dead (low-flow) areas can reduce desalination rates while also raising the total leakage. However, the ionic flux in this device is still enough under normal operating conditions to ensure reasonable performance. In conclusion, researchers will now have some flexibility in designing device structures that are not perfectly symmetric (real-life case), and hence we share the model files to facilitate future research with 3D modeling of these electrochemical deionization devices.