Lightweight, portable oxygen concentrators that operate using an ultra rapid, sub one second, adsorption cycle based on advanced molecular sieve materials are disclosed. The amount of sieve material utilized is a fraction of that used in conventional portable devices. This dramatically reduces the volume, weight, and cost of the device. Innovations in valve configuration, moisture control, case and battery design, and replaceable sieve module are described. Patients with breathing disorders and others requiring medical oxygen are provided with a long lasting, low cost alternative to existing portable oxygen supply devices.