A downhole fluid separation apparatus can include multiple sections connected together with connectors, the connectors providing fluid communication between annuli in adjacent ones of the sections, and between inner conduits in adjacent ones of the sections. Each connector can include at least one flow passage providing communication between an inner conduit of each of the connected sections, and another flow passage providing communication between an annulus of each of the connected sections. A bypass valve can be included that opens in response to a predetermined differential pressure between an exterior of the apparatus and the inner conduits.