A process for conducting chemical extractions in a conduit extractor containing fibers, the process comprising the steps of: (a) introducing a first stream containing a reactive species proximate an upstream end of a plurality of fibers positioned longitudinally within the conduit extractor, wherein (i) the first stream constitutes a phase substantially constrained to the surface of the fibers (ii) the first stream comprises a composition selected from the group consisting of: an aqueous solution containing an organic co-solvent; and an organic solvent; and (iii) the end of the fibers opposite the upstream end thereof constitutes a downstream end thereof and is disposed proximate a collection vessel; (b) introducing a second stream comprising vegetable oil or fat containing an extractable species into the conduit extractor proximate the upstream end of the plurality of fibers in the same direction of flow as the first stream, wherein the second stream constitutes a substantially continuous phase that is in contact with and is substantially immiscible with the first stream, at a flow rate, temperature, and pressure whereby the reactive species in the constrained phase and the extractable species of the continuous phase interact to effect extraction of at least some of the extractable species from the continuous phase into the constrained phase; (c) receiving the constrained phase and the continuous phase in the collection vessel, wherein (i) the constrained phase comprises a layer in a first portion of the collection vessel and (ii) the continuous phase comprises a layer in a second portion in the collection vessel; and (d) withdrawing separately from the collection vessel the layer comprising the continuous phase and the layer comprising the constrained phase. (a) introducing a first stream containing a reactive species proximate an upstream end of a plurality of fibers positioned longitudinally within the conduit extractor, wherein (i) the first stream constitutes a phase substantially constrained to the surface of the fibers (ii) the first stream comprises a composition selected from the group consisting of: an aqueous solution containing an organic co-solvent; and an organic solvent; and (iii) the end of the fibers opposite the upstream end thereof constitutes a downstream end thereof and is disposed proximate a collection vessel; (i) the first stream constitutes a phase substantially constrained to the surface of the fibers (ii) the first stream comprises a composition selected from the group consisting of: an aqueous solution containing an organic co-solvent; and an organic solvent; and an aqueous solution containing an organic co-solvent; and an organic solvent; and (iii) the end of the fibers opposite the upstream end thereof constitutes a downstream end thereof and is disposed proximate a collection vessel; (b) introducing a second stream comprising vegetable oil or fat containing an extractable species into the conduit extractor proximate the upstream end of the plurality of fibers in the same direction of flow as the first stream, wherein the second stream constitutes a substantially continuous phase that is in contact with and is substantially immiscible with the first stream, at a flow rate, temperature, and pressure whereby the reactive species in the constrained phase and the extractable species of the continuous phase interact to effect extraction of at least some of the extractable species from the continuous phase into the constrained phase; (c) receiving the constrained phase and the continuous phase in the collection vessel, wherein (i) the constrained phase comprises a layer in a first portion of the collection vessel and (ii) the continuous phase comprises a layer in a second portion in the collection vessel; and (i) the constrained phase comprises a layer in a first portion of the collection vessel and (ii) the continuous phase comprises a layer in a second portion in the collection vessel; and (d) withdrawing separately from the collection vessel the layer comprising the continuous phase and the layer comprising the constrained phase.