NOVELTY - Conversion of C4 olefins involves: obtaining a C4 feed stream comprising C4 paraffins and C4 olefins, including 1-butene and 2-butene; reacting stream in metathesis reactor to form second stream; fractionating second stream to form product streams(s), and a recycle stream; returning recycle stream to reactor; and passing recycle stream and/or C4 feed stream through facilitated transport membrane to remove butanes and form purge stream(s) comprising butanes.    USE - For conversion of C4 olefins; and for producing a selected butene (claimed).    ADVANTAGE - The method provides an efficient process for removal of butanes from a metathesis process to produce olefins by exhibiting reduction in capital costs, reduction in number of necessary pieces of operating equipment, increase in the production rate of products and reduction in poisons to the reactor system; by employing facilitated transport membrane for the removal of butanes from the recycle stream and/or C4 feed stream. The method for the conversion of C4 olefins has production rate of the product streams(s) of greater than (greater than or equal to 10, preferably greater than or equal to 20)%, than the production rate using a process in which approximately equivalent reaction and fractionation equipment is used, without facilitated transport membrane. The apparatus for the conversion of C4 olefins has production rate of the product streams(s) of greater than greater than or equal to 20%, than the production rate using a process in which approximately equivalent reaction and fractionation equipment is used, without facilitated transport membrane. The method for the production of a selected butene; has the production rate of a product stream i.e. the first stream of (greater than or equal to 20, preferably greater than or equal to 40)% greater than the production rate by a process in which splitting and isomerization equipment of equivalent size is used without a facilitated transport membrane; and utility consumption of (greater than or equal to 10, preferably greater than or equal to 20)% lower than the utility consumption for a process in which approximately equivalent quantities of C4 olefin product are obtained using a C4 feed stream of the same composition, without facilitated transport membrane. The apparatus for the production of a selected butene has a production capacity greater than or equal to 20% greater than the production capacity of an apparatus, which includes substantially the same metathesis reactor and plurality of fractionation towers, without facilitated transport membrane. As the method does not involve the solvent extraction, it avoids the use of various solvents that can contain nitrogen compounds that are poisonous to the isomerization and metathesis catalysts, such as N-methyl pyrrolidine and furfural.    DETAILED DESCRIPTION - Process (P1) for the conversion of C4 olefins involves:    (a1) obtaining a C4 feed stream comprising C4 paraffins and C4 olefins, including 1-butene and 2-butene;    (b1) reacting the C4 feed stream in a metathesis reactor to form a second stream;    (c1) fractionating the second stream to form one or more product streams containing ethylene, propylene, pentenes and/or hexenes, and a recycle stream primarily containing C4 olefins and C4 paraffins;    (d1) returning the recycle stream to the metathesis reactor; and    (e1) passing at least one of the recycle stream and the C4 feed stream through a facilitated transport membrane to remove butanes and form at least one purge stream comprising butanes.    INDEPENDENT CLAIMS are included for the following:    (1) a process (P2) for production of a selected butene involving: (a2) obtaining a C4 feed stream comprising C4 paraffins and C4 olefins; (b2) splitting the C4 feed stream to form a first stream comprising a first butene and a second stream comprising a second butene; (c2) isomerizing at least a part of the second stream to convert a portion of the second butene to the first butene; (d2) recycling at least some of the isomerized part of the second steam and/or the C4 feed stream to the splitting step (b); and (e2) passing a portion of the C4 feed stream and/or the second stream through a facilitated transport membrane to remove butanes and form at least one purge stream comprising butanes;    (2) an apparatus (A1) for the conversion of C4 olefins comprising: a metathesis reactor; several fractionation towers positioned downstream from the metathesis reactor for producing a recycle stream and at least one of an ethylene stream, a propylene stream, and a hexene stream; and at least one facilitated transport membrane for removing butanes positioned in at least one of a first location upstream from the reactor and a second location along the recycle stream; and    (3) an apparatus (A2) for producing a selected butene comprising: a butene splitter to split a C4 feed stream to form a first stream comprising a first butene and a second stream comprising a second butene; an isomerization reactor to isomerize at least a part of the second stream in order to convert at least a portion of the second butene to the first butene; and a facilitated transport membrane to remove butanes from at least a portion of at least one of the C4 feed stream and the second stream.