A perfluoroacyl peroxide is usually produced by stirring a hydroxide such as potassium hydroxide or sodium peroxide and hydrogen peroxide (or a metal peroxide such as Na2O2) together with a halogenated alkyl compound dissolved in an organic solvent.  A perfluoroacyl peroxide usually has low thermal stability, and the yield of a peroxide may be decreased due to autolysis by heat of reaction.  Further, since a perfluoroacyl peroxide is usually hydrolyzed, a competitive reaction of a reaction of formation of a perfluoroacyl peroxide and a reaction of hydrolysis of the perfluoroacyl peroxide occurs, and as stirring or emulsification becomes intense, the hydrolysis is accelerated and as a result, the recovery rate tends to be decreased. 
Patent Document 1 discloses a process for continuously producing a peroxyester by passing an acid chloride, a hydroperoxide and an aqueous alkali metal hydroxide through continuous two reactors with mechanical stirring.  The peroxy ester disclosed in Examples of this Patent Document is one containing only carbon, hydrogen and oxygen, and this Patent Document discloses no Example relating to production of a perfluoroacyl peroxide. 
Patent Document 2 discloses a process for continuously producing a fluorocarbon acyl peroxide by reaction a hydroxide, a peroxide and an acyl halide with continuous stirring.  This Patent Document 2 discloses that the reaction product is vigorously stirred by means of ultrasonic waves, a static mixing device or the like to complete the reaction in a shorter time thereby to obtain a peroxide with good yield.  However, Example 13 discloses a process for producing perfluoropropionyl peroxide [CF3CF2(C═O)O]2, but the yield is based on starting material C2F5COCl, and in a system without addition of a surfactant, the yield is from 18 to 23% and is very low.  Further, the yield is improved to 43% by addition of a surfactant, but the yield is still low, and in a case where the surfactant is harmful when the product is used, a process to remove the surfactant is required.  Further, the use of the surfactant is undesirable since it is a compound (CF3CF2CF2CF2CF2CF2CF2COONH4) analogous to PFOA of which bioaccumulation potential is pointed out. 
Patent Document 3 disclose a process for producing a fluorocarbon acyl peroxide by the batch by reacting a hydroxide, a peroxide and an acyl halide under batch conditions.  This Patent Document 3 discloses a process for producing perfluoropropionyl peroxide [CF3CF2(C═O)O]2 in Example 2, and the yield is at a level of 82% based on the starting material C2F5COCl.  Although the reaction time is not disclosed in this Example, there is a problem in productivity since the reaction is carried out by the batch. 
Patent Document 4 discloses a continuous process for preparing a perfluoroorganic peroxide by means of a microreactor.  By the microreactor, the flow path of the reactor is very narrow, and the reactor volume per unit reactor length is small.  Thus, in order to secure a sufficient retention time to complete the reaction, it is necessary to make the flow rate of the reaction liquid to be supplied to the reactor be low, or to make the reactor be long.  However, when a large amount of production is required, by the former means, since the amount of production of each reactor is small, a very large number of microreactors are required, and instrumentation devices therefor are also increased.  Further, the latter means has a disadvantage such that the pressure loss of the flow path will be significant due to the reactor being long.  Accordingly, preparation by means of such microreactors is also problematic for production of a large amount of a perfluoroorganic peroxide.