# Elements of Chemical Reaction Engineering: Mole Balances

• Print
This chapter is from the book

## 1.3 Batch Reactors (BRs)

A batch reactor is used for small-scale operation, for testing new processes that have not been fully developed, for the manufacture of expensive products, and for processes that are difficult to convert to continuous operations. The reactor can be charged (i.e., filled) through the holes at the top (see Figure 1-5(a)). The batch reactor has the advantage of high conversions that can be obtained by leaving the reactant in the reactor for long periods of time, but it also has the disadvantages of high labor costs per batch, the variability of products from batch to batch, and the difficulty of large-scale production (see Industrial Reactor Photos in Professional Reference Shelf [PRS] on the CRE Web site, www.umich.edu/~elements/5e/index.html). Figure 1-5(a) Simple batch homogeneous batch reactor (BR). [Excerpted by special permission from Chem. Eng., 63(10), 211 (Oct. 1956). Copyright 1956 by McGraw-Hill, Inc., New York, NY 10020.] Figure 1-5(b) Batch reactor mixing patterns. Further descriptions and photos of the batch reactors can be found in both the Visual Encyclopedia of Equipment and in the Professional Reference Shelf on the CRE Web site.

A batch reactor has neither inflow nor outflow of reactants or products while the reaction is being carried out: Fj0 = Fj = 0. The resulting general mole balance on species j is If the reaction mixture is perfectly mixed (Figure 1-5(b)) so that there is no variation in the rate of reaction throughout the reactor volume, we can take rj out of the integral, integrate, and write the mole balance in the form

#### Equation 1-5 Let’s consider the isomerization of species A in a batch reactor Batch Reactor

As the reaction proceeds, the number of moles of A decreases and the number of moles of B increases, as shown in Figure 1-6.

We might ask what time, t1, is necessary to reduce the initial number of moles from NA0 to a final desired number NA1. Applying Equation (1-5) to the isomerization rearranging, and integrating with limits that at t = 0, then NA = NA0, and at t = t1, then NA = NA1, we obtain

#### Equation 1-6 This equation is the integral form of the mole balance on a batch reactor. It gives the time, t1, necessary to reduce the number of moles from NA0 to NA1 and also to form NB1 moles of B.
{"ft_lang_label":"__label__en","ft_lang_prob":0.91583395,"math_prob":0.97363186,"size":2322,"snap":"2020-45-2020-50","text_gpt3_token_len":565,"char_repetition_ratio":0.14020708,"word_repetition_ratio":0.015345269,"special_character_ratio":0.23858742,"punctuation_ratio":0.11111111,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95080256,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"im_url_duplicate_count":[null,2,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null,1,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2020-10-25T14:43:51Z\",\"WARC-Record-ID\":\"<urn:uuid:f8646932-fdb7-4d0d-8d58-62ba662841df>\",\"Content-Length\":\"47513\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:680be9d2-b89b-40c0-b358-fd572049cfd7>\",\"WARC-Concurrent-To\":\"<urn:uuid:61048df1-8312-434e-a557-51e43dc12b8d>\",\"WARC-IP-Address\":\"159.182.167.70\",\"WARC-Target-URI\":\"https://www.informit.com/articles/article.aspx?p=2475565&seqNum=3\",\"WARC-Payload-Digest\":\"sha1:IWU6BIQXAS5ULJMBV3BBFPJ3TLCD74QB\",\"WARC-Block-Digest\":\"sha1:IWJ74ZQA2ORUZFTFVBPDOP7LEYT46WJA\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2020/CC-MAIN-2020-45/CC-MAIN-2020-45_segments_1603107889173.38_warc_CC-MAIN-20201025125131-20201025155131-00296.warc.gz\"}"}