This document discusses sizing vessels for batch plants producing single and multiple products. For a single product plant producing 500,000 lbs/year, the cycle time and number of batches are calculated to determine the required vessel sizes. For a two-product plant, the production time for each product is determined based on demand to calculate the batch size and optimal vessel sizes for each stage.

1. SIZING OF VESSELS IN
BATCH PLANTS

2. Sizing Of Vessels In Batch Plants
For sizing of vessels in batch plants we will consider the equipment sizing for
the single product plants, the idea for the sizing is illustrated here by an
example:
Example 1: Single product plant
Assume we have two stage plant and we want to produce 500000 lb/year of
product C. The plant is assumed to operate 6000 hours per year. The recipe of
producing C is as follows:
1) Mixture 1 lb A, 1 lb B and react for 4 hours to form C. The yield is 40% in eight
and the density of the mixture is 60 lb/ft3
2) Add 1 lb solvent and separate by centrifuge during 1 hour to recover 95% of
product C. The density of the mixture is 65 lb/ft3

3. Sizing Of Vessels In Batch Plants
1 lb solvent
1 lb A 1.2 lb A,B
2.24lb
1 lb B 0.8 lb C A,B, solv.
0.76 lb C
Figure 1: Mass balance for batch plant
Reaction Separation

4. Sizing Of Vessels In Batch Plants
The specific volume for Stage 1 is V = 1/60 = 0.0166ft3 / lb mix. In this we
have
S1 = 0.0166 * 2 / 0.76 = 0.0438 ft3/lb
Similarly for Stage 2 the specific volume is V= 0.0153ft3/lb mixture. Thus the
size factor is
S2= 0.0153 * 3 / 0.76 = 0.0604 ft3/lb
If we use one unit per stage and operate with zero wait transfer. The cycle
time is
CT = max {4,1} = 4 hrs
This, then implies that the number of batches t be processed in 6000 hrs is
No. Batches = 6000 hrs / 4 hrs per batch = 1500 batches

5. Sizing Of Vessels In Batch Plants
Since the product demand is 500000 lb the batch size of the final product is
B = 500000 / 1500 = 333lb
We can then easily compute the volume of two vessels :
V1 = S1 B = 0.0438 * 333 = 14.6 ft3
V2 = S2 B = 0.0604 * 333 = 20.1 ft3
Since the bottleneck is in stage 1, we might consider placing two units
operating in parallel out of phase. The cycle time is then
CT = max {4/2,1} = 2 hrs

6. Sizing Of Vessels In Batch Plants
This implies we can produce twice as many batches 3000 each of 166lb, or
half the original batch size.
In This way the size are as follows:
V1 = 7.3 ft3
V2= 10 ft3
Although the total volume 24.6 ft3 is smaller than the case of 1 unit per stage
34.7 ft3 we require a total of 3 vessels, 2 in Stage 1 and 1 in Stage 2. Depending
on the cost correlation we may or may not achieve reduction in the investment
in the cost.

7. Sizing Of Vessels In Batch Plants
 Example 2: Multiple product plant
Let us consider a plant consisting of two stages that manufactures two
products A and B. The demand are 500000 lb/year for A and 300000 lb/year for
B and the production time considered is 6000 hrs. Data on processing time size
factors and cleanup time are given in table.
Table 1: Data for sizing Two-Product Plant
Product Processing Times (hr.) Size Factors (ft3/lb prod)
Stage 1 Stage 2 Stage 1 Stage 2
A 8 3 0.08 0.05
B 6 3 0.09 0.04
Cleanup times: 4 hours A to B, B to A

8. Sizing Of Vessels In Batch Plants
Here, single product campaigns has been consider. The production cycle is
taken as 1000 hrs which implies that over 1 year the cycle will be repeated 6
times.
From Fig. 2 it is clear that the effective time for production in each cycle is 992
hrs.
‫؞‬ 𝑡 𝐴 + 𝑡 𝐵 = 992 hrs. (Eq. 1)
tA tB
4 4
1000 hrs
Figure 2: Time allocation for production of A and B

9. Sizing Of Vessels In Batch Plants
 The batch size Bi of product i is given by
Bi =
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖
𝑛𝑜.𝑏𝑎𝑡𝑐ℎ𝑒𝑠 𝑖
=
𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖
𝑡𝑖
/𝐶𝑇𝑖
Here ti and CTi are the total production time and cycle time for each product.
 The production of A and B in each campaign is 500000 / 6 = 83333 lb. and
300000/6 = 50000 lb.
 By equating the batch sizes we get,
83,333
𝑡 𝐴
/8
=
50,000
𝑡 𝐵
/6
𝑡 𝐴 = 2.22 𝑡 𝐵 (Eq. 2)

10. Sizing Of Vessels In Batch Plants
 From Eq.1 and Eq. 2 we get,
tA = 684 hours , tB = 308 hours
 Hence, BA = BB = 974 lb.
 From the batch size the required volumes for each product in two stage can
be calculated by
Vij=SijB
Volumes Vij (ft3)
Product Stage 1 Stage 2
A 77.9 48.7
B 87.7 39.0

11. Sizing Of Vessels In Batch Plants
 Finally the largest volume to be selected in each stage are given by
Vj = max {Vij}
So, V1 =87.7ft3 , V2 = 48.7ft3

12. Reference
 Systematic Methods of Chemical Process Design By Lorenz T. Biegler/
Ignacio E. Grossmann / Arthur W. Westerberg
Thank You