From: Joel H. Schultz

To: Phil Heitzenroeder, Richard J. Thome

Subject: Update of Cryogenic Refrigerator Sizing and Costing for FIRE\*
2.14 m Reference Machine

Date: December 14, 2001

Firewire:NSO No WBS7_121401_UpdateCryoRefrigSizeCostFIRE\*.doc

**Introduction**

The FIRE cryoplant and nitrogen distribution system provides liquid
nitrogen to the TF and PF magnet systems to recool the magnets after
pulses and for cooldown from room temperature. The magnet system is
flushed out with helium, immediately before each pulse, in order to
prevent the formation of radioactive N13. This chapter describes the
magnet cooling circuit, the overall cryoplant topology, the cryogenic
loads, and the sizes of the cryoplant components.

**I. Magnet Cooling Circuit**

The magnets are cooled by circulating liquid nitrogen through cooling
lines (TF), and radial flow through magnet interpancake space (CS and PF
coils). Liquid nitrogen is blown out and replaced by pressurized helium,
before pulses, in order to eliminate the creation of N13 through neutron
irradiation. A negligible amount of N13 is still formed in the shielded
nitrogen atmosphere of the nuclear island, but it is sufficiently low
that no nitrogen holdup system is now required (See Sect. 5.10).

The TF inside and outside legs are cooled separately by cooling lines
that are fed through adjacent gun-drilled holes in each of the TF coil
turns. One set of lines turns inwards and cools the TF inside leg and
the inner halves of the upper and lower legs, the other the outside leg
and the outer halves. The line inlet and outlet points are located at
the high and low points of the profile to facilitate draining of liquid
nitrogen prior to a pulse.

The central solenoid and poloidal field coils are cooled radially
between double pancakes. As in CIT, the flow direction is from the
outside to the inside to prevent outer layer heating and turn-turn
delamination. A can around the outside of the Central Solenoid acts as a
distribution header. The pancakes are individually insulated, but there
is no ground wrap around the entire coil, because of the need for radial
flow.

**II. Load Assessment**

Cryogenic loads, requiring the circulation of liquid nitrogen, include
the following:

> 1\) Radiation from the inner vacuum vessel warm surface to the inner
> magnet surface

2\) Radiation from the outer magnet surface to the cryostat walls and
the ducts

> 3\) Radiation from the transfer lines to its cryostat walls

4\) Conduction through cold mass supports

> 5\) Joule heating of the TF and PF coils during full-power and 2/3
> power pulses
>
> 6\) Neutron and gamma heating of the TF and PF coils during pulses

7\) Heat conduction and Joule heating in the high-current leads

> 8\) Cold mass cooldown from room temperature
>
> 9\) Removal of nuclear after heat

The load parameters that are most relevant to assessing these loads are
accumulated in Table I. The dominant load is the ohmic dissipation of
the TF coil.

Table I- Key Cryogenic Load Parameters

  ------------------------------------------ ----------- ----------------
  Parameter                                  Units       Value

  Ediss, TF                                  (MJ)        16.14

  Ediss, PF                                  (MJ)        6.84

  ncircuits                                              8

  ntransfer lines                                        3

  L,xfer line                                \(m\)       200

  tdwell                                     \(s\)       10,800

  Npulses, full-power                                    3000

  Npulses, 2/3 current                                   30,000

  Max pulses/storage                                     8

  Max pulses/week                                        20

  Max no. RT cooldowns                                   50

  Storage tank drawdown                                  0.8

  Storage tank boiloff                                   0.1

  J/cooldown                                 (GJ)        110

  J/cooldowns, lifetime                      (GJ)        5,500

  Pradiation, in                             (kW)        59.0

  Pradiation, outside                        (kW)        7.48

  Pconduction                                (kW)        3.145

  P,xfer lines                               (kW)        15

  Pleads, TF                                 (kW)        10.4

  Pleads, PF                                 (kW)        11.1

  Pdiss, TF                                  (MW)        1.49

  Pdiss, PF                                  (MW)        0.633

  Pdiss, total                               (MW)        2.21

  Pleads, total                              (kW)        21.52

  Pidle                                      (kW)        95.4

  Ptotal                                     (MW)        2.234

  lN2 flow, Total                            (kg/s)      15.13

  Volume, lifetime, total lN2                (gal)       8.78 x 10^8^

  lN2 usage/pulse                            (kgal)      53.49

  lN2 Storage tank requirement               (kgal)      594.4
  ------------------------------------------ ----------- ----------------

The nitrogen storage tanks are sized for a two-day supply of nitrogen at
4 shots/day. The energy needed for cooldown from room temperature was
calculated to be equal to 12 days of idling losses. Therefore, the
magnet system is kept cold over the weekend and there are only 50 room
temperature cooldowns during the machine life. The refrigerator is not
sized for daily cooldown from room temperature. The magnets are kept
cold overnight and weekends, and only warmed up to room temperature
during maintenance periods. Despite the increase in the peak temperature
to 370 K at the end of a pulse, the energy required for cooldown is
nearly five times higher than that for recool, and it would take 12 days
for heat leakages to warm the magnets to room temperature. Heaters are
used on vent lines to prevent condensation plumes of liquid nitrogen.

**III.** **Cryoplant Topology**

The overall cryoplant design of FIRE was originally based on those of
CIT[^1] and BPX[^2]. Major design features include the following:

1.  Large liquid nitrogen storage tanks and fill stations are used,
    instead of a closed-cycle nitrogen refrigerator. However, in FY99,
    FIRE agreed with CIT, BPX, and Alcator that truck deliverires from a
    commercial air liquefaction plant must be most economical, because
    of the pulsed nature of the load. This was reviewed in FY00 and both
    BOC/AIRCO and Air Liquide recommended the construction of dedicated
    on-site or near-site nitrogen plants. The design still includes
    on-site liquid nitrogen storage.

2.  FIRE uses the Alcator C-Mod method of one pump and individual
    regulator valves for each flow circuit. This provides close to
    optimized cooldown and has proven to be very reliable.

3.  A subcooler is used, as in the BPX and CIT designs, in order to
    provide 80 K liquid nitrogen to the coils. The boiling temperature
    of nitrogen at 10 atmospheres is 105 K.

4.  The secondary circuit of CIT is eliminated by BPX and FIRE. The
    amount of radioactive nitrogen-13 generated in FIRE is small,
    because of the much smaller volume of unshielded nitrogen inventory.
    Even without holdup, the nitrogen-13 discharge would be within
    allowables for most site boundaries[^3]. The cryogenic system
    provides one day's holdup for nitrogen-13, which has a half-life of
    ten minutes.

+-----------------------------------+-----------------------------------+
| ![](me                            | ![](media/image2.                 |
| dia/image1.wmf){width="3.30625in" | wmf){width="3.4916666666666667in" |
| height="3.84375in"}               | height="3.745833333333333in"}     |
|                                   |                                   |
| Figure 1: Option 1: Temporary     | Figure 2: Option 2: Open Nitrogen |
| Storage of Irradiated Gas after   | Loop with Helium Purge            |
| Pulse, Open Secondary             |                                   |
+-----------------------------------+-----------------------------------+
| ![](media/image3                  | ![](me                            |
| .wmf){width="3.282638888888889in" | dia/image4.wmf){width="3.45625in" |
| height="4.200694444444444in"}     | height="4.302083333333333in"}     |
|                                   |                                   |
| Figure 3: Option 3-Closed-loop    | Figure 4: Option 4: Closed-Loop   |
| Secondary N2 Circuit (BPX/CIT)    | Helium Secondary                  |
+-----------------------------------+-----------------------------------+

The relative costs of the five options are compared in Table II:

Table II: Relative Costs of Five Refrigerator Topology Options

  ----------------- ----------------- ----------------- -----------------
  Refrigerator      PACE, min         PACE, max         Total
  Option                                                

  1a Open N2,       9.04              12.2              16.7
  Holdup all N2                                         

  1b Separate       5.51              8.64              11.8
  holdup streams                                        

  2 Open N2, He     5.46              8.59              11.8
  purge                                                 

  3 Closed-loop lN2 5.97              9.1               14.6
  Secondary                                             

  4 Closed-loop He  13                16.1              22.1
  Secondary                                             
  ----------------- ----------------- ----------------- -----------------

The performance tradeoffs are summarized as numerical rankings in Table
III:

Table III: Cost/Performance Rankings of five refrigeration system
options

  -------------------------- ------ ----------------------- -------------
  Refrigerator Option        Cost   N13 Generated/Released  Recool Time

  1a Open N2, Holdup all N2  4      3                       2

  1b Separate holdup streams 2      4                       5

  2 Open N2, He purge        1      2                       2

  3 Closed-loop lN2          3      5                       1
  Secondary                                                 

  4 Closed-loop He Secondary 5      1                       4
  -------------------------- ------ ----------------------- -------------

Option 2 was selected as the new reference design, because it had the
best overall combination of low cost, radioactivity, and recool time, as
shown in Table III. All parameters have been updated to correspond to
the CY2002 FIRE\* reference design at Ro=2.14 m.

##### IV.. Cost Algorithm

New pricing information was solicited on the cost of vacuum-jacketed
piping, unjacketed piping, elbows, and valves. A new set of cryogenic
equipment costing equations were derived on the basis of the data base
and are listed in Table IV. Although impressively large at first glance,
the data base is still not adequate. In particular, we haven\'t obtained
good recent pricing on large cold boxes, nitrogen gas bags, heaters or
blowers. However, because of the need to begin comparing different
design options, an interim set of costing equations was derived, based
on previous cost studies. This will be updated as new information
becomes available.

Table IV: Cryogenic Equipment Costing Equations

+-----------------------+-----------------------+-----------------------+
| Component             | Equation              | Notes                 |
+-----------------------+-----------------------+-----------------------+
| Pump/Compressor       | \$273/gpm             | Liquid nitrogen,      |
|                       |                       | Barber-Nichols quote  |
+-----------------------+-----------------------+-----------------------+
| Cold Box              | \$4500/T~o~ (Q)^0.7^  | Slack formula,        |
|                       |                       | ratioed to BPX        |
|                       |                       | subcooler cost x 1.5  |
|                       |                       | for inflation, Q is   |
|                       |                       | in W; T~o~ is the     |
|                       |                       | outlet temperature    |
+-----------------------+-----------------------+-----------------------+
| Vacuum jacketed pipe  | \$164 D~i~ (\$/m)     | Di=Inner diameter in  |
|                       |                       | inches,PHPK quote     |
+-----------------------+-----------------------+-----------------------+
| Unjacketed pipe       | \$73/m (Dt)           | Dt=Inner diameter     |
|                       |                       | thickness product in  |
|                       |                       | inches, Stainless     |
|                       |                       | Tubular Products      |
+-----------------------+-----------------------+-----------------------+
| Valves                | \$267 D~i~^2.27^      | PHPK quote; relative  |
|                       |                       | prices from BPX;      |
| Throttle              | \$180 D~i~^2.27^      |                       |
|                       |                       | D~i~ in inches.       |
| Shutoff               | \$140D~i~^2.27^       |                       |
|                       |                       |                       |
| Relief                |                       |                       |
+-----------------------+-----------------------+-----------------------+
| Controller            | \$150 k-Hardware      | 40 % deflation since  |
|                       |                       | BPX                   |
|                       | \$250 k-Labor         |                       |
+-----------------------+-----------------------+-----------------------+
| Blower                | \$300/hp              | BPX x 1.5 for         |
|                       |                       | inflation             |
+-----------------------+-----------------------+-----------------------+
| Nitrogen heaters      | \$250/kW              | Scaled from           |
|                       |                       | intepretation of BPX, |
|                       |                       | x 1.5 for inflation   |
+-----------------------+-----------------------+-----------------------+
| Filters               | \$500/gpm             | Scaled from           |
|                       |                       | interpretation of     |
|                       |                       | BPX, x 1.5 for        |
|                       |                       | inflation             |
+-----------------------+-----------------------+-----------------------+
| Storage Bag           | \$30/m^3^             | Robinson\'s eqn. x    |
|                       |                       | 1.5 for inflation     |
+-----------------------+-----------------------+-----------------------+
| Storage Tank          | \$8/gal (250 MAWP)    | Taylor-Wharton quotes |
|                       |                       |                       |
| (vacuum insulated)    | \$5/gal (40 MAWP)     |                       |
+-----------------------+-----------------------+-----------------------+
| Local I&C             | \$400 k               | 40 % deflation since  |
|                       |                       | BPX                   |
+-----------------------+-----------------------+-----------------------+
| Contingency           | 16 % of PACE subtotal | Ratioed from BPX      |
+-----------------------+-----------------------+-----------------------+
| Assembly,             | 18 % of PACE total +  | Ratioed from BPX      |
| Installation & Test   | contingency           |                       |
+-----------------------+-----------------------+-----------------------+

The cryogenic load for all options is summarized in Table I:

# V. Sizing of the Design Options

A sizing workbook was developed for the four design options with five
worksheets. The first (reference) option of storing the radioactive gas
after a shot for three hours between shots was subdivided into an Option
A, in which all of the nitrogen used in one shot, including that used
for recooling, is stored temporarily, and an Option B, in which the
magnets are purged both before and after a shot, and only the purged
gases are stored. Option 2, described below in more detail, is sized in
Worksheet 3 of the Workbook "Mag Refrig Design Scaled to 2.14 m.xls".

## Sizing of Option2: Open Nitrogen Loop with a Helium Purge

If the liquid nitrogen were purged by helium before a pulse, then
essentially no radioactive gas would be generated by the pulse. Any
imperfectly shielded nitrogen atmosphere in the cel is not considered
here. There would then also be no need to purge the magnet vapor after a
shot and recool could begin immediately with no temporary storage. The
disadvantage is that pressurized helium storage and a helium-nitrogen
heat exchanger have to be added to the cryogenic system. There is also a
modest amount of helium that is vented and has be to be purchased.
Option 2 is illustrated by Figure 5 and sized in Table V.

![](media/image2.wmf){width="5.9in" height="6.320138888888889in"}

Figure 2: Open Nitrogen Loop with Helium Purge

The sizes of the cryogenic refrigerator components in Option 2 are
listed in Table V.

Table V: Component Sizes of Option 2 with an Open Nitrogen Loop, Helium
Purge, and without Temporary Storage

  ----------- -------------------------------------------- ---------------
  **Units**   **Parameter**                                **Value**

  (kgal)      **lN2 Storage tank requirement**             594.4

              nstorage tank shutoff valves                 4

  (in)        Dstorage tank shutoff valves                 12

              Nitrogen Supply to Magnets                   

  \(m\)       Lcold nitrogen piping                        200

  \(m\)       L 8\" lN2 vacuum-jacketed pipe               100

  (kg/s)      Average nitrogen pumping reqmnt              15.13

              Peak/average pumping ratio                   2

  (kg/s)      Peak nitrogen pumping reqmnt                 30.26

  (gpm)       Peak nitrogen pumping reqmnt                 594.4

              nRegulator valves to magnets                 3

  (in)        Dregulator valves to magnets                 10

              nfilters                                     4

  (gpm)       Total gpm, premagnet filters                 594.4

              nMisc 12\" shutoff valves                    6

  (in)        Dmisc shutoff valves                         12

              **Purge requirements**                       

              Equivalent flush cycles                      4

  \(m\)       Flush length                                 50

  (in)        Di, flushed pipes                            12

  (m\^3)      V, flushed pipes                             3.6483

  (m\^3)      V, magnet channels, headers                  1

  (m\^3)      V, total flushed volume                      4.6483

  (m\^3)      V, all flush cycles                          18.59

  (kg)        M, He gas purges                             197.088

              nshots/Pressurized He tank capacity          4

  (m\^3)      Volume, 18 atm pressure vessel,supply        271.845

  (in)        Di, shutoff valve, He purge stream           12

  \(m\)       L,addit\'l pipe, separate flush exhaust      100

  (in)        Di, regulator valve, He purge stream         12

  \(s\)       Total flush time                             600

  (kg/s)      Average mass flow, flush stream              0.32848

  \(W\)       Q,He-lN2 heat exchanger                      1908.3

  (kW)        Average heater power, flush stream           0

  (in)        Di,addit\'l pipe, separate flush exhaust     12

  (in)        t,addit\'l pipe, separate flush exhaust      0.375

  \(s\)       Emptying time before shot                    600

  (kg/s)      Blower capacity                              272.4

  (hp)        Blower power                                 3,120

  \(m\)       Lcold exhaust pipe                           100

  \(m\)       Lwarm exhaust pipe                           100

  (in)        Dicold exhaust pipe                          16

  (in)        Diwarm exhaust pipe                          16

  (in)        n,vent valves x Di,vent valves               2x12

  (kg/s)      Peak mass flow through gas storage line      30.26

  (kW)        Heater power                                 64.66
  ----------- -------------------------------------------- ---------------

**VI. Costing of the Design Options**

Having sized the individual components and proposed a set of costing
equations, it is now possible to compare the costs of the five design
options. Each option was costed according to the costing rules in Table
IV. The cost of Option 2 is given in Table VI, below.

Table VI: Cost of Option 2 with an Open Nitrogen Loop, Helium Purge, and
without Temporary Storage

  -------- ---------------------------------- ----------- --------- ---------
  Units    Parameter                          Value       Unit Cost Cost

                                                                    (k\$)

  (kW)     Subcooler Heat removed from 1o     1081        4500      1107.18
           stream                                                   

  (kgal)   lN2 Storage tank requirement       594.3       5000      2971.8

  (in)     Dstorage tank shutoff valves       12          180       202.8

  \(m\)    L 8\" lN2 vacuum-jacketed pipe     100         164       131.2

  \(m\)    L 8\" lN2 vacuum-jacketed pipe     100         164       196.8

  (gpm)    Peak nitrogen pumping reqmnt       594.4       273       162.3

  (in)     Dregulator valves to magnets       10          267       149.2

  (gpm)    Total gpm, presubcooler filter     594.3       500       297.18

  (gpm)    Total gpm, premagnet filters       594.3       500       297.18

  (in)     Dmisc shutoff valves               12          180       304.2

  (kgal)   Volume, 18 atm pressure vessel     71.8        5000      359

  (in)     Di, shutoff valve, He purge stream 12          180       50.7

  \(m\)    L,addit\'l pipe, separate flush    100         73        32.85
           exhaust                                                  

  (in)     Di, regulator valve, He purge      12          267       75.2
           stream                                                   

  \(W\)    Q,He-lN2 heat exchanger            1908        10000     24.74

  (hp)     Blower power                       3120        300       937

  (in)     Dicold exhaust pipe                16          73        58.4

  (in)     Diwarm exhaust pipe                16          73        58.4

  (in)     Di,vent valves                     12          180       101.4

  (kW)     Heater power                       6466        250       3233

           Instrumentation and Control                    400       400

  (M\$)    PACE, subtotal, min                                      6.08

  (M\$)    PACE, subtotal, max                                      9.58

  (M\$)    Contingency                                    0.16      1.53

  (M\$)    PACE+Contingency                                         11.1

  (M\$)    Assembly, Installation & Test                  0.18      2.00

  (M\$)    Grand Total                                              13.1
  -------- ---------------------------------- ----------- --------- ---------

Although Option 2 requires a helium cold box and temporary helium
storage, their cost is relatively low, since the helium isn\'t needed
for magnet heat removal, but merely for purging the nitrogen volume.

.

The closed-loop helium secondary is the most expensive of the five
options, because of the requirement for a cold box, compressor, and
helium storage tank that is adequate for magnet cooldown.

The minimum value assumes that nitrogen vendor provides all of the
liquid nitrogen storage tanks and the pipes and valves to the entrance
of the reactor cell. The maximum value assumes that these are purchased
by the project.

The minimum value assumes that nitrogen vendor provides all of the
liquid nitrogen storage tanks and the pipes and valves to the entrance
of the reactor cell. The maximum value assumes that these are purchased
by the project. The cost and cost/performance comparisons of the five
options are given above in Tables II and III.

**VII. Cost of Nitrogen**

The cost of the cryogenic refrigeration system remains small in
comparison with the cost of nitrogen over the course of the project. The
energy dissipation in the TF coils is known to be 14.1 GJ in a single
simulation and 6.0 GJ in the PF coils. Scaled energy dissipation in the
TF coil is based only on P. Titus' observation that overall dissipation
seems to track hot spot temperature over a variety of paths to that hot
spot temperature. The lifetime ohmic dissipation is based on the
specification of 3000 full-power shots and 30,000 shots at 2/3 of peak
current, along with an assumption that the partial power shots averaged
4/9 the dissipation of the full-power shots. Titus has shown a broad
range of tradeoffs between nitrogen and power supply requirements vs.
cooldown time. We retain the previous assumption of 4/9 dissipation for
this study, although it's somewhat arbitrary, because we don't have any
better logic and don't want to confuse independent effects. This study
is focused on calculating the change in cost, due to increasing the size
of FIRE from Ro=2.0 m to Ro=2.14 m.

BOC gave pricing for a 10 year lease and a 15 year lease, as listed and
scaled in Table VII:

Table VII: Nitrogen Cost Estimates

  ----------------- ----------------- ----------------- -----------------
  Total Cost        Units             2.0 m FIRE        2.14 m FIRE

  10 Year           (M\$)             143               163
  Commitment                                            

  15 Year           (M\$)             107/118.5         123
  Commitment                                            
  ----------------- ----------------- ----------------- -----------------

The penalty for purchasing more nitrogen/year over 10 years seems
ridiculously high, but is based on a quote of 20 cents/100 cu ft of
liquid nitrogen for a 10 year lease and 15 cents/100 cubic feet for 15
years. It's always possible that the BOC representative didn't
understand that it was a fixed total, but that's what I got. Also, the
reason for the second cost for the 15 year lease/2.0 m FIRE is that the
price/100 cubic feet is a constant, down to 75 % of nominal usage. After
that it would be flat, so that BOC/AIRCO would collect \$8.5 M/year,
even if the facility never ran.

**VII. Conclusions**

A methodology has been developed for comparing different refigerator
design options.

Three of the five options were relatively inexpensive and difference
between their costs within the uncertainties of the costing exercise.
These were 1) Open N2 system with a helium purge, 2) Open N2 with a
nitrogen purge and two exhaust lines, and 3) Closed-loop lN2 Secondary.

The open N2 system with a helium purge also had high-rankings in low
generation and release of N13 and recool time, although the difference
between all of the sytems may be relatively small in both categories.

The closed-loop lN2 secondary costing is probably optimistic, since it
doesn\'t include an emergency nitrogen holdup system.

Option 2 was selected, Open N2 with a helium purge, the new reference
design with Option 1a, Open N2, N2 purge, and separate holdup as the
backup design.

The costs of the cryogenic refrigeration system were updated for the
FIRE\* Option, the CY2002 reference design. The overall cost of the
cryogenic system increased 11 % from to \$11.8 M to \$13.1 M, scaling a
little less rapidly than the 14 % increase in the size of the TF
magnets.

The cost of liquid nitrogen is scaled linearly with the losses and
increases by 14 %, ignoring anomalies in available costing information.

[^1]: R.B. Fleming and G.D. Martin, \"Liquid nitrogen cooling for the
    Compact Ignition Tokamak,\" Knoxville, SOFE 13, 1989

[^2]: R.B. Fleming and G.D. Martin, "System Description, Cryogenic
    System, WBS Q: BPX Design Description Document," Feb 13, 1991

[^3]: H. Khater, Sec. 5.8, this report