H41F-1387: Modeling the Use of Mine Waste Rock as a Porous Medium Reservoir for Compressed Air Energy Storage

The BiMBy DeviceThe mission of BiMBy Power Company, LLC (BPC) is to build large porous medium pressure vessels (US

Patent Pending[1]) using mine overburden/waste rock/tailings (waste rock) to serve as renewable energy

storage reservoirs for compressed gas. The gas stored in the reservoirs may be air which has a low energy

density by volume when compressed, or a clean burning gas such as H2 which has a high energy density by

volume. A single device containing such a porous medium pressure vessel is referred to here as a BiMBy™,

for Big Mass Battery.

A familiar home compressed air storage system is compared to a BiMBy pressure vessel in Fig. 1: porous

waste rock is encapsulated by a liner forming a pressure vessel and overlain by additional waste rock

forming a pressurizing layer; a compressor pumps air into the pressure vessel via air in piping when

renewable energy source (wind or solar power) is available; compressed air is released via air out piping to

run a turbine to generate electricity upon demand. This beneficial use of mine waste rock adds economic

value to the waste rock, is potentially transformative for the mining and renewable energy economies, and

could positively affect regulatory acceptance by offering alternative reclamation options.

Home BiMByFig. 1. A home compressed air energy storage system (left) compared to a BiMBy device (right).

Modeling BiMBy Gas Retention The mathematical model upon which Table 1 is based was kindly provided to the authors by Jerry Fairley2.

Gas pressure within a BiMBy pressure vessel may be modeled as a three-part, discontinuous function: Phase

I, charging during which gas is added to and gas leaks from the pressure vessel; Phase II, storage during

which gas leaks from the pressure vessel; and Phase III, discharge during which gas is released in a

controlled manner and gas leaks from the pressure vessel. Phase III is not considered further.

Phase I, charging for 0 ≤ τ ≤ τ1:

Phase II, storage for τ1 ≤ τ ≤ τ2:

where:

Table 1. Parameters used or values calculated

for each model. V, volume; b, liner thickness; k,

liner permeability; T, temperature; P0, 1 atm;

N0, pump constant; A, area; ϕ, porosity; μ, gas

viscosity; Rs, gas constant; Pmax, max pump

pressure; t1, time at end of Phase I; t2, time at

end of Phase II; t10%, estimated time at 10%

loss; PPVmax max pressure vessel pressure; P(t1),

pressure at t1 ; P(t1), pressure at t1; f2=P(t1)/P(t1).

1Donelick, R.A., Donelick, M.B., and Arehart, G.B., US Patent Pending (utility).2Fairley, Jerry, unpublished, Modeling pressure transients and the impacts of material properties on an in-situ compressed air energy storage system. manuscript

dated October 17, 2016, 10 p.

𝜃 𝜏 = 4𝛽 + 1 + 𝛽𝛿 2

2𝛽∙ 1 + 𝛽𝛿 + 4𝛽 + 1 + 𝛽𝛿 2 tanh

4𝛽+(1+𝛽𝛿 )

2𝜏

4𝛽 + 1 + 𝛽𝛿 2 + 1 + 𝛽𝛿 tanh 4𝛽+(1+𝛽𝛿 )2

2𝜏

− 1 + 𝛽𝛿

2𝛽

𝜃 𝜏 =𝛿

2∙ 2𝜃1 + 𝛿 + 𝛿 tanh

𝛽𝛿

2(𝜏 − 𝜏1)

𝛿 + 2𝜃1 + 𝛿 tanh 𝛽𝛿

2(𝜏 − 𝜏1)

−𝛿

2

𝜃 =𝑃 − 𝑃0

𝑃max − 𝑃0, 𝜏 =

𝑡𝑁0𝑅s𝑇

𝑉𝜙,𝛽 =

𝑘𝐴(𝑃max − 𝑃0)

𝑁0𝑅s𝑇𝜇𝑏, 𝛿 =

𝑃0

𝑃max − 𝑃0

Potential BiMBy Benefits• Lowers the carbon footprint of burned coal and tar sands oil

Re-purposes the overburden moved during mining to enable construction of on-demand renewable energy

power plants; as low as natural gas for compressed air energy storage; much lower for H2 storage.

• Saves coal/tar sands jobs and creates renewable energy jobs in coal/tar sands communities

Needed coal/tar sands is mined to produce needed electricity now and needed energy storage later.

• Creates new opportunities to lower costs and increase profits at metal mines

This renewable energy storage play in mine waste rock is potentially transformative for the mining and

renewable energy economies.

• Offers new strategies to clean up NPL Superfund sites – “est mundum”

Berkeley Pit. Yerington Pit. Drain and stabilize pit, construct BiMBy pressure vessel and isolate pollution

sources, operate encapsulated pressure vessel at positive gas pressure, eliminate pit lake and associated

groundwater pollution sources.

• H2 storage potential is in the bank

Built to contain H2 but used for compressed air.

• Long-lived on the order of a century

Built with control over all materials and structures, including structures designed to self-heal after

deformation events.

• Potential major piece of the US energy storage puzzle needed to stabilize future grid

US Coal after 20 years* US Metals after 20 years**

CAES 2.0 x 108 kW∙h 7% of US need 2.4 x 108 kW∙h 8% of US need

H2 2.8 x 109 kW∙h 93% of US need 3.2 x 109 kW∙h 108% of US need.

*CAES = compressed air energy storage; porosity 0.30, fraction used in BiMBy pressure vessel 0.20, average air pressure 5 atm, average H2 pressure 1 atm; CAES

0.30∙0.20∙5.00∙[3.0 x 109 t∙y-1/1.75 t∙m-3]∙0.02 kW∙h∙m-3∙20 y; H2 0.30∙0.20∙1.00∙[3.0 x 109 t∙y-1/1.75 t∙m-3]∙1.35 kW∙h∙m-3∙20 y**porosity 0.20, fraction used in BiMBy pressure vessel 0.20, average air pressure 20 atm, average H2 pressure 4 atm; CAES 0.20∙0.20∙20.00∙[1.5 x 109 t∙y-1/

2.00 t∙m-3]∙0.02 kW∙h∙m-3∙20 y; H2 0.20∙0.20∙4.00∙[1.5 x 109 t∙y-1/2.00 t∙m-3]∙1.35 kW∙h∙m-3∙20 y

Coal Strip Mine: Rosebud Mine, Colstrip, MT (over 2 years)

Pressure Vessel k/b equivalent to 1 m of dry concrete

V = 3.5 x 107 m3 Retains 96% of gas pressure after 15 h storage.

A = 2.9 x 106 m2

M = 6.1 x 107 t

P = 4.3 x 105 Pa

Pressurizing Layer

VPL = 3.9 x 107 m3

APL = 3.3 x 106 m2

MPL = 6.9 x 107 t

Whole Device

VT = 7.4 x 107 m3

Amap = 1.6 x 106 m2

MT = 1.3 x 108 t

Assume

ρ = 1.75 t∙m-3

ϕ = 0.3 scalar

See Table 1

photo: http://billingsgazette.com/news/state-and-regional/montana/rosebud-county-to-reap-million-in-protested-taxes-after-state/article_97128908-6e9b-505a-

8019-ae62d0de6910.html, Larry Mayer

Energy Storage Capacity

CAES 9.0 x 105 kW∙h 0.03% of US need

H2 1.4 x 107 kW∙h 0.47% of US need

Tesla Powerwalls (13.5 kW∙h at $5500 each)

CAES 67k at $366M

H2 1.1M at $5.8B

Parameter

or Value

Case 1

Unlined

Case 2

Lined

Shotcrete

Case 3

Lined Wet

Concrete

Case 4

Rosebud

Coal

Strip Mine

Case 5

Berkeley

Open-Pit

Case 6

Yerington

Open-Pit

dimensional

parameter

V, m3 2.0 x 107 2.0 x 10

7 2.0 x 10

7 3.4810 x 10

7 9.3590 x 10

7 5.6973 x 10

7

b, m 1.00 0.01 0.50 1.00 1.00 1.00

k, m2 9.4 x 10-14

1.0 x 10-16

5.0 x 10-18

1.0 x 10-16

1.0 x 10-16

1.0 x 10-16

k/b, m 9.4 x 10-14

1.0 x 10-14

1.0 x 10-17

1.0 x 10-16

1.0 x 10-16

1.0 x 10-16

T, K 293 293 293 293 293 293

P0, Pa 101325 101325 101325 101325 101325 101325

N0, m∙s 0.0015 0.0015 0.0015 0.0015 0.0015 0.0015

A, m2 3.9 x 105 3.9 x 10

5 3.9 x 10

5 2.9053 x 10

6 1.3735 x 10

6 1.2885 x 10

6

ϕ, scalar 0.2 0.2 0.2 0.3 0.2 0.2

μ, N∙s∙m-2 1.81 x 10

-5 1.81 x 10

-5 1.81 x 10

-5 1.81 x 10

-5 1.81 x 10

-5 1.81 x 10

-5

Rs, J∙kg-1

∙K-1 287.058 287.058 287.058 287.058 287.058 287.058

Pmax, Pa 202650 202650 202650 1418550 27661725 8308650

t1, s 32400 32400 32400 32400 32400 32400

t2, s 86400 86400 86400 86400 86400 86400

dimensional

value

t10%, s 35100 45000 12000000 170000 83700 102500

PPVmax, Pa 32227 77608 101290 429060 5295800 2451800

P(t1), Pa 31341 58394 64850 422688 5279303 2431425

P(t2), Pa 1522 37911 64819 404999 4722420 2239722

f2, scalar 4.86% 64.92% 99.95% 95.82% 89.45% 92.12%

non-

dimensional

τ1 1.0219 1.0219 1.0219 0.3914 0.2184 0.3587

τ2 2.7251 2.7251 2.7251 1.0438 0.5823 0.9566

θmax 0.3181 0.7659 0.9997 0.8638 0.5304 0.7413

θ(τ1) 0.3093 0.5763 0.6400 0.3209 0.1916 0.2963

θ(τ2) 0.0150 0.3741 0.6397 0.3075 0.1713 0.2729

β 1.6267 0.1731 0.0002 0.1676 1.6577 0.4631

δ 1.0000 1.0000 1.0000 0.0769 0.0037 0.0123

Raymond A. Donelick

Margaret B. Donelick

BiMBy Power Company, LLC

1075 Matson Road

Viola, Idaho 83872 U.S.A.

donelick@apatite.com

www.apatite.com

Acknowledgements: Ray and Margaret are

grateful to Sean Willett (ETH) for

suggesting we consider porous media and

Jerry Fairley (University of Idaho) for

generously providing us his mathematical

model of a BiMBy.

Open-Pit Metal Mine: Berkeley Pit, Butte, MT

Pressure Vessel k/b equivalent to 1 m of dry concrete

V = 9.4 x 107 m3 Retains 89% of gas pressure after 15 h storage.

A = 1.4 x 106 m2

M = 1.9 x 108 t

P = 5.3 x 106 Pa

Pressurizing Layer

VPL = 3.4 x 108 m3

APL = 3.7 x 106 m2

MPL = 6.8 x 108 t

Whole Device

VT = 4.3 x 108 m3

Amap = 1.8 x 106 m2

MT = 8.7 x 108 t

Assume

ρ = 2.00 t∙m-3

ϕ = 0.2 scalar

See Table 1

photo: https://www.nasa.gov/images/content/162655main_image_feature_697_ys_4.jpg

Open-Pit Metal Mine: Yerington Pit, Yerington, NV

Pressure Vessel k/b equivalent to 1 m of dry concrete

V = 5.7 x 107 m3 Retains 92% of gas pressure after 15 h storage

A = 1.3 x 106 m2

M = 1.1 x 108 t

P = 2.5 x 106 Pa

Pressurizing Layer

VPL = 1.1 x 108 m

APL = 2.3 x 106 m2

MPL = 2.2 x 108 t

Whole Device

VT = 1.7 x 108 m3

Amap = 1.1 x 106 m2

MT = 3.4 x 108 t

Assume

ρ = 2.00 t∙m-3

ϕ = 0.2 scalar

See Table 1

photo: https://commons.wikimedia.org/wiki/File:Anaconda_Copper_Mine,_Near_Yerington,_Nevada_(15700705511).jpg#file Ken Lund, 2014 CC-BY-SA-2.0

Energy Storage Capacity

CAES 5.3 x 106 kW∙h 0.18% of US need

H2 7.4 x 107 kW∙h 2.48% of US need

Tesla Powerwalls (13.5 kW∙h at $5500 each)

CAES 391k at $2.2B

H2 5.5M at $30B

Energy Storage Capacity

CAES 2.0 x 107 kW∙h 0.66% of US need

H2 2.6 x 108 kW∙h 8.55% of US need

Tesla Powerwalls (13.5 kW∙h at $5500 each)

CAES 1.5M at $8.1B

H2 19M at $105B