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.
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