Note: Descriptions are shown in the official language in which they were submitted.
1155301
This invention relates to methods of recovering energy
from abandoned coal mines and waste banks and particularly to a
method of combustion of wasted coals in place with utilization
of the resultant heat energy in production of transportable
energy such as electricity.
A significant economical consideration as well as a
significant pollution problem of all past and current coal
mining practices is the so called "wasted" coal. In general
"wasted" coal falls in two catagories (a) underground coal in
which due to the exigencies of the underground mining operations
often contain as much coal as was extracted, and (b) above
ground coal in coal refuse piles, which are accumulations on the
surface of reject material from coal preparation plants and from
underground mining operations, commonly known as spoil piles or
boney piles.
The underground coal, generally in the form of coal
pillars, frequently will become ignited and will burn for years
unless controlled. The same is true of above ground waste
piles. In both cases the uncontrolled burning of the coal is
both a great waste of useful energy and a significant hazard to
public health and safety because of the emission of toxic and
obnoxious fumes and the destruction of residential and
commercial buildings in the vicinity. Such fires once
established can smolder for decades and their extinguishment by
conventional methods of sealing, dig-out and quench is costly
and hazardous.
The magnitude of the problem of extinguishing such
fires can be appreciated by the fact that the cost estimates for
extinquishing presently existing "waste" coal fires on abandoned
lands in burning waste banks in the United States alone would be
'~
1 1553~ 1
$468 million, and the cost of controlling existing fires in
inactive coal deposits would be $75.6 million. This would of
course merely be a fix for the present fire problem and would
not remove the potential for further fires nor does it take into
consideration the value of the "wasted" coal as a source of
energy, which I believe to be in the same general area as the
cost of extingishing the fires, i.e. about $550 million.
I have developed a method of solving the problems
inherent in these "wasted" coals both above and below ground.
My invention eliminates both the environmental problems and the
high cost of extinguishing such fires. By my practice an
important new energy source, based upon the use of these wasted
coals, is made available.
I have discovered that vast new quantities of energy
are made available by in situ combustion of wasted coals under
exhaust ventilation control conditions which allow for total
management of the hot gases produced, followed by the utiliza-
tion of the hot gases to produce process heat, steam or
electricity. rrhis solves once and for all the problems of fire
and acid water formation which are inherent in every abandoned
coal mine or waste bank. In addition it eliminates the problem
of leaking of smoke, fumes and gases which have made prior
positive pressure efforts at burn out unacceptable environ-
mentally.
It has herefore been proposed to recover the energy
from underground wasted coal by coal gasification through
controlled burning underground. Unfortunately, this has not
proven to be a satisfactory solution to the "wasted" coal
problem for a variety of reasons. First it i5 difficult to
control the rate of combustion to produce a sastisfactory fuel
11553~ 1
gas. Second it is equally difficult to control the gaseous products to prev-
ent their escape in undesirable places because the controlled burning is done
under positive pressure.
According to the present invention, there is provided a process
for recovering energy from in situ wasted coal located at or adjacent to the
area from which mined comprising the steps of:
(a) first creating at least one channel through the in situ
wasted coal without removing the wasted coal from its location at or adjacent
to the mining area;
(b) igniting the wasted coal in said channel while at the same
location to cause subsurface in situ combustion to occur;
(c) activating gas control means to subject wasted coal, at
least in said channel, to a controlled negative gaseous pressure arop relative
to ambient gaseous pressure applied at a preselected zone;
(d) connecting said wasted coal, at least at said channel, to a
source of air remote from said preselected zone to induce the air to permeate
through the wasted coal to the channel and thereby in the subsurface combus-
tion step produce hot gaseous products of combustion, said products being
drawn from said zone; and
(e) thereafter utilizing said hot gaseous products of combustion
in a heat exchange relationship to recover the heat energy therefrom.
Preferably, the hot gaseous products of combustion are passed
through an after burner where air or fluid fuel is added to produce substan-
tially complete stoichiometric combustion of the hot gaseous products of com-
bustion drawn to said point and hot gaseous products are used to produce one
of steam, hot water, electricity and processed heat. The gaseous products of
combustion leaving the heat exchange relationship are preferably cleared of
particulates and S02 and thereafter discharged to atmosphere. Most preferably
an aqueous scrubber is utilized to clean the particulates. In connecting
the wasted coal to a source of air in Step (d), preferably at least one air
inlet conduit is placed from the surface into the wasted coal to provide for
-- 3 --
1 15530 1
the entrance of air thereinto.
In the foregoing general description, we have set out certain
objects, purposes and advantages of our invention. Other objects, purposes
and advantages of this invention will be apparent from a consideration of the
following description and the accompanying drawings in which:
Figure 1 is a data-time plot for simulated in situ burning of rub-
bleized coal;
Figure 2 is a graph of exhaust temperature as a function of coal
and water content;
Figure 3 is a sketch of a model coal seam combustion channel;
Figure 4 is a graph of fractional heat loss and exhaust temperature
with channel size scaling factor;
.~
- 3a -
1 15530 1
Figures 5a and 5b illustrate two possible borehole
arrangements usable in this invention;
Figure 6 is a graph of distance of negative pressure
effect in a coal waste pile;
Figure 7 is a graph of efficiency of heat transport in
a petal;
Figure 8 is a graph of pressure drop vs. pipe distance
for transporting thermal power; and
Figure 9 is a schematic flow diagram of a process of
the invention.
The present invention can perphaps be best understood
by reference to controlled tests using the technique in rubble-
ized coal and solid coal.
Test 1
Approximately 40 tons of coal rubble (stoker grade)
were sealed in a trench to simulate an underground coal seam
approximately 35 feet long, 8 feet high and 6 feet wide. An
axial channel of 1 square foot cross-section was formed in the
coal rubble by means of a metal grate to define an in situ coal
burning zone. One end of the channel was connected to an
insulated exhaust pipe and fan, and the other end to a valved
inlet air pipe. Two additional valved air inlet pipes were also
positioned along the channel. The exhaust fan (15,000 scfm, 18
inch H20 head capacity) was connected to the insulated exhaust
pipe to enduce and maintain a negative pressure on the trench so
as to induce an airflow into the channel through the inlet pipes
to sustain combustion of the coal and at the same time exhaust
the hot products of combustion from the channel in the coal
bed. The test was operated continuously for 33 hours and during
that time the thermal output of the ln situ combustion process
1 ~ 553~ 1
was readily controlled between 1.0 and 1.7 Mw~ and the exiting
combustion products were at very high temperature (about 1,600
C). Except for SO2 the exhaust gas was exceptionally clean in
terms of low concentrations of CO, NOX, and particulates.
Figure 1 shows data-time plots obtained in this experiment from
mesurements of the flue gas at a position some 20 feet
downstream of the channel exit (i.e. after some afterburning
with dilution air). It is noteworthy that while the observed
S2 emission (1,100 ppm) is commensurate with the sulfur content
of the coal (2 wt-pct), the observed NOX emission (110 ppm) is
considerably lower than what might be expected on the basis of
the fuel-nitrogen (1 = wt - pct). The NOX emission is actually
about a factor of 5 less than values reported for pulverized
fuel combustors. Likewise, the particulate emissions appeared
visually to be quite small.
It is also noteworthy that during the entire test
(ignition, steady burning, and cool down), the exhaust
ventilation control system enabled total management of the
combustion gas flow. Despite air leakage into the trench and
total burnout and cave-in of a portion of the trench, no
combustion products escaped to the atmosphere except through the
exhaust system.
It is clear from this work that the controlled ln situ
burning of coal can be carried out efficiently, cleanly, and
with total management of the heat and gases produced by
following the practice of this invention.
It can also be anticipated from this test that the
concept of ln situ combustion at negative pressure would be a
feasible approach to elimination of the environmental problems
of "wasted" coal fires. Thus, ln situ combustion methodology
1 1553~ 1
could be applied to accelerate the burning of abandoned mine and
waste bank fires simultaneously with total management of their
air pollutant emissions and with utilization of the thermal
energy produced -- eventually leading to complete burnout of the
combustibles and elimination of their potential for acid water
formation and reignition.
Test 2
In a second test a solid block of coal having a
channel therein was enclosed in a second sealed trench and
burned as in test 1. The results obtained in this test were
similar to those in test 1, however, in this test the measured
particulate emissions averaged only 0.008 lb/106Btu over a 45
hour burning period. This would indicate that even better
results may be expected from combusting solid in situ
underground wasted coal depositions than from loose wasted coal.
It is interesting to calculate some ~ T values for
reasonable estimates of the material parameters. Taking
Pittsburgh seam coal at stoichiometric combustion, and using the
following equations:
~H 1 ~ H
aT = ~Hc eJ v
v P
0 +
where O = mh/mO = xw/xc, the ratio of mass of water to mass of
coal in the refuse.
0 = mair/me, the stoichiemetry of the coal combustion process
(air/fuel ratio)
we would have 0 = 12 and a Hc = 7,600 cal/g. The heat of
evaporation of water is 540 cal/g. The value chosen for the
1155301
heat capacity of the mixture in the burn zone (coal, combustion
products, water vapor, inert material) is weighed towards a high
wat:er vapor content and assumed to be 0.5 cal/g - C.
Figure 2 shows the calculated combustion temperature
for various coal and water contents of the refuse. The boundary
line drawn at 800 C in figure 2 is a "guesstimate" of the
minimum temperature required for rapid chemical reactions which
would insure self propagating combustion. A "typical" refuse
pile containing 35 pct combustible and an equal amount of water
falls into the region of susta-ined combustion yielding an
exhaust gas of almost 950 C (1,740 F). These calculations
indicate that sustained combustion can occur in refuse
containing substantial quantities of water (2 to 3 times the
coal content). This is consistent with the fact that waste bank
fires continue to burn despite their exposure to the elements
and often despite attempts to extinguish them by saturation
sprinkling. The calculated results also suggest that most coal
refuse piles have enough fuel to sustain a fire provided that
sufficient air can be drawn into the interior of the piles.
Heat Loss from Channel Burning in Abandoned Coal Mines
Whereas propagating coal refuse fires results in the
accumulation of heat in inert material which is always
intimately mixed with the fuel (i.e., internal to the burning
system) the geometry of abandoned mine fires results in heat
accumulating in roof and floor strata which are external to the
coal burning system. Thus, the heat which is conducted away
from the burning coal must now be considered as an energy loss
which will affect the exhaust temperatures, and could conceiv-
ably extinguish burning under certain conditions of seam
thickness and channel dimensions. This problem of heat loss
~ 15530 1
during channel burning in a coal seam has received mathematical
treatment by the U.S. Bureau of Mines and the results pertinent
to the problem of burnout of abandoned mine fires are summarized
in this section.
The model of channel burning considered is shown in
fic3ure 3. Here a rectangular channel of length (1) and width
(w) in a coal seam of thickness (h) moves at a linear surface
burning rate (B) through the seam. A constant ventilating air
and exhaust gasflow occurs along 1. The effective channel width
remains constant by the process of continuous coal burning on
one side of the channel and continuous or periodic roof fall
along the opposite side of the channel. Heat is lost from the
system by thermal conduction to the roof and floor strata, but
only while the strata define the upper and lower boundaries of
the channel. Consideration of the quasi-steady-state energy
balance during the effective exposure time period leads to:
-1 C (0+1)
( ~ T) = P + 4 ~ ¦ w
~ Hc ~S~ HCh ~r~ B
where A = the thermal conductivity of the strata (assumed
constant),
K = the thermal diffusivity of the strata,
~ S = the density of the strata,
and the remaining symbols have the same definitions given in the
previous section.
The fractional heat lost EL and the fraction of energy
transmitted in the exhaust EH are given by the expressions:
E = 4~ ~ T ¦ w
L ~s ~HCh ~ ~K B
and C (0+1) a T
E = P
H ~ H
8.
1 ~553~1
The equation EL = 4~ T 1 w indicates
that the fractional heat loss increases with decreasing seam
thickness and with increasing channel width. Figure 4 is a plot
of both EL and a T versus the scaling factor ~ for a
stoichiometric air/fuel ratio, ~ = 12, and values of the
material parameters which are given in table 1. Again, assuming
a criterion of ~ T ~ 800 C for self-propagated burning, a heat
loss as high as 4G pct could be sustained at a value of
Jw/h2 -~ 0.7 cm~l/2. Thus for 180 cm (6 feet) thick seam, the
effective width of the burning channel must be less than 1.6 x
104 cm (550 feet), which is most likely to be the case. It is
interesting to note that the temperature criterion ( > 800 C)
would be met even for seams as thin as 30 cm (1 foot). As shown
in figure 4, a channel exhaust temperature of 1,000 to 1,200 C
(1,800 to 2,200 F) should be expected, which is in good agree-
ment with the combustion results obtained in some underground
coal gasification trials.
TABLE 1. - Input data for numerical calculations
~ cal/cm-sec-C 4 x 10-4
B cm/sec 2 x 10 4
c cal/g 7 x 103
~s g/cm3 1.3
Cp cal/g-C 0 4
X cm2/sec 10-4
Effective Burn Control Volume in a Waste Bank
To achieve negative pressure burning according to this
invention in a porous waste bank it is necessary to suck on a
region inside the bank using an exhaust fan operating through a
3 0 1
piping system inserted into the bank. Two possible approaches
are depicted schematically in figure 5. Figure 5a depicts the
use of multiple inlet air boreholes surrounding a single exit
borehole. Figure 5b depicts the use of a single exit borehole
with air being drawn through the surface of the bank ("blind"
borehole method). The question is what volume of waste bank can
be aerate(l by exhausting at the exit borehole. This will
establish the efEective volume of the bank under in situ
combu~tion control.
A simple approach to estimating this volume is to
apply Darcy's Law to the "blind" borehole geometry with the
assumption that the gasflow within the bank is uniform, steady,
and converges spherically towards the tip of the exit borehole.
Darcy's equation for l-dimensional steady flow through
a porous medium can be written as:
q = k A (dP/dx)
Where q = the gas volume flow rate in cm3/sec.
k = the permeability of the porous medium in Darcys,
~ = the gas viscosity in centipoise,
A = the effective cross-sectional flow area in cm2,
and dP/dX = the pressure drop across the bed in atm/cm.
A steady flow at the tip of the blind borehole, and
uniform convergent flow in the bank requires that q be constant
across a spherical cross-sectional area situated at a distance x
from the borehole. If ~ is the solid angle in steradians which
defines the flow region, the cross-sectional area as a function
of x is:
A = 4~ x
and
q = 4~ k x2 dP
dx
10 .
1 ~5~30 ~
With a constant q, ~ and (k//~ ), the
equation q = 4~k x2 ~ can be integrated to yield:
~ dx
- 1 = 4 ~Y~ k /P - P ~
Xl Xo j ~ lJ
For the porous flow situation being considered, the integration
limits can be taken as
Pl (xl) = 1 atm (ambient pressure)
PO(XO = d) = maximum negative pressure at one borehole
diameter distance, d, away from the tip
of the borehole.
This yields the following expression for the affected distance x
in the waste bank
= _ 4~r~a P ~ k~ + 1
1 ~ q/ d
here ~ ~ = the effective vacuum (a positive quantity) that
can be applied at the exit borehole.
Numerical solutions for xl with various sized
boreholes are shown in figure 6, or the case where~ = 0.02
centipoise (i.e., air), ~ P = 0.1 atm (i.e., 1.47 psi or 38.6-
in H20 vacuum), and
~ = 0.5 (i.e., a hemispherical flow region). The numerical
solutions in figures 6 are asymptotic.
To achieve large burn volumes, x, would have to be
large (i.e. ~ 300 cm or 10 feet), and q/k close to the minimum
value for which solutions to the last equation are obtained. In
those cases
(q/k)cr = 4 ~r~ ~ Pd
is the asymptotic limit for large x, and defines the achievable
practical flow rate. For example, in a waste bank having
~ 1553~ 1
dimensions much larger than d, and having a permeabiltiy of 103
Darcys (approximatley 10 times that of a pile of sand), an
exhaust flow rate of 106 cm3/sec (2,130 scfm) could be achieved
with a 30-cm (l-foot) diameter exit borehole. Larger flow rates
could be achieved, but only by sacrificing the effective burn
volumes in the bank. For example, an exhaust flow three times
greater (6,390 scfm or 3 x 106 cm3/sec) from the same bank and
borehole leads to a value of xl = 100 cm (or 3 feet). Thus, a
blind borehole would have to be positioned some 3 feet below the
surface of the bank in order to maintain a negative pressure
burning region, i.e., to draw in sufficient air for complete
combustion of the waste and exhaustion of the hot gaseous
products.
This simple approach to porous flow does not take into
account the effects of changing permeabilty with increasing
zonal burnout or the effects of nonuniformities either in the
permeability or the gasflow, all of which are expected to occur
in an actual burnout. However, the calculations do indicate
that the maintenance of a negative pressure combustion zone in a
porous bank should be feasible, provided that sufficient suction
is available from the exhaust fan.
Effective Burn Control Volume in an Abandoned Mine
The burn control volume for an abandoned mine, as in
controlled burnout of a waste bank, depends upon the airflow
induced by the exhaust fan system. If all the original mine
entries and stoppings remained in good condition, simple
ventilation network calculations would yield reasonable
estimates of the possible airflow. This, of course, is hardly
to be expected for old workings on fire where stopping and roof
collapse have undoubtedly occurred. However, since one must
12.
1 ~.5~301
start some place, the abandoned mine fire geometry for the
current purposes is idealized as the propagating channel burn
depicted in figure 3. This will enable some estimate of the
relationship between channel size and ventilation fan
requirements. The calculations presented draw heavily on U.S.
Bureau of Mines results previously reported in connection with
an _ situ coal combustion and coal mine fires.
Referring to figure 3, the total mass rate of coal
burning coal is
Mt = ~ SBAs~
where ~s = the coal density,
B = its constant linear burning rate (identical to the
rate of movement of the channel through the
coal seam),
and As = hl is the area of the burning coal surface. For a
stoichiometry defined by an air/fuel ratio of 0, the total
volumetric exhaust flow rate is
. B(0+1)A
q= ~s
M/V
where M = the average gram molecular weight of the gaseous
combustion products
and V = their specific molar volume.
From previous U.S. Bureau of Mines studies the
pressure drop across the burning channel is estimated to be
~ P =~ ~ Q ex cm-H O
where ~ (cm) = the channel length,
Ax (cm2) = its cross-sectional area
Qex = the thermal power level of the exhaust flow
in kilowatts,
and
o~ = an empirical constant equal to 0.17 for the
given parameter units.
1~5530
Since Qex = ~sBAs ~Hc
where a H~ is the heat of combustion of coal, we obtain:
C ( I;~S ~ H c )
and ~P = ~(~SBa HC)2 ~ 3
hl/2V5/2
For the coal parameters in table 1 (keeping in mind
that for o~ = 0.17, the a Hc of 7 x 103 cal/g must be expressed
as 239 KW-sec/g), and assuming that hl/2 W5/2 ~ w3 (which would
be exactly the case for a square channel with h = w = Ax 1/2),
the equation ~ P =c<(~sB~ Hc) becomes:
~ P = 6.6 x 10 4(~ cm-H2O
Here we see that the pressure drop is very sensitive to the
ratio of channel length to channel width. For example, an ~/w
= 25 would require a a P of 10.3 cm-H20 (0.15 psi) which should
be readily achieved with conventional exhaust fans. However
an ~/w = 75 leads to a ~ P of 278 cm-H20 (4.2 psi) which would
pose a more severe constraint on fan size.
To relate the equation A P = 6.6 x 10 4(~3 cm-H2O to
burning volume, we need to know the effective width of the
burning channel, a matter which is probably site selective. A
reasonable "guesstimate" would be w no less than one-half the
seam thickness, which for a 180-cm (6-feet) thick bed and a
nominal ~P of 10.3 cm-H20, would lead to a ventilated burn
channel length of 2,250 cm (75 feet).
B(~+l)A
The exhaust volume is given the equation q= es s
which for reasonable material parameter values (~ = 12; ~ = 30
g/mole; V = 2.24 x 104 cm3/mole (STP); also see table 1) yields
q = 2.52 A = 2.52 (h~ ) cm /sec (STP)
~ ~S5~0 1
For the channel burning case above where h = 180 cm.
= 2,250 cm ~ P = 10.3 cm-H20, the volumetric flow rate would be
106 cm3/sec (STP) or 2,190 sefm. well within the range of
conventional exhaust fans. At 1,000 C the power level
generated by the exhaust flow would be ~ 2 Mw. Th~ fan air
horsepower, which is the product of ~ P and q multiplied by an
appropriate conversion factor, would in this case be 1.4 ahp,
again a very nominal value. The fan power requirements are
discussed in somewhat greater detail in the next section. These
theoretical results are based on a highly idealized in situ
burning geometry. In abandoned mines, channel blockages and
roof cave-ins could easily affect the ventilation pressure drop
and the ventilation airflow to the burning coal surface;
however, on the basis of the idealized geometry, there would
appear to be no fundamental difficulties in achieving
ventilation controlled burnout of the combustible in an
abandoned mine.
Fan Power Requirements for Burnout Control
While the design of an exhaust fan ventilation system
for burnout control will have to be site selective, it is useful
to establish some general requirements in engineering units for
fan capacity and motor size. This is necessary to elucidate the
value of the energy conversion efficiency that is available
through ln situ combustion techniques.
We consider coal to have a heating value of 10,000
Btu/lb (5.55 kcal/g) and a nominal carbon to hydrogen ratio of
unity. The complete combustion reaction can be approximated by
CH + 1.2502 + 4.62N2 C2 + H20 + 4.62N2
~J ,_
1 mole 5.87 moles air 6.12 moles exhaust
coal
From molecular weight considerations, it is readily
1 15~30 1
seen that 0.388 lb of air (5.87 moles or 4.7 scf) is required to
combust 0.0286 lb of coal. This leads to 6.12 moles of gaseous
exhaust (4.9 scf) having a sensible heat content of 58.4 Btu/ft3
(STP).
We now consider an exhaust thermal power output of 1
Mw for 5.7 x 104 Btu/min). This requires an exhaust flow rate
of combustion products of 976 scfm and a coal combustion rate of
5.7 lb/min.
The air horsepower (ahp) required to drive this
exhaust flow is given by
ahp --~P(in-H~0) x q(scfm)
348
If we assume that a relatively high pressure drop of
100 in-H20 (3.8 psi) will be required to ventilate the required
burn control volume, the fan air horsepower requirements for a 1
Mw thermal output is 15.4 ahp. With 70 pct fan efficiency, the
electrical power requirement for the fan motor will be 22 hp (or
0.0164 Mw). Assuming no losses or additional energy expenditure
(eg. for scrubbing systems, thermal conversion systems, etc),
the energy recovery for the ln situ combustion technique would
be
thermal energy outPut = 61
electrical energy input
This factor, which is independent of Qex~ is considerably
greater than the value of 3 to 4 reported for underground coal
gasification. Even when a thermal to electrical energy
conversion efficiency of about 30 pct is taken into account, the
energy recovery factor is still quite large, i.e.
thermal energY output = 20
thermal equivalent electrical energy input
Thermal losses would, of course, lower the recovery0 factor by a proportional amount, but on the other hand,
16.
~155~
decreased fan pressure re~uirements (i.e. a P ~10O in-H20)
would increase the recovery factor proportionally.
Surface Transport of Hot Exhaust Products
So far the technical discussions have centered on the
in situ combustion process itself and not on the utilization of
heat produced during burnout. In general, the approach to
utilization of heat would be much the same as almost any high-
temperature (1,000 C), ambient-pressure flue gas (eg. to supply
process heat, utility steam, electricity generation) except that
utilization or conversion would have to be on-site. This is
because it is not feasible to transport heat energy over long
distances. However, the question still arises as to what
distance would be defined as on-site, or how far the hot flue
gas can be moved before thermal losses, and exhaust pipelines
cost become prohibitive. In essence this will define the
maximum distance between the exit borehole and the energy
utilization facility. Estimates of this maximum distance and
its parametric relationship to thermal power level and pipeline
size are readily obtained from considerations of heat loss and
pressure drop through the surface pipe system.
For the heat loss calculation, we consider the steady-
state radial flow of heat into a pipe wall of thickness o whose
inner surface is maintained at constant temperature Tal and
whose outer surface temperature is at constant ambient
temperature To~ For a pipe wall having constant thermal
physical properties, the rate of heat flow per unit length of
pipe Qa is given by
2 ~ ~ T -T
Q a = p a o
ln (l+ ~/a)
where A P = the thermal conductiity of the pipe wall,
1l553~l
a = the inside radius of the pipe,
and ~ = the wall thickness.
For a small section of pipe having a length of ~ L =
(L;2-Ll), and an axial temperature difference defined by Ta(Ll) =
Tl and Ta(L2) = T2, the total heat rate of heat loss to the wall
will be determined by the equation above using an average inner
surface temperature
Ta = (Tl + T2)/2 = T1 - ~ T/2
for the section ~ L. Here, ~ T = T2 ~ Tl is the change in
temperature across the section ~ L. Assuming a uniform and
well-mixed hot gasflow through the pipe, ~ T is also the change
in temperature of the gas due to the wall heat loss.
The energy balance for the pipe section ~L is then
ln(l+ ~/a) (Tl _ To _ a T/~)(~ L) = C (
where mg = the mass flow rate of the gas,
and Cp = its specific heat.
Solving for ~ T/~ L in the zero limit of ~ L yields a
simple differential equation
dT/dL 2~ p(Tl To)
~gcp ln(l+~/a)
for the change in gas temperature with pipe length. Integrating
between the limits T(L = O) = TeX, the exit borehole exhaust
temperature, and T(L) = TL, the gas temperature at distance L
along the pipe, we obtain
TL To = exp r- 2~ L 1
TeXTo . l mgC ln(l+~/a) J
Recognizing that QL = mgCp (TPL - To), it is seen that the left-
hand side of the above equation is also the friction of the
exhaust thermal power flowing through the pipe distance L (i.e.,
EH = QL/Qex) This last equation can also be written as
18.
~15~01
j 2~A~T -T ~L
E = exp _ p~ ex oJ
H Qex ln(l+~ /a)
Here we see that the thermal transport efficiency
increases exponentially with increasing power level and
decreasing gas temperature. Figure 7 depicts several curves of
EH vs L for various power levels of flue gas at TeX = 1,000 C
(1,830 F), and various values of the pipe size factory S /a.
As expected, the transport efficiency depends strongly on
Qex~ ~ /a and L.
Assuming that a value of ~/a = 0.1 to 0.2 might be
reasonable we see that 10 Mw, 100 Mw, and 1,000 Mw power levels
could be effectively transported 104 cm (328 feet), 105 cm
(3,280 feet), and 106 (32,800 feet) respectively, before heat
loss becomes excessive.
Considering pipe heat loss alone, the combustion
products from a controlled burnout of "wasted" coal could be
transported an adequate distance for on-site utilization,
particularly at the higher power levels. However, the pressure
drop associated with a desired gasflow rate or thermal power
level is another important constraint.
To estimate the pressure drop a P for a given hot
gasflow we considered the pipe flow equation
p = f ~V2 w
2 A
where ~ and v = the gas density and gas velocity,
respectively,
Aw and Ax = the pipe wetted surface area and cross-
sectional area, respectively,
and f = a wall friction factor which is
dimensionless when the parameter values are
expressed in the cgs system of units.
For a circular pipe AW/AX = 2 ~YaL/~Ya2, and
19 .
301
recognizing that the total steady state mass flow rate mg is
m = OvA = ex
g I x C /T -T )
p~ ex OJ
th~e equation ~P = f r ex I L becomes
~ 1 P( ex ) , --~
Here, we see the pressure drop is very sensitive to the pipe
radius and thermal power level. ~ P decreases with increasing
'a' and decreasing Qex. On the other hand the thermal transport
efficiency, EH, increases with decreasing 'a' and increasing
Qex. Thus both a P and EH must be considered together in
setting specifications for the surface heat transport pipe.
The last equation is plotted in figures 8 as ~ P vs L
for some power levels of interest assuming f = 0.01 (i.e. smooth
wall, turbulent flows). For a 100 cm-H20 (36 in H20) pressure
drop and a 105-cm (3,280-foot) distance, a 10 Mw, and 100 Mw,
1,000 Mw power level would require a pipe radius of 45 cm, 113
cm, and 288 cm, respectively. An 80 pct heat transport
efficiency under these same conditions would require the wall
thickness of the pipe to be approximately 50 cm, 10 cm, and
2 cm, respectively.
From these considerations, it can be expected that
piping cost for surface transportation of high temperature flue-
gas will be significant.
In Figure 9 we have schematically illustrated a plant
for utilization of my invention.
In the foregoing specification I have set out certain
preferred practices and embodiments of my invention, however, it
will be understood that this invention may be otherwise embodied
within the scope of the following claims.
20.
