International Journal o f Mining Engineering, 1983, 1, 43-56

A dynamic programming approach in designing underground coal slurry haulage systems H A S A N S E V I M and T U N C E L M. Y E G U L A L P Henry Krumb School of Mines, Columbia University, New York, New York 10027, USA

Received 28 October 1982

Summary

Underground hydraulic haulage systems (UHHS) are emerging as an alternative to conventional systems with the potential of eliminating haulage bottlenecks, and health and safety hazards in under- ground coal mines. Currently, identified problems associated with the application of UHHS are: 1. the lack of engineering design data; 2. the need for new equipment development; 3. better instrumentatidn and control; and 4. the need for optimum design methodology.

This paper deals with the fourth problem. A dynamic programming model has been developed to evaluate UHHS in different stages; starting from the coal faces up to a surge bin or to the preparation plant on l~he surface. Given a system layout and the number of faces, the model determines, at each stage, the equipment (pump-pipe combination) that minimizes the cost per tonne of coal handled. Equipment type, surge capacities, slurry characteristics, and local and cumulative costs are determined at each stage. The paper summarizes the approach, its limitations and underlying assumptions, and demonstrates the use Of the model with a numerical example.

Key words: Mine transport; coal mining; coal slurry; hydraulic transport; dynamic programming

Introduction

Underground coarse-coal slurry transport systems are considered to have potential for eliminating existing haulage bottlenecks and reducing health and safety hazards in under- ground coal mines.

Since the 1960s several mines from different countries have reported operating slurry systems associated with hydromining or excess mine water disposal (Borecki, 1960; Condolios, 1963; Harzer and Geller, 1978; Ofengenden and Dzhvarsheishvili, 1981). But these systems are mostly partial applications of the concept due to problems inherent in underground slurry transport. The problems associated with coarse-coal slurry haulage can be summarized into four categories in view of the findings of several investigators (Dahl et al., 1974, 1977; Link et al., 1975; Link, 1976; Gregory, 1977; Miscoe, 1977; McCain et al., 1981): 1. rheological problems of coarse-particle slurries; 2. operational problems associated with system equipment; 3. automation of the system; and 4. an efficient or optimum design.

0263-4546/83 $03.00 + .12 © 1983 Chapman and Hall Ltd.

44 Sevim and Yegulalp

The first three of these problems require the use of large-scale or prototype facilities to study the coarse-particle slurry properties, test equipment performances, and develop and operate control systems. The US DOE started-operating such a facility in Bruceton, Pennsylvania in 1981 (Miscoe and Faddick, 1980). In the near future when reliable infor- mation becomes available through this research facility, more realistic design of underground hydraulic haulage systems (UHHS) will be possible. However, the fourth item - the problem of optimum design, which is the subject of this paper - still remains unanswered. A literature survey revealed that a global optimization of such a system has not yet been done.

Underground hydraulic haulage system

An underground hydraulic haulage system (UHHS) can be synchronized with any kind of mining method. In this paper only the room-and-pillar method will be considered due to the availability of pertinent data from previous studies. In this system mining is accomplished by acont~nuous miner (cM) hooked up to an optional shuttle car which operates as a temporary storage vessel instead of its usual task of haulage. A feeder-breaker that crushes the large-size coal to a predetermined top size is attached to the shuttle car. Since the produc- tion of the CM is not continuous, despite its name, the shuttle car and the feeder-breaker serve as surge bins and regulate the feed to the slurry mixing tank located at the tail-end of the feeder-breaker. Coal is mixed with water in the mixing tank at a specified rate and fed by a screw or injection-type feeder to the suction end of a centrifugal pump. The pump is connected by two flexible hoses to rigid slurry and fresh-water pipes in order to allow the manoeuvring of the units at the face as the continuous miner trams back and forth. As mining advances, more rigid pipe sections are added to the pipeline system. When the CM finishes a cut, it moves to the next face. The shuttle car and feeder-breaker follow as soon as they are empty and a new cycle starts.

A booster pump may be required somewhere in the panel entry, depending on the distance from the face to the submain. In the submain there may be several slurry lines emerging from different panels, and these may run independently or can be merged or mixed in a surge tank and then pumped at a more regulated rate.

The main haulage system is probably one of the most critical parts of the whole system since it has to cope with a wide spectrum of flow rates, ranging from zero flow (all faces non-operating) to a maximum of Q (all faces operating). The main is also the most reason- able place where a large surge tank can be located to regulate the slurry flow.

In the submains and mains there will be a number of booster pump stations to provide the necessary head for pumping the slurry to the shaft bottom. The spacing of these stations is a function of the general layout of the mine as well as the capackies of the pumps.

At the shaft bottom, slurry is collected in a surge tank (large enough to drain the hoist pipe or even larger if it is designed to collect the incoming flows from different sections and provide a regulated flow to the surface) and hoisted from there by a series of high-head centrifugal pumps, hydrohoists or pipefeeders (Sakamoto, 1967; Wakabayashi, 1979; Siebert et al., 1980; Offengenden and Dzhvarsheishvili, 1981).

It should be noted that slurry characteristics (concentration, density, flow rates) fluctuate

Design of underground coal slurry haulage systems 45

due to inherent variability of coal output at the face. Variable speed drives which are coupled with centrifugal pumps can partially overcome these variations by changing pump rpm. Burnett et al. (1978, 1979), in describing a new concept to eliminate system transients, mention the necessary sophistication in automation in order to trigger the variable speed drives. A new device, however, called the helical inducer, senses the change in the system pressure due to transients and promptly adjusts itself so that the centrifugal pump balances off the system pressure. The study presented here was limited to the usage of centrifugal pumps siLnce reliable job performance and cost data were easily accessible. The model that will be described in this paper, however, is geared to accept input from other hydro- transport equipment currently being developed when the pertinent data become available.

Problem statement

The above brief system description suggests that the slurry generated at the coal face will pass through a few stages before it reaches the surface. The location of these stages and the selection of equipment at each stage (including the size of the surge tanks) will result in different slurry characteristics, power requirements and, consequently, different costs. If 'cost per tonne hauled' is chosen as the objective function, then the problem to solve is to find the configuration (or layout or arrangement) and size of equipment and surge tank capacities within that configuration which minimize this objective function.

If only two adjacent stages and constant flow are considered in the optimization process, the problem can be solved as suggested by Link et al. (1974) or by Transflux International (1979). The idea proposed by these studies is the minimization or maximization of the value of an objective function at each stage independently. This idea is displayed schematically in Fig. 1. It simply suggests that as the pipe size increases, the cost of the pipe increases, while pumping power cost decreases due to smaller friction losses in larger diameter pipes. The cost of a larger diameter pipe will inherently reflect the cost of additional water in the pipe which is required to maintain the minimum velocity and the incremental cost of a higher capacity pump to handle the increased quantity of slurry. There is, however, a point where

~D

C 0 I'--

Total Cost/Tonne

\ ' ~ / _ Cost of Pipe \ ~ / / and Inherent

MinimumTotaicost __ _ ~ , Costs/Tonne

, ~ 1 ~ Power Cost/Tonne i I

0 Dop t Pipe Diameter D

Fig. 1. Optimum pipe diameter for minimum total cost (after Link et al., 1974).

46 Sevim and Yegulalp

an increase in the cost of the pipe surpasses the savings in pumping power cost. The optimum pump-pipe combination would be the one that would be indicated by the minimum of the total cost curve.

it is important to note that this optimization argument is valid for systems between any two points A and B, or a single unit, where there are no inputs or outputs interfering with the system. The situation in UHHS is, however, quite different; there is more than one unit, serially connected, discharging the slurry to the next unit, with other unit(s) possibly merging with the main line to form a network-like system. Therefore, an independent optimum design of an upstream, or merging unit, will affect the design of the downstream units since the flow characteristics (concentration, specific gravity, quantity of slurry, etc.) of the former will be the inputs of the latter. As a consequence, a unit isolated from the rest of the system and optimized independently may contribute negatively to the rest of the system. Thus, the minimization of the total cost shown in Fig. 1 must be applied to the system as a whole and not unit by unit.

The implication of this argument is that the solution lies in the global optimization of the system. Consequently, all alternatives of flow characteristics are considered (using all possible pipe types) at each unit, and their outputs become inputs to adjacent units.

If each alternative solution is enumerated during this process the approach becomes lengthy and cumbersome, especially when the number of units and the number of pipes to be considered at each unit increases. Fig. 2 sketches a two-face operation where only three pipe sizes are considered to carry slurry from each face. Slurry transported in 0.26 m pipe from stage 1 can be transferred into 0.26, 0.36 or 0.46 m pipes at stage 2. (These connections are not shown on the figure:) Similarly, 0,36 and 0.46 m pipes of stage 1 can transfer into 0.26, 0.36 or 0.46 pipes of stage 2. The number of transport modes in stage 2 then becomes equal to 32 = 9 (geometrically increasing). At stage 3 the situation is more complex; nine transport modes of face 1 will be merging with the other nine modes of face 2 to form 92 = 81 new modes. As the number of pipe sizes and stages increase, the problem becomes prohibitively large.

Stage 1 Stage 2 Stage 3 Stage 4 Face 1 ~

,

,

,, m - d i a m e t e r s t a t e

B - . 3 6 m - d i a m e t e r s ta te Face 2 C - . 4 6 m - d i a m e t e r s ta te

Fig. 2. Schematic representation of pipes carrying slurry in a given two-face operation.

Design o.f underground coal slurry haulage systems 47

An optimization tool, namely, dynamic programming, which uses the same reasoning as explained above, but with a very efficient algorithm, can be used to solve this type of problem. The optimum design that will be obtained through the use of the dynamic programming model will emerge after computations are terminated for the last stage.

The final value of the objective function will be the determinant of such a design. It should be noted here that different objective functions will lead to the selection of different designs.

Dynamic programming formulation

Every dynamic programming formulation must have a clear definition of stages, states at each stage, boundary conditions, optimal value function, a recursive relation associated with it, and, finally, an optimal policy function.

In an UHHS, pump stations, surge tanks and pipe merging locations can be identified as 'stages', with alternatives of pipes at each station as 'states'. Fig. 3 shows, schematically, probable stages in a given alternative of a two-face operation. The numbers along the solid line in this figure represent the length of each unit in metres. The 0.26, 0.36 and 0.46 m pipes in ]Fig. 2 are the states at each stage of that particular two-face operation.

When cost per tonne is considered as the design criterion 'the optimal value function' can be defined as: V(X, i): the total value of the minimum cost per tonne alternative, connecting all upstream transportation units to the pump station X and pipe i; where X = 1, 2 . . . N; N is the number of stages in the system; i = 1, 2 . . . K; K is the number of states at each stage. The appropriate recurrence relation for this optimal value function can be written as:

V(X, i) = min {V(X - 1,j) + ayi} (1) j=I,...,K

where @ is the immediate cost of connecting statej of stage X - 1 to state i of stage x; and

Face 1 F a c e 2 6. .

tO tO CO CO CO CO

(D tO

/ g J

j , J

f

CO

CO

3 2 7

5 -- - -

4

O~ 0 t.O

03 0 (.0

k k ©

\

152

1. Face pump stat ion 2 .Pane l entry booster

pump stat ion 3. Pipe merging locat ion

in the submain 4. Surge tank in the

m main 5 .Booste r pump station

in the main 6. Shaft bottom hoist

station

Fig. 3. Schematic representation of stages in a given two-face operation.

48

(x-1)=3 I I a11=4 .26 i V(x-l,1)= 1 1 ~ ~6~,,~. l , I I

V(X-I'2)= 131~_~ . ~ N N t ~ }

V(x-l,3)= 14 ~ Fig. 4. Best first path determination.

x = 4

V(x,1)

V(x,2 )

V(x,3)

Sevim and Yegulalp

V(X - 1, j) is the total value of the minimum cost alternative corresponding to state j of stage X - 1.

Fig. 4 schematically represents these statements between stages 3 and 4 for the case in which only three pipe sizes (states) are considered. V(X - 1, 1), V(X - 1, 2) and V(X - 1, 3) are the minimum cumulative total cost values for 0.26, 0.36 and 0.46 m diameter pipes, respectively, and X - 1 represents the third stage. 'The recurrence relation' for state 1 (0.26 m pipe) of stage X = 4 can be written as:

{V(3, 1) + al1 } ---- 11 + 4 =17

V(4, 1) = rain{V(3, 2) + a21} = 13 + 3 =16 (2)

{V(3, 3) + a31} = 14 + 4 =18.

The minimum cumulative cost at stage 4 is 16 and it favours connecting stage 3 to stage 4 with a 0.36 m pipe. The meaning of this is that if during the process of optimization we end up selecting state 1 (or 0.26 m pipe) outgoing from stage 4, the best input to that state will be a 0.36 m pipe (state 2) from stage 3. The same computation will be done for state 2 and 3 of stage 4 and the 'optimal policy function', which is defined as 'the rule that associates the best first decision with each subproblem' (subproblem is the pipe selection between two adjacent stages), will mark the selected paths between these two stages. We will not know, however, the best path until we reach the last stage where min[V(N, i)] (i = 1 . . . K) will be found which will indicate the best outgoing pipe from there. The input to that pipe from the preceding stage will then be traced from 'best first paths' already marked by 'optimal policy function' during forward processing (the method described here is called 'forward dynamic programming'). The optimum design is obtained in this manner by simply tracing back from 'best first paths' until the faces are reached. 'Boundary conditions' are the obvious values that the optimal value function takes for states of either the first or last stage. In the application to UHHS these are the costs of transporting one tonne of coal from each face to the next stage t~y all possible pipe alternatives.

Design ,ff underground coal slurry haulage systems

Assumptions and limitations

49

The content of this paper is confined to a deterministic dynamic programming model with the following limitations and assumptions due to the volume of material involved:

1. Only the room-and-pillar mining method is considered for all production faces. 2. All faces are assumed to be operating in a synchronized fashion, i.e. they start and

stop production simultaneously. This assumption, although unrealistic, allows one to consider a design capable of handling the peak demand for haulage.

3. Location of pump stations, surge tanks and pipe lengths are externally supplied to the model. The number of serial pumps at each station is, however, determined optimally in the model.

4. The hydraulic hoisting at the mine shaft is assumed to be accomplished by a set of serially-coupled centrifugal pumps. They can, however, be replaced easily by a pipe-feeder or hydrohoist in the model.

5. Average operating and delay statistics of continuous miners, obtained from Transflux International Ltd (1979), are used to represent the face mining system's operating characteristics.

6. A minimum 'variable cost' concept is used as the optimum 'design-criterion' where the costs include only the fixed and variable cost elements associated with the construction, installati[on and the operation of the planned slurry system, i.e.

(Pump + pipe + surge tank investments)/ Cost per tonne of coal hauled = tonne + power cost/tonne + water pumping (3)

and handling/tonne + water purchase/tonne

Pump cost is further broken down as pump, motor, valve and variable speed drive costs. This variable cost concept serves the purpose of comparing alternative slurry systems and, consequently, finding the best combination of equipment and operating characteristics.

7. Maximum allowable coal concentration by weight is assumed to be 45%. 8. Head losses in the system are obtained by calculating first the losses that would occur

for an equal amount of water fowing in the system by using Darcy's formula, and then upgrading them by using McElvain's (1974) correlation.

The head loss calculation theory in settling slurries such as coarse-coal slurry is not well established. Several researchers have come up with differing correlations of the variables, and these are summarized and evaluated in different studies. The approach explained above is adopted in the model due to its practicality; but can easily be replaced by other cor- relations.

9. Pump selection routine is adopted from Transflux International Ltd (1979) where a data bank was formed of the characteristics of 21 different pumps. Their performance areas are further divided into subsections formed by head-capacity curves (corresponding to different rpm values) and iso-efficiency curves. When small subsections are chosen the intersection of iso-efficiency and head-capacity curves can be represented by small polygons. The polygons are plotted all together, and in areas where more than one pump can handle the flow, the one with the highest efficiency is selected, thus always leading to the selection

50 Sevim and Yegulalp

of a pump with the highest performance. The efficiency attributed to the selected pump is obtained by linearly interpolating between the left- and right-hand-side efficiency lines. This efficiency is later degraded by McElvain's (1974) empirical formula in order to adopt it to slurry transportation. The degraded version is used in the remainder of the model which inherently indicates that the system operates under full control, i.e. no variability in the concentration and flow quantity.

10. The equations for investment costs are also adopted from Transflux International Ltd (1974). This data bank which was put together in 1976-77 has been updated by price escalation indexes.

11. Twelve different commercially available pipes (forming 12 states at each stage) are entered in the data ranging from 0.1 to 0.9 m internal diameter.

12. An estimated rate of $0.04 kWh -1 is assumed for power cost. 13. Water-pumping andwater-purchasilag costs are assumed to be bl.06 m -3 and k5.28

m -3, respectively. 14. Reclamation rate of water is assumed to be 88%. The remaining 12% is purchased as

fresh water at b5.28 m -3 rate. 15. Maintenance cost is assumed to be 10% of the investment costs. 16. The following depreciation schedule is considered: (a) pumps and related equipment:

15 years; (b) pipes: 15 years; (c) surge tank in the submain: five years; and (d) surge tank in the main: 20 years.

Numerical example

The dynamic programming approach explained above provides an overall optimum solution to UHHS for a given number of faces operating under a deterministic production scheme and specifies: pipe diameters, pump types and operating regimes, slurry concentrations, flow rates, water requirements, surge tank capacities, slurry velocities, power requirements, production rates, and associated costs at each stage in the mine as well as the final optimum cost per tonne at mine portal.

For illustration and comparison purposes four alternative layouts in a four-section mine are considered. These four alternatives are shown schematically in Fig. 5. The optimum pipe sizes and surge tank capacities are shown in the sketches for each layout.

Table 1 exhibits, in detail, the values of design parameters of type 3 UHHS. The first two columns indicate the stage number and the number of sections at each stage. At stage 3 (or at submain) pipes coming from sections 1 and 2 merge to form the new section 1, and sections 3 and 4 merge to form the new section 2. (This is also shown schematically in Fig. 5 type 3.) These two new sections dump their output into two separate surge tanks located at the main (or stage 4), each with a capacity of 309 m 3 and a cost of $33 300 (columns 6 and 7). Both sections run independently in the main as sections 1 and 2 of the main booster station (or stage 5) and finally merge at the shaft bottom to form a new section called 'section 1' of stage 6. Column 3 shows the amount of coal produced from each section during a shift. The slurry output from the last stage is 11.76 m 3 mill -1 indicating a total slurry output of 11.76 x 480 w_ 5645 m 3 per shift. The first four rows of column 5 show the

Design of underground coal slurry haulage systems 51 Face Area Face Area 4 3 2 1 .30 4 3 2 1 .30

t ~I ~~ ~09m3 t I t ~618m3 Type 1 Type 2 4 3 2 1 .30 4 3 2 1 .30

l l ~'~ !4~09rn3 ~[~ t ~ t34 t618m 3 .34 .34 Type 3 Type 4 Fig. 5. Four different pipeline layouts for a four-face hydraulic transportation system.

amount of water necessary at each face to prepare a slurry of 45% concentration by weight. Column 8 indicates that slurry flows only in 17.3 rain of a cycle (see section 2 for the definition of cycle: duration of a cycle is calculated to be 52.1 rain in this example) during which 5.22 m 3 of water per minute is added to crushed coal. Notice that there are 8.1 of these cycles during a shift (column 9). After the surge tanks at stage 4, however, the flow becomes continuous within two cycles of 240 min each (columns 8 and 9).

As seen in column 10, the only place where the slurry is diluted from its original concen- tration of 45% is at the shaft bottom. This can also be verified from the slurry flow of sections 1 and 2 of stage 5 which brings a total of 2 x 4.8 = 9.6 m 3 rain -1 to the shaft bottom. There, an additional 11.76 - 9.60 -- 2.16 m 3 min -1 water is blended with 9.60 m 3 min -1 slurry to form a 11.76 m 3 rain 1 diluted slurry. It should be noted that the dilution is necessary when a 0.30 m pipe is chosen at the shaft bot tom (last row of column 22) since the velocity of slurry would be less than the critical or deposition velocity otherwise. A 0.25 m pipe could handle the flow without dilution but as explained earlier and illustrated in Fig. 1, the incremental cost of power required by a 0.25 m pipe (due to higher frictional losses compared to those of a 0.30 m pipe) is higher than the sum of the incremental cost of water handling and purchasing, and the incremental cost of the pipe and pump that are used when a 0.30 m pipe is selected.

It should be kept in mind that here, at the last stage, we compared only 0.25 and 0.30 m pipes. The 0.30 m selection, however, is a result of an overall optimization; i.e. providing the minimum of all cumulative cost per tonne values at the final stage.

Column 12 indicates that slurry velocity ranges from 2.47 to 3.09 m s -1 along the system. Pump polygon numbers are shown in column 14. From the carpet plot described previously, we find that polygon numbers 16, 17 and 21 correspond to Worthington Co. centrifugal

c~

>

°~ ~

0

f~

qo

a~g

z~ . .=~

O

ca

54 Sevim and Yegulalp

pump type 8M193. Similarly, the polygon number 1 indicates Worthington 6M163, while polygons 22 and 30 correspond to Worthington 10M234. It should be noted that polygon numbers 16, 17 and 21 designate the same type pump, however, each one's operation zone indicates a different efficiency. The cost of pumps given for the sections of stages 4 and 5 are the totals of two serially-connected pumps at these sections. The last number in column 16 indicates that at the shaft bottom five serially connected pumps designated by polygon 16, costing $689 400 all together, are used to hoist the slurryl Columns 17, 18 and 19 show power requirements under different forms. Hoist station power consumption is the largest in the system since a static head of 152 m (the depth of the shaft) needs to be overcome in addition to the friction losses in the hoist pipe. Pump efficiencies shown in column 21 conform with the numbers given in the literature for coarse- particle slurry pumps. The pipe diameters specified for each section are exhibited in column 22.0.25 m diameter pipe is used in all sections up to the merge points in the submain where the combined slurry of sections 1-2 and 3-4 are carried down to the surge tanks in the main by 0.34 m pipes. The outgoing flows from the surge tanks are distributed over two cycles of 240 min each, thus decreasing the amount to be handled to 4.8 m 3 n]l-n -1, Conse- quently, 0.20 m pipes are selected to transport the flows in the main. At the shaft bottom these two flows merge, requiring a 0.30 m pipe for hoisting.

Finally, the last column represents the 'variable cost per tonne' of coal at each section. Table 2 shows the 'variable cost per tonne' distributed over different stages of the mine. In this table 'panel haulage' represents both the face and the panel haulage, and 'main haulage' includes the section where surge tanks are located and the main booster pump station. Column 2 of this table indicates that for type 3 layout, the panel and main haulage account approximately for 70% of the total variable cost per tonne. When this cost is pro-rated to cost per tonne per 100 m, however, 100 m of hoist transportation is approximately 12 times more expensive than 100 m of main haulage as well as five times more than the panel and eight times more than the submain haulages.

Table 3 summarizes the 'cost estimations' for all four types of four-face UHHS shown in Fig. 5. The last line of this table, which exhibits the values of the design criterion, suggests that alternative four is the best of the four alternatives considered for this numerical example. One should keep in mind that this is not an exhaustive list of all feasible alter-

Table 2. Distribution of variable cost (type 3-4 face haulage).

Stage name

Variable Variable Percentage of cost/tonne/ cost/tonne ($) total cost 100 m ($) 1 2 3

Panel haulage Submain haulage Main haulage Shaft hoist

0.2293 29 0.022 42 0.0789 10 0.013 96 0.3109 39 0.009 66 0.1742 22 0.114 28

Design of underground coal slurry haulage systems

Table 3. Cost estimations for four types of four-face UHHS.

55

Cost type Alternative 1 Alternative 2 Alternative 3 Alternative 4

Total variable investment ($1000) 5313

Variable capital and maintenance cost ($/tonne) 0.528

Power cost ($/tonne) 0.271 Water co,;t ($/tonne) 0.028 Total variable cost

($/tonne) 0.827

4656 5031 4374

0.468 0.497 0.436 0.231 0.269 0.229 0.028 0.028 0.028

0.727 0.794 0.693

natives for a four-face UHHS, and one may find a better alternative by considering other feasible layouts.

For comparative purposes the same four types discussed above are tried with the local optimization model suggested by Transflux International Ltd (1974). The tota! variable costs were $0.861, 0.737, 0.826 and 0.703 for types 1, 2, 3 and 4, respectively, thus justifying the approach of global optimization in systems like UHHS.

Conclusion

The model and approach presented in this paper are the results of the first attempts at overall optimization of the UHHS design. The results are valid but with strong assumptions; namely, tihe deterministic production scheme and synchronized work schedule at the faces. The present model, however, apart from being a better approach than previously reported ones in the sense of its global validity, provides a basis for future work. The natural extension of this effort is the identification of stochastic processes that characterize the operation of coal-face activity and modification of the model to reflect such behaviour. An optimum design can then be obtained with a modified stochastic-dynamic programming model. Development of such a model is currently being undertaken by the authors.

References

Borecki, M. (1960) Hydraulic transport in Polish hard coal mines, Mining Journal April, 254. Burnett, M., Reed, C.H., Harvey, A.C. and Miscoe, A.J. (1978) A coarse coal injector for hydraulic

haulage developed for the US Department of Energy, Hydrotransport 5, paper F4. Burnett, M., Harvey, A.C. and Rubin, L.S. (1979) A self-controlling slurry pump developed for the

USDOE, Hydrotransport 6, paper G2. Condolios, E. (1963) Pumping ores up vertical shafts, CIM Bulletin March. Dahl, H.D. and McCain, D.L. (1974) Continuous underground slurry transport of coal,

Mining' Congress Journal May.

56 Sevim and Yegulalp

Dahl, H.D. and Eston, E.P. (1977) Update on slurry transportation from face to cleaning plant, Mining Congress Journal December.

Gregory, F.W. (1977) Hydrotransport of Solids Underground, Mining Technology Clearing House, Burton-on-Trent, Staffordshire, UK.

Harzer, H. and Geller, L.B. (1978) German experience in hydraulic coal mining and its application to Canadian conditions, CIM Bulletin January.

"Link, J.M. (1976) Hydraulic transportation of coal from the face, Mining Congress Journal September. Link, J.M., Andrew, A. and Faddick, R.R. (1975) Feasibility of Hydraulic Transportation in Under-

ground Coal Mining, Colorado School of Mines Research Institute for the Bureau of Mines. Link, J.M., Lavingia, J.N. and Faddick, R.R. (1974) The economic selection of a slurry pipeline,

Hydrotransport 3, paper K3. McCain, D.L., Doerr, E.R. and Rohde, E.G. (1981) Slurry transport system operation, presented at

the SME-AIME Fall Meeting, Denver, Colorado, November. McElvain, R.E. (1974) High Pressure pumping, Skillings Mining Review 63. Miscoe, J.A. (1977) Hydraulic transportation for coal mining, presented at the Workshop on

Materials Handling for Tunnel Construction, Keystone, Colorado, August. Miscoe, J.A. and Faddick, R.R. (1980) US Department of Energy hydraulic transport research

facility for coarse coal, in Proceedings of the Fifth International Technical Conference on Slurry Transportation, Lake Tahoe, Nevada, March.

Ofengenden, N.E. and Dzhvarsheishvili, A.G. (1981) Technology of Hydromining and Hydro- transport of Coal, Terraspace, Inc., Rockville, Maryland.

Sakamoto, M. (1967) Hydraulic Transport of Granular Solids, Hitachi Hydrahoist, brochure from Hitachi, Ltd.

Siebert, H., Kortenbusch, W. and Harzer, H. (1980) Further experience with horizontal and vertical hoisting of coarse ROM coal at the Hansa Hydromine, Hydrotransport 7.

Transflux International Ltd (1979) Evaluation of Alternate Hydraulic Transport Concepts for Coal Haulage in Underground Mines, Report to US Department of Energy, Contract No. ET76-C- 01-9033.

Wakabayashi, J. (1979) Slurry pumped 3000 feet vertically, Coal Age June, 84-7.