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The Control of Hydro Power Distribution Systems in Deep Mines
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The Control of Hydro Power Distribution Systems In Deep Mines R.W.
scan and
D.G. W YMER
Engineering Systems Branch, Chamber of Mines Research Organization, Johannesburg, SA
Abstract. The concept of hydro power in deep mines is based on the exploitation of the hydrostatic head that can be gained as refrigerated cooling water descends in shaft pipe columns from the surface, to provide hydraulic power for machines at the working face. This paper describes the work done on two important aspects of the controlled distribution of the high pressure water within a mine , namely the control of pressure under normal operating conditions, and the control of flow in an emergency situation following a pipe breakage. Suitable methods of control have been determined using theoretical techniques to model the steady and unsteady flow behaviour of the water in the pipeline, and taking into consideration the environmental constrain t s on the types of control devices that can be used. The preferred approach is one in which the high pressure water itself is used as the control medium . The control valves themselves can be fairly conventional in design, but in the case of pipe break protection it is shown that a less conventional approach based on the use of a hydraulic fuse gives improved control performance. Keywords . Pipeline systems; m~n~ng; power system control; control valves; pressure control; flow control; computer-aided system design; modelling . INTRODUCTION quantities of equipment demanding regular maintenance underground, such as electrical power supply equipment and high pressure pumps, which otherwise would be required for the generation of hydraulic power c l ose to the working areas . Additionally, it was rea l ized that the available quantities and pressures of water, as determined by the cooling requirements and working depths respectively, were generally more than sufficient for the powering of machinery . Thus, a mine could introduce hydro power without necessarily increasing its total water handling capacity and without install i ng addi t ional pumps .
In South African gold mines, the mining activities at the face are labour intensive and represen t a high proportion of the total cost of mining . Mechanization of these activities can bring about an improvement in this situation through an in crease in productivity, and the Research Organization of the Chamber of Mines has been involved for many years in the development of various types of hydraulically powered mining equipment for this purpose. Because of the harsh conditions prevailing at the working faces, the only hydrauliC fluid considered sufficiently economic and practical for use with the equipment in the long term is water (Wymer, 1984) . Meanwhile, high pressure water jets are being used to an increasing extent for cleaning broken rock from the working faces (O'Seirne, Gibbs and Siderer, 1982). Thus, there is a developing need generally for wa t er- hydraulic power in South African gold mines .
In view of these various attractions, the concept was investigated in great detail, to determine more pr ecisely the design requiremen t s for a viable working system. Part of t his inves t igation involved the development of a suitable cont r ol system des i gn for the high pressure distribution network, particularly to ensure that machines were supplied at the correct hydraulic pressures, and to safeguard personnel and equipment in the event of a pipe failure . This paper outlines the techniques used in this part of the investigation to predict the behaviour of water in a mine hydro power system under various conditions, and describes some of the basic hydraulic control devices that were found to be required .
Many such mines operate at depths of 3 000 m and more, and require large quantities of refrigerated water for maintaining acceptable ambient temperatures underground . The preferred arrangement is to chil l the water on the surface, and then to transport it to the underground workings in pipes . The depths of the workings are such that substantial water pressures (typically 10 MPa to 20 NPa) can be developed as the wa t er descends, and many mines recover the hydrostatic energy through Pelton turbines to generate e l ectrical power. This also minimizes the temperat u re rise of the water . If, however, the water is maintained at high pressure and is distributed in this form to the working areas, it can fulfil a dual function of providing both cooling and hydraulic power to the face.
ANALYTICAL TECHNIQUES The simplest approach to the design of a control system for a hydrauliC reticulation network is based on steady state considera t ions. Variables associated with piping systems are related by algebraic equations which account for friction losses. A common expression for long straight pipes is the Oarcy- Weisbach equation (Streeter, 1966) :
There are many advantag e s of this 'hydro power' approach, not lea st being the elimination of large
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146
~P = 8fLf Q2 lT 2 DS
where LIP f L
f D
Q
(1)
pressure loss along pipe length (Pa) friction factor length of pipe (m) density of fluid (kg/m 3 ) internal diameter of pipe (m) volumetric flow rate (m 3 /s)
Similar expressions are used for other pipeline components. While such expressions are very useful, they give no indication of dynamic effects which occur when the system conditions are chacged in any way. Although it is possible to calculate the state of a hydraulic network before and after an event such as a pipe rupture, an equation such as (1) gives no idea as to how long it takes to reach the new state. Moveover it gives no indica-
ox
dP dt
4fv 2 c:lQ
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TTD2
ox
Q(t) = Qf exp (a+bt)-l ex p( a+bt)+ 1
Equations (2) and (3) are a set of non-linear partial differential equations and, since there is no known analytic solution, they must be solved numerically using a computer. This is normally done using the 'method of characteristics' as described by Streeter and Wiley (1967), Fox (1977) and Chaudhry (1979). Conditions at the ends of the pipes in a network may be matched using equations (or characteristic curves) describing the operation of the connecting devices. In this way the entire water reticulation system may be simulated. Such a simulation has been developed to assist in the analysis of hydro power reticulation systems and to evaluate control systems designs. Equations (2) and (3) may be simplified by making certain approximations and considering only idealized cases. Although such simplified equations can quickly give a rough idea of system behaviour without the need for a computer, and are often used in preference by pipeline system designers, some important features are lost. This is illustrated using two examples, typical of events that may occur in a mine hydro power system. These examples are based on Fig. 1, which shows schematically a portion of such a system. It is assumed in each example that the water flow rate is initially 0,03 m3 /s.
(6)
4fQ f 1fD3 (Qf+Qo) I n - - - - - bto (Qf-Qo)
a
initial time Qo
Parameters f, D and f are as defined previously and v is the velocity of propagation of a pressure wave in the water. Note that in the steady state (dQ/dt = 0, op/ox = -LlP/L) equation (2) reduces to the Darcy-Weisbach expression (1).
(5)
final flow as calculated from equation (1)
where Qf
(2)
where P is the pressure and Q is the flow at a distance x along the pipeline, at a time t.
2
Since 6P changes from one constant value to another, equation (5) may be solved (Boyce and DiPrima, 1965) to give:
b
(3)
(4)
L
dQ = _ ~ Q Q + ~ 6P dt V D3 4fL
hammer', induced by sudden changes. Such dynamic effects can be calculated only by using the following differential equations for a deformable pipeline (Streeter and Wylie, 1967): _ ~ QIQI_ TTD2 oP TT D3 4f ox
.LIP
L
Then equation (2) becomes:
tion of the size of pressure waves, or 'water
dQ dt
P(out) - P(in)
oP
initial flow
For this example, taking the initial time as zero and the friction factor as 0,025: Q(t) =
exp (0,459+4,237t) °, 133 exp(0,459+4,237t) +
(7)
The system response, calculated accurately using equations (2) and (3), and approximately from equation (7), is shown in Fig. 2. Although the simplified expression gives a good indication of the settling time, it does not predict accurately the initial rate of change of flow or the peak flow. Example 2: Sudden closure of the isolating valve in the horizontal pipeline. By making the following substitution: dP dt
dP dx
v-
and by assuming that the pressure and flow rate change instantaneously to new steady values, equation (3) can be rewritten as .LIP = -4fv 6Q
rfD2
(8)
where.4P is the magnitude of the pressure rise, and 4Q is the reduction in flow rate. The system response, again calculated accurately using equations (2) and (3), and approximately using equation (8), is shown in Fig. 3. In the case of the approximate solution, the large diameter vertical pipeline has to be ignored, with a full reflection being assumed at the connection point at the bottom of the shaft. Thus, the pressure wave is assumed to oscillate in square wave
Example 1: Sudden 'clean break' failure of the horizontal pipeline, 500 m from the shaft. In this case, the pressure drop over the horizontal length of pipeline changes instantaneously from its normal, low operating value to 18 MPa. In order to simplify equation (2), it is assumed that the pressure varies linearly along the pipeline, that is:
form with a periodicity of 4L/v (approximately 2,5 s in this example) as it is reflected back and forth along the horizontal pipeline. The exact solution predicts that the pressure will rise initially to 21t MPa, followed by a more gradual increase to 23 MPa. Successive pressure peaks are progressively attenuated because of friction in the pipeline. The approximate solu-
Control or Hydro Power Distribution Systems tion predicts a similar initial rise in pressure, but underestimates the peak value slightly, and, of course, does not show the effect of friction losses. These two examples show that the approximate expressions (6) and (8) can be used to gain insight very quickly into certain aspects of t he response of a system, but only in simple idealized situations . In particular, only single lengths of pipe with a uniform diameter can be considered. To predict completely the response of a full hydro power network, it is necessary to develop a mathematical simulation and, for each element within the network, to solve the basic equations (2) and (3).
CONTROL SYSTEM DESIGN CONSIDERATIONS Special considerations are necessary when designing a control system for a hydro power distributtion network in a deep mine . The pipework configuration is unusual, in that it is extensive in both the horizontal and vertical planes, and the environmental conditions impose constraints on the types of control equipment that can be used. The first and most obvious considerat ion is the existence within the system of high pressures , typically between 10 and 20 MPa. All control valves located in the line underground must be capable of withstanding these pressures with an appropriate safety margin. In some cases, this has precluded the use of certain designs of control valve which would otherwise have been attractive for this application . A second consideration is that, if a structural failure should occur, a runaway flow situation will develop as described in the previous section, and the affected section of the line should be shut down automatically to minimize the hazard to equipment and personnel. For instance, referring again to the schematic in Fig. 1, if the horizontal pipeline ruptured completely at a point 100 m from the shaft, equation (1) predicts that the flow rate would rise to 0,3 m3 /s, with an exit velocity of 38 m/s o The reaction force on the broken pipe would be 140 kN, which could cause the pipe to break away from its supports. If an attempt were made to stop this flow suddenly with an automatic valve, the pressure upstream of the valve would rise to nearly 60 MPa, according to equation (8). This could in turn cause a further structural failure of the pipeline . By contrast, failure of the same pipeline pressurized to 18 MPa by a positive displacement pump would result in no increase in flow rate or velocity. The pressure in the line would fall almost to zero, the pipe reaction force would be negligible, and the sudden closure of a valve after the rupture would produce a pressure wave of less than 6 MPa. Thirdly, there are several environmental considerations which affect the choice and location of control equipment. Close to the working faces, the atmosphere is hot, humid, corrosive and dusty, and working spaces are confined and inaccessible. Consequently, the reliability of control devices is likely to be poor, particularly in cases where external pneumatic or electrical power is required. Therefore the use of all but the simplest control devices should be avoided . In the main access tunnels, the environment is less harsh and space is less restricted, so there are fewer constraints on the types of control devices that can be used. However, most commercially available pipeline valves are controlled and actuated using
147
an external pneumatic or electrical power supply and such supplies can be interrupted during the day-to-day operation of a mine . Although temporary back-up systems can be considered, the most satisfactory approach is to use controllers and actuators working directly from the high pressure water in the pipeline. Few valves of this type are available commerCially, but some speciallydeveloped prototypes are being evaluated . Finally, the quality of the water must be considered. After passing through hydraulic machines in the working areas, the water exerts a cooling effect by coming into contact with the freshly exposed rock surfaces. In doing so, it picks up large quantities of salts and fine rock particles, and becomes chemically contaminated by blasting fumes. In conventional mining, many of the suspended particles are removed by settling , but nothing is done to remove dissolved contaminants . The concept of hydro power offers a broader economic base for the justification of bulk water treatment to remove these contaminants, so the water in the high pressure section of a hydro power system could be relatively pure. However, for economic reasons, it is unlikely that the dissolved and suspended matter will be removed entirely in the treatment plant. Additionally, it is known already that large quantities of solid particles can be generated from time to time within the pipeline by corrosion, scaling, deterioration of internal coatings, and debris introduced during installation and maintenance . Therefore, all control system components must be capable of withstanding moderate quantities of impurities in the water for long periods, and large quantities for short periods . This applies particularly to water- operated controllers and actuators, since these will tend to be more susceptible to damage or malfunction. This may impose special constraints on the designs of such components, and is the subject of current investigations. NORMAL OPERATING CONDITIONS CONTROL OF PRESSURE Water must be supplied to machines in the working areas at pressures compatible with machine requirements to ensure safe and efficient operation. The control of pressure must automatically take into account variations in line losses over short time periods, due to changing demands during the working shift, and over long periods when factors such as pipe scaling and extensions to the system become significant. Pressures will also vary with location in the mine, because of differences in elevation between the various working areas. The hydraulic equipment under development for operation on high pressure water tends to be capable of working over a wide range of pressures (typically 12 to 18 MPa). Studies have shown that in most cases pressure control may be carried out using pressure regulators in the main trunk lines, as shown in Fig. 1, away from the harsh environment of the working areas, with the variations in line losses in the intervening pipework not compromising unduly the level of control achieved . Besides enabling the reliability of the control components to be improved conSiderably, this approach introduces substantial cost savings through the use of larger, but much fewer, pressure regulators.
EMERGENCY CONDITIONS - CONTROL OF FLOW Normally, the water flow rate is controlled automatically, according to the demands of the machines operating at the face, by the hydraulic
148
R. W. Swt.t and D. G. Wymer
resistance and mechanical inertia of the machines themselves. In an emergency situation occurring as a result of a pipe breakage, this control is lost, and must be replaced by some form of flow control within the pipe system to avoid the type of runaway flow situation discussed earlier in the paper. Three basic types of device have been considered for this purpose, the flow control orifice, the safety shutdown valve and the hydraulic fuse. Flow Control Orifices The pressure drop through an orifice increases as the square of the flow rate. Thus, in a runaway flow situation, a suitably sized orifice will assist in dissipating the hydrostatic head, and will restrict the final flow rate to a lower value, as illustrated in Fig. 4. Although this will only reduce, rather than eliminate, the hazards associated with a pipe break, the use of orifices can be regarded as a simple, fail-safe back-up to more sophisticated flow control devices. Safety Shutdown Valves These devices are essentially isolating valves controlled and actuated externally, preferably using high pressure water taken directly from the line. The isolating valves themselves are available commercially from several manufacturers, in a range of sizes and pressure ratings more than adequate for this application. Suitable high pressure water controllers and actuators for the automatic operation of these valves are currently under development. A disadvantage of a safety shutdown valve is that it tends to respond slowly, so that in a pipe rupture situation the flow will have already reached its full runaway value before the valve can close. In the meantime, the high velocity water jet issuing from the broken pipe may have caused considerable damage, and the large reaction force may have pulled the pipe from its supports, causing further damage. Additionally, in view of the greatly increased flow rate, the valve must now be closed much more slowly to avoid excessive water hammer, delaying even further the shutdown process. Referring to the system shown schematically in Fig. 1, assume, for example, that the isolating valve shown 250 m from the working face is now a safety shutdown valve, and that its control system has a delay of 0,5 s. If a pipe fails suddenly, close to the working face, a negative pressure wave will arrive at the valve 0,17 s later, and after a further delay of 0,5 s the valve will start to close. The pressure immediately upstream of the valve will then rise in a manner dependent on the closing time. Fig. 5 shows what happens if the valve closing time is 1 s, according to the predictions of a simulation based on equations (2) and (3). The pressure drops initially as a runaway situation develops, and then rises suddenly as the valve closes. After peaking at 27 MPa, the pressure then oscillates with appreciable amplitude for more than 10 s. This behaviour could easily cause further failure of the pipe system. Fig. 6, on the other hand, shows the situation if the valve closing time is 10 s. After the initial delay, the pressure rises slowly and, on completion of valve closure, peaks at only 21 MPa. The subsequent oscillations are minor, and are soon dissipated. In this case, there should be no chance of a further pipe failure.
Hydraulic Fuses A schematic representation of a hydraulic fuse in its simplest form is shown in Fig. 7. It is essentially a globe-type valve, in which the closure element is normally held away from its seat by a coil spring. As the flow increases, a pressure difference develops within the valve, generating a force on the closure element opposing the spring, and the valve starts to close. During the final stages of approach, the pressure difference across the seat increases very rapidly, causing the valve to close with a 'snap' action. The pressure upstream will then hold the valve tightly closed until the pressure downstream is restored. This can only be accomplished once the failed pipe has been repaired. The advantages of this type of device over a safety shutdown valve are that it is simple in construction and entirely self-actuated, it reopens automatically, and it responds extremely rapidly. Considering the same pipe failure situation as before, but with the valve in Fig. 1 now being a hydraulic fuse, and assuming this hydraulic fuse snaps shut when the flow reaches 0,06 m3 /s (twice the normal maximum value), the system behaviour predicted by the simulation is as shown in Fig. 8. Despite the almost instantaneous closure, the pressure rises only to 22t MPa because the flow has not been allowed to reach its runaway value. This pressure peak can be reduced even further if complete shut-off of the hydraulic fuse is avoided. This can be achieved, for example, by simply drilling a hole through the closure element. The effect is illustrated in Fig. 9, which shows the predicted behaviour when the previous pipe failure situation is controlled by a hydraulic fuse containing a 10 mm diameter leakage hole. The maximum pressure is reduced to 21 MPa, and the subsequent oscillations are attenuated much more rapidly than in the previous case. The flow rate through the hydraulic fuse~ shown in Fig. ID, quickly settles to 0,013 mJ/s after the event, giving an exit velocity at the open end of the pipe of less than 2 m/so This is unlikely to cause any significant damage, and can be shut off at some later stage with a manual isolating valve. A further advantage of having a leakage path through the hydraulic fuse is that, following repair of the damaged pipe, the isolated section of line can be repressurized through the leakage hole in a controlled manner without the need for an external by-pass line around the hydraulic fuse. CONCLUS IONS The development of a suitable control system for a hydro power distribution network in a mine depends on the ability to predict the steady and unsteady flow behaviour of the water in the pipeline. Accurate prediction necessitates the use of a mathematical simulation technique based on the numerical solution of a set of governing differential equations, although simplified expressions can be used to give a rough idea of system behaviour in very simple, idealized cases. A simulation has been developed successfully for hydro power systems in deep mines, and has been used to formulate a suitable control systems approach. The pipework configuration and environmental conditions associated with a mine hydro power system affect in a major way the preferred design and location of hydrauliC control devices, resulting in a need for new types to be developed. A particularly desirable feature is that the control devices must not depend on external pneumatic or electrical power supplies, but must rather use the
149
Control of Hydro Power Distribution Systems energy in the high pressure water itself.
REFERENCES
Under normal operating conditions, the pressures within the system must be regulated automatically, but the characteristics of the hydraulicallydriven mining equipment are such that the level of control need not be very strict. This enables the number of control devices to be minimized, and avoids the necessity for them to be located close to the workings, where the environment is particularly harsh.
Boyce, E.B. and DiPrima, R.C. (1965). Elementary Differential Equations and Boundary Value Problems, 2nd ed. Wiley, New York. Chaudhry, M.H. (1979). Applied Hydraulic Transients. Van Nostrand Rheinhold, New York. Fox,~ (1977). Hydraulic Analysis of Unsteady Flow in Pipe Networks. MacMillan, London. O'Beirne, D., Gib bs, L.S. and Seiderer, A. (1982). The use of high-pressure water-jetting in gold-mine stoping operations. In H.W. Glen (Ed.), Proceedings, 12th CMMI Congress, S. Afr. Inst. Min. Metall. (or Geol. Soc. S. Afr.), Johannesburg. Streeter, V.L. (1966). Fluid Mechanics, 3rd ed. McGraw-Hill, New York. Streeter, V.L. and Wylie, E.B. (1967). Hydraulic Transients, McGraw-Hill, New York. Wymer, D.G. (1984). The use of emulsions and water in underground hydraulic systems, In Proceedings, Symp. on the Current Use of Hydraulics in the Mining Industry, Minemech 84, S. Afr. Inst. Mech. Engrs., Johannesburg.
Using the mathematical simulation to predict flow behaviour following a pipe breakage, three types of control device have been investigated for controlling flow in the affected pipework, to avoid the damaging effects of a runaway flow situation. Simple flow restriction orifices offer some degree of control, but are viewed rather as a back-up to other more sophisticated devices. Safety shutdown valves can isolate completely the affected pipework, but do not respond rapidly enough to prevent the flow from rising to its full runaway value, and must therefore close slowly to avoid excessive water hammer. A less conventional approach uses a hydraulic fuse which is a lowinertia, self-actuated device capable of responding so rapidly that it can, quite safely, isolate the line almost instanteously before a full runaway condition has been reached. ACKNOWLEDGEMENT This work formed part of the research and development programme of the Research Organization, Chamber of Mines of South Africa.
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150
R. W. SCOlL and D. C. Wymer 0,20
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The Control of Hydro Power Distribution Systems In Deep Mines R.W.
scan and
D.G. W YMER
Engineering Systems Branch, Chamber of Mines Research Organization, Johannesburg, SA
Abstract. The concept of hydro power in deep mines is based on the exploitation of the hydrostatic head that can be gained as refrigerated cooling water descends in shaft pipe columns from the surface, to provide hydraulic power for machines at the working face. This paper describes the work done on two important aspects of the controlled distribution of the high pressure water within a mine , namely the control of pressure under normal operating conditions, and the control of flow in an emergency situation following a pipe breakage. Suitable methods of control have been determined using theoretical techniques to model the steady and unsteady flow behaviour of the water in the pipeline, and taking into consideration the environmental constrain t s on the types of control devices that can be used. The preferred approach is one in which the high pressure water itself is used as the control medium . The control valves themselves can be fairly conventional in design, but in the case of pipe break protection it is shown that a less conventional approach based on the use of a hydraulic fuse gives improved control performance. Keywords . Pipeline systems; m~n~ng; power system control; control valves; pressure control; flow control; computer-aided system design; modelling . INTRODUCTION quantities of equipment demanding regular maintenance underground, such as electrical power supply equipment and high pressure pumps, which otherwise would be required for the generation of hydraulic power c l ose to the working areas . Additionally, it was rea l ized that the available quantities and pressures of water, as determined by the cooling requirements and working depths respectively, were generally more than sufficient for the powering of machinery . Thus, a mine could introduce hydro power without necessarily increasing its total water handling capacity and without install i ng addi t ional pumps .
In South African gold mines, the mining activities at the face are labour intensive and represen t a high proportion of the total cost of mining . Mechanization of these activities can bring about an improvement in this situation through an in crease in productivity, and the Research Organization of the Chamber of Mines has been involved for many years in the development of various types of hydraulically powered mining equipment for this purpose. Because of the harsh conditions prevailing at the working faces, the only hydrauliC fluid considered sufficiently economic and practical for use with the equipment in the long term is water (Wymer, 1984) . Meanwhile, high pressure water jets are being used to an increasing extent for cleaning broken rock from the working faces (O'Seirne, Gibbs and Siderer, 1982). Thus, there is a developing need generally for wa t er- hydraulic power in South African gold mines .
In view of these various attractions, the concept was investigated in great detail, to determine more pr ecisely the design requiremen t s for a viable working system. Part of t his inves t igation involved the development of a suitable cont r ol system des i gn for the high pressure distribution network, particularly to ensure that machines were supplied at the correct hydraulic pressures, and to safeguard personnel and equipment in the event of a pipe failure . This paper outlines the techniques used in this part of the investigation to predict the behaviour of water in a mine hydro power system under various conditions, and describes some of the basic hydraulic control devices that were found to be required .
Many such mines operate at depths of 3 000 m and more, and require large quantities of refrigerated water for maintaining acceptable ambient temperatures underground . The preferred arrangement is to chil l the water on the surface, and then to transport it to the underground workings in pipes . The depths of the workings are such that substantial water pressures (typically 10 MPa to 20 NPa) can be developed as the wa t er descends, and many mines recover the hydrostatic energy through Pelton turbines to generate e l ectrical power. This also minimizes the temperat u re rise of the water . If, however, the water is maintained at high pressure and is distributed in this form to the working areas, it can fulfil a dual function of providing both cooling and hydraulic power to the face.
ANALYTICAL TECHNIQUES The simplest approach to the design of a control system for a hydrauliC reticulation network is based on steady state considera t ions. Variables associated with piping systems are related by algebraic equations which account for friction losses. A common expression for long straight pipes is the Oarcy- Weisbach equation (Streeter, 1966) :
There are many advantag e s of this 'hydro power' approach, not lea st being the elimination of large
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R. W. Scott and D. C. Wymer
146
~P = 8fLf Q2 lT 2 DS
where LIP f L
f D
Q
(1)
pressure loss along pipe length (Pa) friction factor length of pipe (m) density of fluid (kg/m 3 ) internal diameter of pipe (m) volumetric flow rate (m 3 /s)
Similar expressions are used for other pipeline components. While such expressions are very useful, they give no indication of dynamic effects which occur when the system conditions are chacged in any way. Although it is possible to calculate the state of a hydraulic network before and after an event such as a pipe rupture, an equation such as (1) gives no idea as to how long it takes to reach the new state. Moveover it gives no indica-
ox
dP dt
4fv 2 c:lQ
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ox
Q(t) = Qf exp (a+bt)-l ex p( a+bt)+ 1
Equations (2) and (3) are a set of non-linear partial differential equations and, since there is no known analytic solution, they must be solved numerically using a computer. This is normally done using the 'method of characteristics' as described by Streeter and Wiley (1967), Fox (1977) and Chaudhry (1979). Conditions at the ends of the pipes in a network may be matched using equations (or characteristic curves) describing the operation of the connecting devices. In this way the entire water reticulation system may be simulated. Such a simulation has been developed to assist in the analysis of hydro power reticulation systems and to evaluate control systems designs. Equations (2) and (3) may be simplified by making certain approximations and considering only idealized cases. Although such simplified equations can quickly give a rough idea of system behaviour without the need for a computer, and are often used in preference by pipeline system designers, some important features are lost. This is illustrated using two examples, typical of events that may occur in a mine hydro power system. These examples are based on Fig. 1, which shows schematically a portion of such a system. It is assumed in each example that the water flow rate is initially 0,03 m3 /s.
(6)
4fQ f 1fD3 (Qf+Qo) I n - - - - - bto (Qf-Qo)
a
initial time Qo
Parameters f, D and f are as defined previously and v is the velocity of propagation of a pressure wave in the water. Note that in the steady state (dQ/dt = 0, op/ox = -LlP/L) equation (2) reduces to the Darcy-Weisbach expression (1).
(5)
final flow as calculated from equation (1)
where Qf
(2)
where P is the pressure and Q is the flow at a distance x along the pipeline, at a time t.
2
Since 6P changes from one constant value to another, equation (5) may be solved (Boyce and DiPrima, 1965) to give:
b
(3)
(4)
L
dQ = _ ~ Q Q + ~ 6P dt V D3 4fL
hammer', induced by sudden changes. Such dynamic effects can be calculated only by using the following differential equations for a deformable pipeline (Streeter and Wylie, 1967): _ ~ QIQI_ TTD2 oP TT D3 4f ox
.LIP
L
Then equation (2) becomes:
tion of the size of pressure waves, or 'water
dQ dt
P(out) - P(in)
oP
initial flow
For this example, taking the initial time as zero and the friction factor as 0,025: Q(t) =
exp (0,459+4,237t) °, 133 exp(0,459+4,237t) +
(7)
The system response, calculated accurately using equations (2) and (3), and approximately from equation (7), is shown in Fig. 2. Although the simplified expression gives a good indication of the settling time, it does not predict accurately the initial rate of change of flow or the peak flow. Example 2: Sudden closure of the isolating valve in the horizontal pipeline. By making the following substitution: dP dt
dP dx
v-
and by assuming that the pressure and flow rate change instantaneously to new steady values, equation (3) can be rewritten as .LIP = -4fv 6Q
rfD2
(8)
where.4P is the magnitude of the pressure rise, and 4Q is the reduction in flow rate. The system response, again calculated accurately using equations (2) and (3), and approximately using equation (8), is shown in Fig. 3. In the case of the approximate solution, the large diameter vertical pipeline has to be ignored, with a full reflection being assumed at the connection point at the bottom of the shaft. Thus, the pressure wave is assumed to oscillate in square wave
Example 1: Sudden 'clean break' failure of the horizontal pipeline, 500 m from the shaft. In this case, the pressure drop over the horizontal length of pipeline changes instantaneously from its normal, low operating value to 18 MPa. In order to simplify equation (2), it is assumed that the pressure varies linearly along the pipeline, that is:
form with a periodicity of 4L/v (approximately 2,5 s in this example) as it is reflected back and forth along the horizontal pipeline. The exact solution predicts that the pressure will rise initially to 21t MPa, followed by a more gradual increase to 23 MPa. Successive pressure peaks are progressively attenuated because of friction in the pipeline. The approximate solu-
Control or Hydro Power Distribution Systems tion predicts a similar initial rise in pressure, but underestimates the peak value slightly, and, of course, does not show the effect of friction losses. These two examples show that the approximate expressions (6) and (8) can be used to gain insight very quickly into certain aspects of t he response of a system, but only in simple idealized situations . In particular, only single lengths of pipe with a uniform diameter can be considered. To predict completely the response of a full hydro power network, it is necessary to develop a mathematical simulation and, for each element within the network, to solve the basic equations (2) and (3).
CONTROL SYSTEM DESIGN CONSIDERATIONS Special considerations are necessary when designing a control system for a hydro power distributtion network in a deep mine . The pipework configuration is unusual, in that it is extensive in both the horizontal and vertical planes, and the environmental conditions impose constraints on the types of control equipment that can be used. The first and most obvious considerat ion is the existence within the system of high pressures , typically between 10 and 20 MPa. All control valves located in the line underground must be capable of withstanding these pressures with an appropriate safety margin. In some cases, this has precluded the use of certain designs of control valve which would otherwise have been attractive for this application . A second consideration is that, if a structural failure should occur, a runaway flow situation will develop as described in the previous section, and the affected section of the line should be shut down automatically to minimize the hazard to equipment and personnel. For instance, referring again to the schematic in Fig. 1, if the horizontal pipeline ruptured completely at a point 100 m from the shaft, equation (1) predicts that the flow rate would rise to 0,3 m3 /s, with an exit velocity of 38 m/s o The reaction force on the broken pipe would be 140 kN, which could cause the pipe to break away from its supports. If an attempt were made to stop this flow suddenly with an automatic valve, the pressure upstream of the valve would rise to nearly 60 MPa, according to equation (8). This could in turn cause a further structural failure of the pipeline . By contrast, failure of the same pipeline pressurized to 18 MPa by a positive displacement pump would result in no increase in flow rate or velocity. The pressure in the line would fall almost to zero, the pipe reaction force would be negligible, and the sudden closure of a valve after the rupture would produce a pressure wave of less than 6 MPa. Thirdly, there are several environmental considerations which affect the choice and location of control equipment. Close to the working faces, the atmosphere is hot, humid, corrosive and dusty, and working spaces are confined and inaccessible. Consequently, the reliability of control devices is likely to be poor, particularly in cases where external pneumatic or electrical power is required. Therefore the use of all but the simplest control devices should be avoided . In the main access tunnels, the environment is less harsh and space is less restricted, so there are fewer constraints on the types of control devices that can be used. However, most commercially available pipeline valves are controlled and actuated using
147
an external pneumatic or electrical power supply and such supplies can be interrupted during the day-to-day operation of a mine . Although temporary back-up systems can be considered, the most satisfactory approach is to use controllers and actuators working directly from the high pressure water in the pipeline. Few valves of this type are available commerCially, but some speciallydeveloped prototypes are being evaluated . Finally, the quality of the water must be considered. After passing through hydraulic machines in the working areas, the water exerts a cooling effect by coming into contact with the freshly exposed rock surfaces. In doing so, it picks up large quantities of salts and fine rock particles, and becomes chemically contaminated by blasting fumes. In conventional mining, many of the suspended particles are removed by settling , but nothing is done to remove dissolved contaminants . The concept of hydro power offers a broader economic base for the justification of bulk water treatment to remove these contaminants, so the water in the high pressure section of a hydro power system could be relatively pure. However, for economic reasons, it is unlikely that the dissolved and suspended matter will be removed entirely in the treatment plant. Additionally, it is known already that large quantities of solid particles can be generated from time to time within the pipeline by corrosion, scaling, deterioration of internal coatings, and debris introduced during installation and maintenance . Therefore, all control system components must be capable of withstanding moderate quantities of impurities in the water for long periods, and large quantities for short periods . This applies particularly to water- operated controllers and actuators, since these will tend to be more susceptible to damage or malfunction. This may impose special constraints on the designs of such components, and is the subject of current investigations. NORMAL OPERATING CONDITIONS CONTROL OF PRESSURE Water must be supplied to machines in the working areas at pressures compatible with machine requirements to ensure safe and efficient operation. The control of pressure must automatically take into account variations in line losses over short time periods, due to changing demands during the working shift, and over long periods when factors such as pipe scaling and extensions to the system become significant. Pressures will also vary with location in the mine, because of differences in elevation between the various working areas. The hydraulic equipment under development for operation on high pressure water tends to be capable of working over a wide range of pressures (typically 12 to 18 MPa). Studies have shown that in most cases pressure control may be carried out using pressure regulators in the main trunk lines, as shown in Fig. 1, away from the harsh environment of the working areas, with the variations in line losses in the intervening pipework not compromising unduly the level of control achieved . Besides enabling the reliability of the control components to be improved conSiderably, this approach introduces substantial cost savings through the use of larger, but much fewer, pressure regulators.
EMERGENCY CONDITIONS - CONTROL OF FLOW Normally, the water flow rate is controlled automatically, according to the demands of the machines operating at the face, by the hydraulic
148
R. W. Swt.t and D. G. Wymer
resistance and mechanical inertia of the machines themselves. In an emergency situation occurring as a result of a pipe breakage, this control is lost, and must be replaced by some form of flow control within the pipe system to avoid the type of runaway flow situation discussed earlier in the paper. Three basic types of device have been considered for this purpose, the flow control orifice, the safety shutdown valve and the hydraulic fuse. Flow Control Orifices The pressure drop through an orifice increases as the square of the flow rate. Thus, in a runaway flow situation, a suitably sized orifice will assist in dissipating the hydrostatic head, and will restrict the final flow rate to a lower value, as illustrated in Fig. 4. Although this will only reduce, rather than eliminate, the hazards associated with a pipe break, the use of orifices can be regarded as a simple, fail-safe back-up to more sophisticated flow control devices. Safety Shutdown Valves These devices are essentially isolating valves controlled and actuated externally, preferably using high pressure water taken directly from the line. The isolating valves themselves are available commercially from several manufacturers, in a range of sizes and pressure ratings more than adequate for this application. Suitable high pressure water controllers and actuators for the automatic operation of these valves are currently under development. A disadvantage of a safety shutdown valve is that it tends to respond slowly, so that in a pipe rupture situation the flow will have already reached its full runaway value before the valve can close. In the meantime, the high velocity water jet issuing from the broken pipe may have caused considerable damage, and the large reaction force may have pulled the pipe from its supports, causing further damage. Additionally, in view of the greatly increased flow rate, the valve must now be closed much more slowly to avoid excessive water hammer, delaying even further the shutdown process. Referring to the system shown schematically in Fig. 1, assume, for example, that the isolating valve shown 250 m from the working face is now a safety shutdown valve, and that its control system has a delay of 0,5 s. If a pipe fails suddenly, close to the working face, a negative pressure wave will arrive at the valve 0,17 s later, and after a further delay of 0,5 s the valve will start to close. The pressure immediately upstream of the valve will then rise in a manner dependent on the closing time. Fig. 5 shows what happens if the valve closing time is 1 s, according to the predictions of a simulation based on equations (2) and (3). The pressure drops initially as a runaway situation develops, and then rises suddenly as the valve closes. After peaking at 27 MPa, the pressure then oscillates with appreciable amplitude for more than 10 s. This behaviour could easily cause further failure of the pipe system. Fig. 6, on the other hand, shows the situation if the valve closing time is 10 s. After the initial delay, the pressure rises slowly and, on completion of valve closure, peaks at only 21 MPa. The subsequent oscillations are minor, and are soon dissipated. In this case, there should be no chance of a further pipe failure.
Hydraulic Fuses A schematic representation of a hydraulic fuse in its simplest form is shown in Fig. 7. It is essentially a globe-type valve, in which the closure element is normally held away from its seat by a coil spring. As the flow increases, a pressure difference develops within the valve, generating a force on the closure element opposing the spring, and the valve starts to close. During the final stages of approach, the pressure difference across the seat increases very rapidly, causing the valve to close with a 'snap' action. The pressure upstream will then hold the valve tightly closed until the pressure downstream is restored. This can only be accomplished once the failed pipe has been repaired. The advantages of this type of device over a safety shutdown valve are that it is simple in construction and entirely self-actuated, it reopens automatically, and it responds extremely rapidly. Considering the same pipe failure situation as before, but with the valve in Fig. 1 now being a hydraulic fuse, and assuming this hydraulic fuse snaps shut when the flow reaches 0,06 m3 /s (twice the normal maximum value), the system behaviour predicted by the simulation is as shown in Fig. 8. Despite the almost instantaneous closure, the pressure rises only to 22t MPa because the flow has not been allowed to reach its runaway value. This pressure peak can be reduced even further if complete shut-off of the hydraulic fuse is avoided. This can be achieved, for example, by simply drilling a hole through the closure element. The effect is illustrated in Fig. 9, which shows the predicted behaviour when the previous pipe failure situation is controlled by a hydraulic fuse containing a 10 mm diameter leakage hole. The maximum pressure is reduced to 21 MPa, and the subsequent oscillations are attenuated much more rapidly than in the previous case. The flow rate through the hydraulic fuse~ shown in Fig. ID, quickly settles to 0,013 mJ/s after the event, giving an exit velocity at the open end of the pipe of less than 2 m/so This is unlikely to cause any significant damage, and can be shut off at some later stage with a manual isolating valve. A further advantage of having a leakage path through the hydraulic fuse is that, following repair of the damaged pipe, the isolated section of line can be repressurized through the leakage hole in a controlled manner without the need for an external by-pass line around the hydraulic fuse. CONCLUS IONS The development of a suitable control system for a hydro power distribution network in a mine depends on the ability to predict the steady and unsteady flow behaviour of the water in the pipeline. Accurate prediction necessitates the use of a mathematical simulation technique based on the numerical solution of a set of governing differential equations, although simplified expressions can be used to give a rough idea of system behaviour in very simple, idealized cases. A simulation has been developed successfully for hydro power systems in deep mines, and has been used to formulate a suitable control systems approach. The pipework configuration and environmental conditions associated with a mine hydro power system affect in a major way the preferred design and location of hydrauliC control devices, resulting in a need for new types to be developed. A particularly desirable feature is that the control devices must not depend on external pneumatic or electrical power supplies, but must rather use the
149
Control of Hydro Power Distribution Systems energy in the high pressure water itself.
REFERENCES
Under normal operating conditions, the pressures within the system must be regulated automatically, but the characteristics of the hydraulicallydriven mining equipment are such that the level of control need not be very strict. This enables the number of control devices to be minimized, and avoids the necessity for them to be located close to the workings, where the environment is particularly harsh.
Boyce, E.B. and DiPrima, R.C. (1965). Elementary Differential Equations and Boundary Value Problems, 2nd ed. Wiley, New York. Chaudhry, M.H. (1979). Applied Hydraulic Transients. Van Nostrand Rheinhold, New York. Fox,~ (1977). Hydraulic Analysis of Unsteady Flow in Pipe Networks. MacMillan, London. O'Beirne, D., Gib bs, L.S. and Seiderer, A. (1982). The use of high-pressure water-jetting in gold-mine stoping operations. In H.W. Glen (Ed.), Proceedings, 12th CMMI Congress, S. Afr. Inst. Min. Metall. (or Geol. Soc. S. Afr.), Johannesburg. Streeter, V.L. (1966). Fluid Mechanics, 3rd ed. McGraw-Hill, New York. Streeter, V.L. and Wylie, E.B. (1967). Hydraulic Transients, McGraw-Hill, New York. Wymer, D.G. (1984). The use of emulsions and water in underground hydraulic systems, In Proceedings, Symp. on the Current Use of Hydraulics in the Mining Industry, Minemech 84, S. Afr. Inst. Mech. Engrs., Johannesburg.
Using the mathematical simulation to predict flow behaviour following a pipe breakage, three types of control device have been investigated for controlling flow in the affected pipework, to avoid the damaging effects of a runaway flow situation. Simple flow restriction orifices offer some degree of control, but are viewed rather as a back-up to other more sophisticated devices. Safety shutdown valves can isolate completely the affected pipework, but do not respond rapidly enough to prevent the flow from rising to its full runaway value, and must therefore close slowly to avoid excessive water hammer. A less conventional approach uses a hydraulic fuse which is a lowinertia, self-actuated device capable of responding so rapidly that it can, quite safely, isolate the line almost instanteously before a full runaway condition has been reached. ACKNOWLEDGEMENT This work formed part of the research and development programme of the Research Organization, Chamber of Mines of South Africa.
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Schematic of a portion of a typical mine hydro power system
150
R. W. SCOlL and D. C. Wymer 0,20
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