62design Analysis Boreholes

8/11/2019 62design Analysis Boreholes

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PV PUMPING ANALYTICAL DESIGN AND CHARACTERISTICS OF

BOREHOLES

L.Narvarte, E.Lorenzo, E.Caamao

Instituto de Energa Solar, ETSI Telecomunicacin, Ciudad Universitaria s/n, 28040

Madrid, Spain. Tel: 34 91 5495700 Ext 311. Fax: 34 91 544 63 41.

E-mail:[email protected]

Abstract

PV pump manufacturers usually provide standardized graphic tools relating water output

with PV array power, under given radiation conditions and for constant pumping head.

This paper proposes a simple procedure allowing the use of such graphics for the design

of boreholes showing significant water level variations with the water flow rate, which

lead to important pumping head variations during the day. The procedure requires a

knowledge of three parameters widely used for borehole characterization: static level,

dynamic level and maximum flow rate, and is based on a very simple analytical

description of results from a simulation exercise.

1. Introduction

Since the first installations in 1978 (Barlow et al., 1991), the PV-pumping market has

being consistently growing; some studies indicate more than 10000 PV pumps in

operation up to 1994 and predict about fifty times this figure for 2010 (Commission of the


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European Communities, 1995). Many of them will be devoted to the supply of water to

rural villages from medium heads boreholes of 15 to 50 metres (Kabore, 1994; Lorenzo,

1997). A typical scheme of a PV-pumping system, comprising PV-array, power

conditioning unit, motor-pump unit as well as piping system and storage reservoir is

depicted in Figure1.

The hydraulic power, PH , required to pump water is a function of both, the apparent

vertical head, HV,and the water flow rate, Q(numerically equal to mass-flow rate since

the specific gravity of water is unity), as it is indicated by the formula PH = g.Q.HV,

where g is the acceleration due to gravity. This can be written as follows, if Q is

expressed in (m3h-1),HVin (m), andPHin (W):

VH HQP = 725.2 (1)

Assuming that the pumped water emerges from the outlet at an insignificant velocity, the

output power from the pump needs to cover PH plus the friction losses in the pipes,Pf.

Consequently, the electric power to the input of the motor-pump unit,PEL, is given by

P

P P

EL

H f

MP=

+

(2)

where MPis the efficiency of the motor-pump unit.


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The value of PH+ Pfis, in fact, the mechanical power at the output of the pump. Usually,

it is considered as equivalent to the hydraulic power required to pump water at the flow

rate Q, with a total head,HT, given by

H H HT V f= + (3)

where

H HP

Pf Vf

H

= (4)


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Figure1. Typical scheme of a PV water pumping system for drinking water supply.HVis the vertical head

from the outlet of the water to water level, andHOTis the vertical height from the outlet of the water to

the ground.


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On the other hand, the electric power from a PV system which is composed of a PV-array

and an inverter is given by

P PG

GEL NOM REFA I= (5)

where PNOM is the power of the PV-array under Standard Test Conditions (Irradiance =

1000 W/m2, AM 1.5, Cell Temperature = 25 C), Gis the on plane irradiance, GREFis the

irradiance at STC, Ais an array performance factor considering cell temperature, wiring

and mismatch losses, and Iis the inverter efficiency.

The volume of water pumped throughout the day is given by

QP G

G Hdtd

NOM A MPI

REF Tday

=

2 725. (6)

where MPI MP I= (7)

Because of irradiance and ambient temperature variations, and also due to the dynamic of

the wells, all the above mentioned parameters (G, A, MPI, HV andHT ) vary with time,

so that, to directly solve eqn. (6) is far from being a straightforward task.


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To help designers, PV pump manufacturers usually test the performance of their PV

pumps under various conditions and provide graphic tools allowing to solve eqn. (6)

under given conditions of radiation and ambient temperature, and under the specific

assumption of constant total head. Figure 2 shows performance curves for a particular

power conditioning-motor pump combination, based on an 11 hour Standard Solar Day

(IEC 61725, 1997), SSD, and constant ambient temperature of 30C. Note that this graph

helps to determine the value of PNOMfor given Qd, HT and Gdvalues. In other words, it

allows to size the PV pump for a given water requirement.

Figure2. Graphic tool provided by a PV pump manufacturer.


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Because of its intrinsic simplicity, the use of the Standard Solar Day and constant total

head has been extensively adopted in the past (IT Power, 1984), to the extent of it

becoming a standard serving as technical reference in the procurement procedures for the

most important PV pumping projects (CILSS, 1989).

There is a wide consensus that SSD adequately represents daily irradiance distributions

on a mean monthly basis. However, constant total heads occur only when friction losses

are negligible and the water level is maintained constant inside the borehole. The first can

be assured by using relatively large diameter pipes, which is usually the case, because

costly pumping systems, like PV driven units, should only be considered in conjunction

with efficient conveyance and field distribution techniques. Head friction losses below

5% must be a general requirement for optimal PV systems (that is to say, HF < 0.05HT)

(IES, 1995). However, the constancy of the water level requires pumping rates well

below the maximum capacity of the borehole. This means under-use of water extraction

possibilities and is far from being the optimal case. This paper proposes a simple

procedure to extend the use of the above-mentioned graphic tools to the general case of

boreholes showing large water level variations with flow rate.

2. Dynamics of Boreholes

When pumping, the water level in the borehole tends to drop until the inflow of water

flowing downhill from the surrounding water table balances the rate at which water is

being extracted (see Figure 3). Consequently, the greater the rate of extraction, the greater

the drop in the water level. The actual drop of the level in a given borehole depends on a

number of factors including soil permeability, type and the wetted surface area of the


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borehole below the water table, and the phenomenon obeys the general diffusion laws

(Gibson and Singer, 1979).

Figure 3. Water level variations: diffusion profiles around the borehole.

A pumping test to characterize the draw-down in boreholes is normally done by

extracting water with a portable engine-pump, and measuring the drop in level at a certain

pumping rate, after the water level has stabilized. Then, three data characterize a

borehole after the test: thestatic level, HST, the dynamic level, HDT , and the test flow

rate, QT (see Figure 3). Fortunately, in many countries, boreholes are normally pumped

as a matter of routine to test their draw-down, so that the information from pumping tests

are commonly logged and stored in official records and can be later obtained by potential

users.


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However, it must be taken into consideration that excessive extraction rates on boreholes

can damage the internal surface below the water table and cause voids to be formed

which then lead to an eventual collapse of the bore. Consequently, a maximum flow rate,

QMAX (m3/h), exists for each borehole. Information from borehole pumping tests,

mentioned above, is usually referred to as the maximum flow rate at which water can be

extracted from it (QT = QMAX). As a particular example, Table 1 shows the characteristic

parameters of the boreholes included in some projects designed at the I.E.S.

Location Static Level

HST(m)

Dynamic Level

HDT(m)

Maximum Flow Rate

QMAX(m3/h)

Angola

Rotunda 20 45 7.2

Simoes de Abreu 11 49 8.3

Chamaco 12 32 6.9

Nongiue 20 24 13

Lupale 20 44 5

Mimue 16 53 8.5

Morocco

Oum Erromane 10.8 25 17.3

Abdi 12.7 35 21.6

Iferd 9.8 60 36

Ourika 16.4 18.2 10.8

Ait Mersid 7.9 35 15.5

Data provided by the Boureau Technique de Ouarzazate, Ministere de LInterieur, Royaume du Maroc,

and by the Direao Geral de Aguas do Ministrio da Energia e Petroleos de Angola.


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Table 1. Examples of real boreholes.

In addition to the usual design parameters, we also compute a parameter , defined as:

T

d

ST

STDT

Q

Q

H

HH

=

5 (8)

where Qd is expressed in (m3) and QT in (m

3h-1). Factor 5, expressed in hours, is

empirical and makes easier to use.

Note that depends on the borehole characteristics and also on the PV pumping rate, and

can be understood as a measurement of the extent of the water drop when pumping. Such a

drop may be insignificant either because the borehole performs very stable, ((HDT-HST)

/HST) 0, or because the pumping rate is well below the borehole capacity, Qd/ 5.QT

0 . To give a quick idea, we can establish that < 0.2 means that water drop can be

neglected for designs, which is not the general case, as Table 2 shows. It is worth

pointing out that for a daily water demand of 40 m3, this happens only in two cases. That

is to say, the common approach relying on using the static level together with graphic

tools is not, in general, a correct practise.

Location (Qd= 15 m3) (Qd= 40 m

3)

Angola

Rotunda 0.52 1.39

Simoes de Abreu 1.25 3.33

Chamaco 0.72 1.93


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Nongiue 0.04 0.12

Lupale 0.72 1.92

Mimue 0.82 2.18

Morocco

Oun Erromane 0.23 0.61

Abdi 0.24 0.65

Iferd 0.42 1.13

Ourika 0.03 0.08

Ait Mersid 0.67 1.78

Table 2. Values of the parameter for different boreholes and Qd.

3. PV pumping design

Because irradiance varies with the time of day, the power available for the pump, the

consequential flow rate and total head imposed on the PV pump, also vary with the time.

To analyse precisely the relation between irradiance and flow rate, and to generally

determine the volume of water pumped during a certain period of time are rather complex

tasks. Software tools (Mayer et al., 1992) are available to help with these calculations,

but they are sometimes complex to work with, and they need rarely available information

like internal motor parameters, etc.

On the other hand, it should be taken into account that the task of selecting a proper PV

pump and PV array for a particular application is always done with a certain degree of


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uncertainty which is associated with the variability in solar radiation, which means that,

the water output of a PV pump can be predicted only with relatively low accuracy.

Typically, monthly irradiation values have a variation of 30% over the long-term mean.

Keeping this idea in mind, the use of the above-described graphic tools corresponding to

the constant total head idealization can be extended to general boreholes. Returning once

more to eqn. (6), an equivalent total head, HTE , can be defined as the hypothetical

constant value leading to the same volume of water, that is:

QP

G HG dtd

NOM

REF TE

A MPI

day

=

2 725. (9)

Note that, for a given HTE, eqn. (9) depends neither on borehole nor on pipe

characteristics, but only on climatological conditions and on PV pump characteristics.

In order to explore the possibilities of quick HTEcalculations, we performed a simulation

exercise, using the well-proven DASTPVPS software tool (Baumeister et al., 1993),

consisting of:

1. To determine Qdfrom Gd(0), HOT, HST, HTE, QTand PNOM(where HOTis the vertical

head from the outlet of the water to the ground). All the boreholes described in Table 1

have been simulated for Gd(0)= 4000 Wh/m2, PNOM = 1810 Wp and HOT = 0. We have

used two different daily irradiance profiles, respectively corresponding to the SSD and to

the Typical Meteorological Year contained in the DASTPVPS database. It is worth


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mentioning that the differences between the results from these two irradiance profiles are

insignificant in all the cases, which confirms the above mentioned validity of the SSD, at

least for design purposes.

2. To determine the HTE value leading to the same Qd. This was done by simulating a

hypothetical well with an infinite permeability coefficient, so that the draw-down is

always zero, and testing different HTEvalues until the Qdcalculated in the previous steps

is reached.

The analysis of a wide collection of simulated situations leads us to propose the general

use of the simple formula:

H H HH H

QQ H QTE OT ST

DT ST

TAP F AP= + +

+( ) ( ) (10)

with dAP QQ = (11)

where = 0.047 (h-1) when Qd is expressed in m

3, and HF(QAP)is the head loss in the

pipes corresponding to QAP. Note that QAP, called apparent flow rate, is an average

flow rate. Table 3 shows some particular results. The low error associated with eqn.

(10), despite its simplicity, merits underlining.

Location Qd

(m3)

HTE(m) from

DASTPVPS

HTE(m) from

Equation (10)

Error

(%)

Rotunda 33.3 26.3 25.4 3.1

It should be noted that DASTPVPS includes a very precise description of the performance of the

motor-pumps, based on a rather large number of experimental tests. Furthermore, DASTPVPS models

the dynamic of boreholes by using the Daray's law, which relates the drawdown with the water output

through the radius of well and the permeability coefficient of the aquifer. Because of t hat we believe

that DASTPVPS results can be considered as a proper reference for other calculation exercises.


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Simoes de Abreu 42.2 20 20.1 -0.3

Chamaco 45.0 18 18.1 -0.7

Nongiue 41.0 20.5 20.6 -0.4

Lupale 32.3 27 27.3 -1.0

Mimue 36.3 24 23.4 2.4

Oum Erromane 53.3 12.8 13.1 -2.4

Abdi 49.8 15 15.3 -2.2

Iferd 54.1 12.2 13.5 10.4

Ourika 47.2 16.5 16.4 0.6

Ait Mersid 54.6 12 12.6 5.1

Table 3. Comparison between theHTEvalues obtained by the simplification of Eq.(10) and by

simulations. The simulation input parameters are: Gd(0)= 4000 Wh/m2;PNOM = 1810 Wp,HOT = 0 m.

The validity of eqn. (10) was later confirmed using simulations with different motor-

pumps, radiation levels, array powers, and different vertical heights. The precise

description of all the cases would be tedious and of little value. Instead, we will only

mention that they cover all the range of possibilities we have been able to imagine, even

comprising DC pumps without maximum power tracking facilities, and non-optimised

pumps, i.e., having the wrong number of impellers. The mean error for all the cases is

around 2%, which clearly shows that eqn. (10) allows us to overcome the complexity

associated to the dynamics of boreholes on PV-pumping design, by reducing the problem

to a hypothetical static one leading to similar water output.


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Moreover, in order to explore further the practical usefulness of eqn. (10), we have used

it in combination with the graphic tools provided by the manufacturers of the pumps, in

order to size the PV array, and again, we have contrasted the results against simulation

values. For each borehole described in Table 1, we have used DASTPVPS to determine

the Qdand theHTEvalues corresponding to the four combinations of Gd = 4000 and 6000

Wh/m2and PNOM = 905 and 1810 Wp (see columns 4 and 5 of Table 4). Then, such Qd

andHTEvalues have been used as input for the graphic tools to obtain a new PNOMvalue

(PNOM (2) in column 6 of Table 4), which ideally must be equal to the one used as

DASTPVPS input. As a matter of fact, deviations between both PNOM values can be

understood as a measure of the validity of the graphic tools. A mere glance at column 7 of

Table 4 leads us to suspect that PV manufacturers generally tend to overestimate the

performance of their motor-pumps. Finally, we have used again the graphic tools, this

time considering HTE values given by eqn. (10). The values of PNOM(3) presented in

column 8 of Table 4 confirm that errors associated to such equation are virtually

negligible.

Locatio

n

Input

Gd

PNOM(1)

(Wh/m2) (Wp)

From

DASTPVPS

Qd HTE

(m3/d) (m)

From PV manufacturer

graphic tools

PNOM(2) Error

(Wp) (P1-P2)/P1

(%)


graphic tools + Eq.(10)

PNOM(3) Error

(Wp) (P2-P3)/P2

(%)

Simoes 6000 1810 54.3 23 1800 0.55 1800 0

4000 1810 42.2 20 1750 3.31 1750 0

6000 905 34.2 18 850 6.08 850 0

4000 905 23.1 15 800 11.6 825 -3.13

Rotunda 6000 1810 46.0 30.0 1850 -2.21 1700 8.12

4000 1810 33.3 26.3 1725 4.70 1675 2.90


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6000 905 24.8 24.5 850 6.08 850 0

4000 905 13.5 22.3 775 14.36 775 0

Nongiue 6000 1810 57.1 21.0 1750 3.31 1750 0

4000 1810 41.0 20.5 1725 4.70 1725 0

6000 905 30.3 20.5 850 6.08 850 0

4000 905 15.9 20.3 775 14.36 775 0

Oum 6000 1810 68.3 13.0 1775 1.93 1800 -1.41

Erroman 4000 1810 53.3 12.8 1750 3.31 1750 0

6000 905 43.5 12.5 900 0.55 900 0

4000 905 29.2 12.0 850 6.08 850 0

Abdi 6000 1810 65.0 15.5 1750 3.31 1775 -1.43

4000 1810 49.8 15.0 1775 1.93 1775 0

6000 905 39.9 14.5 900 0.55 900 0

4000 905 25.5 14.0 825 8.84 825 0

Iferd 6000 1810 68.9 13.0 1825 -0.83 1900 -4.11

4000 1810 54.1 12.3 1800 0.55 1850 -2.78

6000 905 44.6 12.0 900 0.55 950 -5.55

4000 905 30.6 11.0 875 3.31 900 2.86

Table 4. Comparison between the resultant array peak powers whenHTEis used in graphic tools, and the

initial array peak power used as input in the simulation tool. The reduction of boreholes with respect to

Table 1 serves to reduce the size of this paper.

As an example of the difference of using HTEinstead of HST, it is possible to calculate

with graphic tools the required PV size with these two heights for Simoes de Abreu in the

case of Gd(0)= 6000 Wh/m2and Qd= 54 m

3. The result is a nominal peak power of 1800

and 1200 W respectively.


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On the other hand, compatibility between a borehole and a PV pump requires us to be

sure that the flow rate is always below the limit given by QMAX. PV pump manufacturers

also usually provide graphic information about instantaneous output from the pump for

given DC power and total head, as Figure 4 shows. As a rule of thumb, such compatibility

is assured if the output from the pump, corresponding to DC power = 0.8 PNOMandHT=

HDT+ HOT, is lower than QMAX. This condition reflects the fact that the nominal power of

the PV array,PNOM, is given under STC, which are rarely reached in real operation. Note

thatHTEshould not be considered here.

Figure 4. Instantaneous PV pump output for various DC powers and total heads.


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Finally, one danger if large pumps are used in small boreholes is to draw the water down

to the pump intake level, at which stage the pump starts to snore, that is, it draws a

mixture of air and water. A snoring pump can be soon damaged, and therefore should

be avoided by using any of the technical solutions whose efficacy has been already

demonstrated such as maximum frequency stop capabilities of inverters, level switches

incorporated in the inverter, etc. Nevertheless, one good practice is to place the pump

intake at the dynamic level of the borehole, so that the pump will not snore for outputs

smaller than QMAX.

4. Conclusions

PV manufacturers usually provide standardised graphic information about the

performance of their systems, that allows to directly design the proper PV pump for a

given water requirement under the specific assumption of a constant water level.

This paper has presented a simple method to extend such graphic tools to the more

general case of boreholes showing significant water level variations with water flow

rate. Real situations, characterized by pumping head variations along the day, are

conceptually assimilated to the constant head case, by defining an equivalent total head

as the hypothetical constant value leading to the same volume of pumped water.

Furthermore, a simulation exercise, by using a well proven software tool, has led us to

propose a simple equation linking the value of HTEwith the standard information usually

available for boreholes. Compatibility between PV pumps and boreholes has also been

commented on.


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The proposed method allows the complete design of a PV pump (to select a motor-pump-

power conditioning unit, and to size the PV array) for any given water requirement and in

particular solar radiation conditions. Although water needs are not considered in this

paper, it is worth emphasising that they usually represent the largest source of

uncertainties in real situations. References (Kabore, 1995; IT.Power, 1984; Malbranche

et al., 1994; Burgess and Prymm, 1985; Doorenbos and Pruit, 1977) are particularly

suggested for useful further reading on that.

Acknowledgements

This work has been in part supported by contract JOU2-CT92-0161 in the context of the

JOULE II project. We would like to thank the helpful collaboration of Mr. Oliver Mayer,

who gave us every facility to use the PV-pumping software tool DASTPVPS.

Nomenclature

A Array performance factor

I Inverter efficiency

MP Motor-pump efficiency

MPI Motor-pump and inverter efficiency

Relevance of water drop

G (W/m2) On plane irradiance

Gd (Wh/m2) Irradiation on a tilted surface

Gd(0)(Wh/m2) Horizontal daily irradiation


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GREF (W/m2) Irradiance at Standard Test Conditions

HDT (m) Dynamic level

Hf (m) Head loss

HF(QAP) (m) Head loss in the pipes corresponding to QAP

HOT (m) Vertical head from the water outlet to the ground

HST (m) Static level

HT (m) Total head

HTE (m) Equivalent total head

HV (m) Vertical head

PEL (W) Electrical power to the input of the motor-pump

Pf (W) Power to cover friction losses

PH (W) Hydraulic power

PNOM (W) PV array power under Standard Test Conditions

Q (m3/h) Water flow rate

QAP (m3/h) Apparent flow rate

Qd (m3) Volume of water pumped throughout a day

QMAX (m3/h) Maximum flow rate

QT (m3/h) Test flow rate

SSD Standard Solar Day

References

Barlow R., McNelis B., Derrick A. (1991) Status and Experience of Solar PV Pumping in

Developing Countries. In Proc. 10th Europ. PV Solar Energy Conf., Lisbon, Portugal,

pp 1143-1146.


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Baumeister A., Festl T., Mayer O. (1993) DASTPVPS, Manual. Commission of the

European Communities, JOULE Project: JOUL-0048-P. Brussels.

Burgess P., Prymm P. (1985) Solar Pumping in the Future: A Socio-Economic

Assesment, CSP Economic Publications. U.K.

CILSS (1989) Appel dOffres Restreint. In Programme Regional dutilisation de

lenergie solaire Photovoltaque dans les pays du Sahel, CR-VI FED, Ouagadougou,

Burkina Faso

Commission of the European Communities (1995) The world PV Market to 2010.

Directorate Generale for Energy, Brussels.

Doorenbos J., Pruit W.O. (1977) Crop Water Requirements, FAO, Rome.

Gibson U., Singer R. (1979)Manual de los Pozos Pequeos. Limusa, Mexico.

IES (compiled by) (1995) PV Pump Optimization. A Manual to Advise on the

Optimization of PV Centrifugal Pump Systems. JOULE II Project: JOU2-CT92-0161.

Brussels.

International Standard IEC 61725: 1997. Analytical Expression for Daily Solar Profiles.


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IT Power in association with Sir William Halcrow and Partners (1984) Handbook on

Solar Water Pumping. UNDP - World Bank project GLO/80/003, pp. 36-49.

Washington.

Kabore F. (1994) PV Energy for a Sustained and Social Development in the Sahelian

Region. The Regional Solar Program. In The Yearbook of Renewable Energies. James

and James. London.

Lorenzo E. (1997) Photovoltaic Rural Electrification.Progress in Photovoltaics5, 3-27.

Malbranche Ph., Servant J.M., Hnel A., Helm P. (1994) Recent Developments in PV

Pumping Applications and Research in the European Community. In Proc. 12thEurop.

PV Solar Energy Conf., Amsterdam, The Nederlands, pp 476-481

Mayer O., Baumeister A., Ferstl T. (1992) A Novel PC Software Tool for Simulation and

Design of Photovoltaic Pumping System. In Proc. 11thEurop. PV Solar Energy Conf.,

Montreux, Switzerland, pp 1395-1398.


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TABLES

Location Static Level

HST(m)

Dynamic Level

HDT(m)

Maximum Flow Rate

QMAX(m3/h)

Angola

Rotunda 20 45 7.2

Simoes de Abreu 11 49 8.3

Chamaco 12 32 6.9

Nongiue 20 24 13

Lupale 20 44 5

Mimue 16 53 8.5

Morocco

Oum Erromane 10.8 25 17.3

Abdi 12.7 35 21.6

Iferd 9.8 60 36

Ourika 16.4 18.2 10.8

Ait Mersid 7.9 35 15.5

Table 1. Examples of real boreholes.


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Location (Qd= 15 m3) (Qd= 40 m

3)

Angola

Rotunda 0.52 1.39

Simoes de Abreu 1.25 3.33

Chamaco 0.72 1.93

Nongiue 0.04 0.12

Lupale 0.72 1.92

Mimue 0.82 2.18

Morocco

Oun Erromane 0.23 0.61

Abdi 0.24 0.65

Iferd 0.42 1.13

Ourika 0.03 0.08

Ait Mersid 0.67 1.78

Table 2. Values of the parameter for different boreholes and Qd.


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Location Qd

(m3)

HTE(m) from

DASTPVPS

HTE(m) from

Equation (10)

Error

(%)

Rotunda 33.3 26.3 25.4 3.1

Simoes de Abreu 42.2 20 20.1 -0.3

Chamaco 45.0 18 18.1 -0.7

Nongiue 41.0 20.5 20.6 -0.4

Lupale 32.3 27 27.3 -1.0

Mimue 36.3 24 23.4 2.4

Oum Erromane 53.3 12.8 13.1 -2.4

Abdi 49.8 15 15.3 -2.2

Iferd 54.1 12.2 13.5 10.4

Ourika 47.2 16.5 16.4 0.6

Ait Mersid 54.6 12 12.6 5.1

Table 3. Comparison between theHTEvalues obtained by the simplification of Eq.(10) and by

simulations. The simulation input parameters are: Gd(0)= 4000 Wh/m2;PNOM = 1810 Wp,HOT = 0 m.


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Locatio

n

Input

Gd

PNOM(1)

(Wh/m2) (Wp)

From

DASTPVPS

Qd HTE

(m3/d) (m)


graphic tools

PNOM(2) Error

(Wp) (P1-P2)/P1

(%)


graphic tools + Eq.(10)

PNOM(3) Error

(Wp) (P2-P3)/P2

(%)

Simoes 6000 1810 54.3 23 1800 0.55 1800 0

4000 1810 42.2 20 1750 3.31 1750 0

6000 905 34.2 18 850 6.08 850 0

4000 905 23.1 15 800 11.6 825 -3.13

Rotunda 6000 1810 46.0 30.0 1850 -2.21 1700 8.12

4000 1810 33.3 26.3 1725 4.70 1675 2.90

6000 905 24.8 24.5 850 6.08 850 0

4000 905 13.5 22.3 775 14.36 775 0

Nongiue 6000 1810 57.1 21.0 1750 3.31 1750 0

4000 1810 41.0 20.5 1725 4.70 1725 0

6000 905 30.3 20.5 850 6.08 850 0

4000 905 15.9 20.3 775 14.36 775 0

Oum 6000 1810 68.3 13.0 1775 1.93 1800 -1.41

Erroman 4000 1810 53.3 12.8 1750 3.31 1750 0

6000 905 43.5 12.5 900 0.55 900 0

4000 905 29.2 12.0 850 6.08 850 0

Abdi 6000 1810 65.0 15.5 1750 3.31 1775 -1.43

4000 1810 49.8 15.0 1775 1.93 1775 0

6000 905 39.9 14.5 900 0.55 900 0

4000 905 25.5 14.0 825 8.84 825 0

Iferd 6000 1810 68.9 13.0 1825 -0.83 1900 -4.11

4000 1810 54.1 12.3 1800 0.55 1850 -2.78


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6000 905 44.6 12.0 900 0.55 950 -5.55

4000 905 30.6 11.0 875 3.31 900 2.86

Table 4. Comparison between the resultant array peak powers whenHTEis used in graphic tools, and the

initial array peak power used as input in the simulation tool. The reduction of boreholes with respect to

Table 1 serves to reduce the size of this paper.


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LIST OF FIGURE CAPTIONS

Figure 1. Typical scheme of a PV water pumping system for drinking water supply.HVis

the vertical head from the outlet of the water to water level, andHOTis the vertical height

from the outlet of the water to the ground.

Figure 2. Graphic tool provided by a PV pump manufacturer.

Figure 3. Water level variations: diffusion profiles around the borehole.



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HV

HOT

Figure 1. Typical scheme of a PV water pumping system for drinking water supply.HVis

the vertical head from the outlet of the water to water level, and HOTis the vertical height

from the outlet of the water to the ground.


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Figure 2. Graphic tool provided by a PV pump manufacturer.


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Figure 3. Water level variations: diffusion profiles around the borehole. QTis the test

flow rate


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62design Analysis Boreholes

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