1 Optimal Pipelines Sizing for Water Distribution Systems of Micro Irrigation Hassan Ibrahim Mohamed 1 , Nahid Ibrahim Ahmed El Haj 2 , Haitham Ragab El Ramlawi 3 ,Abd El Rahman Mohammed Nour 4 , and Omran Musa Abbas 1 1-Department of agricultural engineering, College of agricultural studies Sudan University of science and technology. 2- Department of Agricultural Engineering. Khartoum State- Ministry of Agriculture and Water Resources 3-Centre of Dry land Farming Research and Studies, Faculty of Agricultural and Environmental Sciences, University of Gadaref 4-Department of agricultural engineering, College of agricultural Technology and Fish sciences -Neeleen University. ABSTRACT The main aim of the present study is to develop optimization process of water pipe networks design through studying the effect of pipe and pump costs on the optimization process in a network with a predetermined layout. Computer simulation and analytical solutions have been used for minimizing the Capital cost of multiple-outlet pipelines of drip water distribution system composed of many pipes with different diameters, while the variation in pressure head is restricted to assure the required outlet discharge uniformity. The present study focuses on developing a cost function design model for pump-pipelines system with emitters distributed along the pipelines. The model has been developed to support the design of micro irrigation systems and to advise farmers to improve drip system performance .The procedure uses the linear programming, in which pipe length with commercial pipe diameter is used as optimum variable and the factors affecting the pressure head along multiple-outlet pipelines are considered. The objective function, to obtain the optimal diameter of each pipe, is based on the capital cost of the piping system, pumps and the cost of energy required for operating the system. The model consists of an objective function that maximizes profit at the farm level, subject to appropriate geometric and hydraulic constraints. The main items considered affecting cost were: operating pressure within the network, the pipe diameter, and the pumping cost which include pumping station and energy. The hydraulic and operational limitations imposed on the system are: limiting maximum and minimum velocity, permissible pipe pressure, defined pressure at outlets, and defined discharge at selected points. Model solution employ WINQSB 6.0, and uses Excel database with information on emitters and pipes available in the market, as well as on crops, soils and the systems under design. The solution procedure is based on an iterative scheme and examined two case studies. Results obtained indicate model capability to cut down costs of pipes as compared to conventional design method. Keywords: optimum network, water pipe network, water least annual cost principle, linear programming, pump-pipelines system design, micro - irrigation network.
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Optimal Pipelines Sizing for Water Distribution Systems of Micro
Irrigation
Hassan Ibrahim Mohamed1, Nahid Ibrahim Ahmed El Haj
2, Haitham Ragab El Ramlawi
3,Abd
El Rahman Mohammed Nour4 , and Omran Musa Abbas
1
1-Department of agricultural engineering, College of agricultural studies Sudan University of science
and technology. 2- Department of Agricultural Engineering. Khartoum State- Ministry of Agriculture
and Water Resources 3-Centre of Dry land Farming Research and Studies, Faculty of Agricultural and
Environmental Sciences, University of Gadaref 4-Department of agricultural engineering, College of
agricultural Technology and Fish sciences -Neeleen University.
ABSTRACT
The main aim of the present study is to develop optimization process of water pipe networks
design through studying the effect of pipe and pump costs on the optimization process in a
network with a predetermined layout. Computer simulation and analytical solutions have
been used for minimizing the Capital cost of multiple-outlet pipelines of drip water
distribution system composed of many pipes with different diameters, while the variation in
pressure head is restricted to assure the required outlet discharge uniformity. The present
study focuses on developing a cost function design model for pump-pipelines system with
emitters distributed along the pipelines. The model has been developed to support the
design of micro irrigation systems and to advise farmers to improve drip system
performance .The procedure uses the linear programming, in which pipe length with
commercial pipe diameter is used as optimum variable and the factors affecting the pressure
head along multiple-outlet pipelines are considered. The objective function, to obtain the
optimal diameter of each pipe, is based on the capital cost of the piping system, pumps and
the cost of energy required for operating the system. The model consists of an objective
function that maximizes profit at the farm level, subject to appropriate geometric and
hydraulic constraints. The main items considered affecting cost were: operating pressure
within the network, the pipe diameter, and the pumping cost which include pumping station
and energy. The hydraulic and operational limitations imposed on the system are: limiting
maximum and minimum velocity, permissible pipe pressure, defined pressure at outlets, and
defined discharge at selected points.
Model solution employ WINQSB 6.0, and uses Excel database with information on emitters
and pipes available in the market, as well as on crops, soils and the systems under design.
The solution procedure is based on an iterative scheme and examined two case studies.
Results obtained indicate model capability to cut down costs of pipes as compared to
conventional design method.
Keywords: optimum network, water pipe network, water least annual cost principle, linear
programming, pump-pipelines system design, micro - irrigation network.
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1. INTRODUCTION
Sustainable irrigated agriculture requires irrigation practices that are environmentally
friendly, economically viable and lead to high irrigation performance (Pereira et al., 2002).
Micro irrigation systems have the potential for achieving high irrigation performance and
offer a large degree of control, enabling accurate water and fertilizer applications according
to crop water and nutrients requirements, thereby minimizing environmental impacts and
providing for increased performance and water productivity. Achieving this requires that
systems are designed and operated in a way that water is applied at a rate, duration and
frequency that maximize water and nutrient uptake by the crop, while minimizing the
leaching of nutrients and chemicals out of the root zone (Hanson et al., 2006). Highly
uniform and timely water application is therefore required (Mermoud et al., 2005; Santos,
1996; Hanson et al., 2006). Drip water distribution network is a system of hydraulic elements
contains (pipes, reservoirs, pumps, valves of different types), which are connected together
to provide the quantities of water within prescribed pressures from sources to the plant.
Hence, micro irrigation system need to be designed and operated based on the selection of
pipeline sizes which is directed to achieve high uniformity of water distribution and
minimum operating costs. The selection of a pipeline size to meet a specific criterion, such as
the minimum annual expenses, has been extensively treated by various researchers
(Haghighi et al., 1989; Barragan et al., 2006; Kang and Nishiyama, 1996; 2002; Demir et al.,
2007; Valiantzas, 2003; Valiantzas et al., 2007). The basic components of a micro -irrigation
system are: the pump/filtration station (consisting of the pump, filtration equipment,
controllers, main pressure regulators, control valves, water-measuring devices and chemical
injection equipment); the delivery system, (includes: the main and sub main pipelines to
transfer water from the source to the manifolds, (filters, pressure regulators, and control
valves); the manifolds, which in turn supply water to the laterals and the laterals that carry
water to the emitters (Pereira and Trout, 1999; Evans et al., 2007). Design of micro irrigation
systems is therefore complex considering the need to select and size all system components
and the need to design for a targeted uniformity of water application (Bralts et al., 1987;
Keller and Bliesner, 1990; Wu and Barragan, 2000).
Main advances in design of micro irrigation systems refer to pipe sizing and layout and to the
selection of emitters because these system components control the potential irrigation
performance and costs. The design options relative to the pump, valves, controllers, filters
and fertilizer devices are generally made after pipes and emitters are selected since they
depend upon related pressure and discharges at the various nodes of the system network
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(Keller and Bliesner, 1990). However, their appropriate selection also influences the
irrigation performance, and they also produce additional head losses that must be
considered when sizing the system. To support and ease design, a variety of models have
been developed such as that for the pump/filtration station (Haghighi et al., 1989), for
assessing emitter uniformity (Barragan et al., 2006), for pipe sizing (Kang and Nishiyama,
1996; 2002; Demir et al., 2007) and for economic optimization of systems (Valiantzas, 2003;
Valiantzas et al., 2007).
Optimization methods for pipe network analysis has been reviewed by Stephenson et al,
(1981) .Their extensive study showed that the dynamic programming schemes are suitable
for pipe size selection of main pipelines. Transportation programming is convenient for cases
in which the pipe routes and size are to be optimally selected. Because of the complex
network analysis schemes algorithms based on linear programming technique has been
developed to minimize system costs (Valiantzas, 2003; Valiantzas et al., 2007). With the
advances in optimization search methods, network analysis has been extended to include
network routes (Cembrowicz et al,. 1996) and other important parameters such as:
management of irrigation systems (Srinivasan and Guimaraes, 1996, Eduardo and Marino,
1990 and Mohtar et al 1991) where the effects of land topography, irrigation method and
land allocation, maximization of land yield, profit and/or management of wastewater reuse
(Afshar and Miguel, 1989) is included. Application of the genetic algorithms for pipe network
optimization is in progress where it may provide some advantages over the classical linear,
dynamic and/or nonlinear programming methods (Dandy et al, 1996, Simpson et al ,1994).
The present work is directed to the study of a single source pump-branching pipes micro
irrigation distribution system for optimum selection of the pipes diameters on the basis of
minimum cost function under limits of hydraulic constraints for achieving high irrigation
performance using linear programming technique.
2. THE MATHEMATICAL MODEL The decision support model was developed to design drip and micro sprinkling systems, and
as a tool to advice farmers about how to improve their micro irrigation systems when using
data obtained during field evaluation of systems under operation. It is employs WINQSP, and
Excel programs and runs in a Windows environment in a personal computer.
The conceptual structure of the model is in presented figure 1, where two main components
are identified: the database and the Hydraulic Procedure. The algorithm is mainly oriented
to design and select the pipe system and emitters for an irrigation sector. The computer
design model has been integrated into three principal modules: the database and layout
module, the design module and the evaluation module. The database module entails
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specifying details of the system alignments and contains information on emitters, pipes, and
crops, soils such as: the emitter and lateral spacing; the lengths of the laterals and the
manifold; and the elevations of the pipes. Once this has been done, then the actual pipe
design can be carried out in the design module. The design module is tailored to iteratively
size the pipe and emitters system for individual laterals using WINQSB algorithm. Output
from this procedure includes: a display of the pipe flow and pressure characteristics;
allowed pressure envelope and the pipe hydraulic grade-line; and a summary table of the
operations performed in the design process.
2.1 Characteristic of the model: The model has been developed for fields with known dimensions on flat terrain. The water
source is assumed to be groundwater provided by a pump located at the centre of field. All
sub main pipes that feed the sub-units via supply pipes are perpendicular to the main lines
and are fed from both sides of the main lines. All pipes are made from polyethylene, and
emitters are fixed on the laterals at a fixed spacing. Each supply, sub main and mainline pipe
is controlled by one independent valve, which is located just at the beginning of the
corresponding pipe. One filter unit is assumed to be located just after the pump. Water is
assumed to be extracted from groundwater by means of a turbine pump system. The main
and sub main pipes are buried while sub-unit pipes (laterals, manifold, supply) are laid on
the ground. Total system cost consists of capital and installation costs plus the present value
of the operating costs over the expected life of the project.
2.2 Formulation of the model:
2.2.1 Model assumption and data input: In the present optimization model the general
configuration of pipes within the field (main and sub main lines) and within the sub-units
(lateral, manifold and supply lines) is fixed. However, since the area and the dimensions of
sub-units in the both X and Y directions change in each iteration of the field division, the
length and the size of all pipes change as well. The model was developed for a field with
given area and known dimensions for which the water source is located at the centre of
field.
2.2.2 Optimization procedure: The model evaluates all combinations of pipe sizes, and shift
patterns. The system cost is evaluated for various pipe sizes. Optimization is carried out by
complete enumeration of all alternatives. The following values are assumed to be known:
(1) The dimensions of the field,,[Fx ,m and Fy, m];
(2) The depth of the water table [Hwt ,m];
(3) The potential evapotranspiration,[ETo mm/day], the crop coefficient, [Kc];
(4) The minimum and maximum percentage of wetted area,[Pw, %];
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(5) The application efficiency of drip irrigation, [Ea, %];
(6) The annual irrigation requirement for the crop, [Air, mm];
(7) The field capacity, FC and the permanent wilting point[ PWP], of soil;
(8) The depth of root zone, [R, m], soil infiltration rate, Isoil (mm/hr) and soil bulk
density Row S (g/cm2);
(9) The portion of the available moisture depletion f (%);
(10) The spacing between emitters,[ dx ], and laterals, dy, respectively (m);
(11) The pipe cost coefficients[ k1,k2, k3]; the pump, cost parameters[ k, a, b];
(12) Efficiencies for the electric motor,[Em], and pump,[ Ep], respectively;
(13) The discount rate,[ i ], and expected project life,[ n, years];
2.2.3 The decision variables in the design of irrigation:
1. The pipe diameters and locations.
2. Pump locations and sizes.
3. Valve and regulator locations.
4. Reservoir sizes and locations.
The objective function: The objective of this optimization is to establish the quantities of the
each of the decision variables that will be used in the irrigation network so as to minimize a
pre-selected criterion. As mentioned previously, the most common criterion for the
optimization of network design is that of minimum cost. In order to achieve this
optimization, the value of the selected criterion is expressed as a function of the quantities
of the decision variables being used in the design.
The decision variables: Normally the quantities of the decision variables that can be used will
be constrained by a number of pre-determined factors. When considering pipe diameters as
decision variables for the design of irrigation networks, the allowable diameters to be used
along a specific path in the network must be equal to or greater than the smallest possible
diameter that will result in the pre-determined allowable head loss along the path. So for
every optimization problem, a set of relationships can be formulated which govern the
quantities of the decision variables that may be incorporated into the objective function.
These relationships are referred to as the constraints of the optimization.
Thus the optimization of the design of single-source branching networks can be formulated
as an LP problem, and it is derived in accordance with Karmeli et al, (1968) as follows:
a- The links of a network are defined by the upstream node, i, and the downstream node, j,
respectively. Then for each link ij in the network being designed a candidate set of
diameters, m, is to be considered. One set of decision variables is given by the length of pipe
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for each of the candidate diameters to be used in each link ij. These lengths are expressed as
X��� and they have associated costs given by C��� per unit length.
b- A second set of decision variables is given by the operating head of the pump at the
source of the network, for each different network loading condition, ℓ. These operating
heads are expressed as XP (l). The discharge at the pump for loading ℓ is QP (ℓ), and k (ℓ) is
the present value of the operating cost of the pump per unit of head and discharge that it
delivers, multiplied by: (a) coefficients reflecting the units in which the head and discharge
are expressed, (b) the efficiency of the pump and (c) the fraction of the total pumping time
during which loading ℓ is operative. Then the cost of operating the pump during loading ℓ is
given by k (ℓ).XP (ℓ) QP (ℓ). Likewise, if we assume that the capital cost of the pump, kc per
unit of power, increases linearly with its maximum operating head XPM, then the overall
capital cost of the pump at the source is given by kc XPM.
The drip irrigation design model described in this paper consists of small permanent system
with semi-automation, thus labor cost is considered to be small.
2.2.4 The Objective Function: The drip irrigation design model described in this paper
consists of an objective function that minimizes the sum of the capital cost and present
value of operating cost subject to appropriate constraints. The system is assumed to be
permanent with semi-automation, thus labor cost is considered to be small. In order to
formulate and solve an optimization problem mathematically it is first necessary to define
the decision variables. The objective function of the LP is given by:
Minimize [K] = ∑ij ∑m
C ijm
Xijm +
∑l
K (l)*XP (l)
*QP (l) +
Kc XPM
----------------------------- (1)
Where: ∑
l the summation of all loading, ∑
m the summation of all candidate pipe diameters m in link ij, ∑
ij the summation of all links ij in the network,
K= the total (present value) cost of the system.
2.2.5 The Constraints: The number of constraints in many cases a large network will generate
a very large LP, consisting of many variables and constraints. In order to maintain the
problem within practical bounds so that it can be solved on readily available computers, it is
particularly necessary to limit the number of constraints. This can generally be done by
careful selection of the head constrains. It will not be necessary to specify these constraints
for each and every node in the network. Hence, the LP should be run initially with a small set
of constraints covering what the designer considers to be the most critical nodes. In many
cases, the combination of topographic effects and the minimum or maximum head
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requirements for ‘less critical’ nodes will ensure that these requirements are automatically
satisfied by specifying the constraints for the ‘more critical’ nodes. The designer should
always check that all the head requirements are met in the optimal solution. If they are not,
then constraints should be added for the nodes that do not meet their respective maximum
or minimum head requirements, and the LP should then be re-run. Four sets of constraints
can be derived for the LP problem:
A- The non-negativity constraints: It is a condition of the LP solution procedure that the
decision variables must all be non-negativity. Thus a set of constrains can be stated as: