Modeling of Fertilizer Transport Through Soil, Case Study: Nile Delta

Abstract

Egypt’s population is estimated at 90 million people. Egypt covers an area of 1,001,449 km² that is mostly desert (Sahara). Only 6% of Egypt’s area is inhabited. Most of the people live in the Nile Delta and the narrow Nile Valley. The majority of Egyptians (43.3%) live in Lower Egypt (north of the country), whereas 37.1% live in Upper Egypt (south).

The total agricultural land area in Egypt is about 3.85 million ha, accounting for almost 3.5% of the total area. Only 5.4% of the land resources in Egypt are qualified as excellent, and the rest is either poor or of low quality (mainly due to salinity problems). The total area cropped annually increased from 4.6 million ha in 1982 to 6.5 million ha in 2003 due to increased cropping intensity, till it reached 6.9 million ha (16.5 million feddan) in year 2009. That is because of the variety between annual and permanent crops which made it possible to permit up to three harvests per year.

In this chapter, the description of Nile Delta was presented including geography, climate, and geology. The types and physical properties of groundwater aquifers including the Nile Delta aquifer were covered. The principles of groundwater contamination with organic and inorganic contaminants including nutrients such as nitrogen, phosphorous, and sulfur were illustrated. The physicochemical reactions (hydrolysis, oxidation–reduction, biodegradation, adsorption, and volatilization) are described in detail.

In addition, information about the agroecological zones and farming systems, particularly in regard to agricultural suitability, was provided. The agricultural production systems, including fertilizer requirements and crop needs, were also described. The recommended rates of fertilizer for the main crops in Egypt were given. Besides, the summarization of several studies, results for the determination of the most suitable time and proper method of fertilizer application on various crops are supplied.

On the other hand, the advection–dispersion equation which describes the contaminants transport process is presented with illustration for the advection, dispersion, and adsorption phenomenon. Different numerical models including finite difference method (FDM), finite element method (FEM), and boundary element method are covered. Also, the most popular computer codes Modular Finite-Difference Groundwater Flow Model (MODFLOW), MT3DMS, Groundwater Modeling System (GMS), Soil and Water Assessment Tool (SWAT), Finite Element Subsurface Flow and Transport Simulation System (FEFLOW), and HYDRUS are presented.

Moreover, the groundwater modeling systems (MODFLOW and MT3DMS) are used to simulate three-dimensional groundwater flow and NO₃ ⁻ transportation processes in El-Menoufia Governorate as a case study, located in the central region of the Nile Delta aquifer. The results highlight areas of groundwater contamination by NO₃ ⁻, which occurred at 40 m depth because of the significant loads and method of nitrogen fertilizer application.

AEZ:

Agroecological zones

BCM:

Billion cubic meters

FAO:

Food and Agriculture Organization of the United Nations

FDM:

Finite difference method

Feddan:

0.42 ha

FEM:

Finite element method

FYM:

Farm yard manure

ha:

Hectare

K₂O or K:

Potash

MALR:

Ministry of Agriculture and Land Reclamation

N:

Nitrogen

P₂O₅ or P:

Phosphate

PDEs:

Partial differential equations

RRTC:

Rice Research and Training Center

1 Introduction

The Nile Delta Quaternary aquifer is considered the main source of groundwater in Egypt. Unfortunately, the groundwater in the Nile Delta aquifer has been heavily polluted by biological activities and some heavy metals. This contamination is mainly due to agricultural activities in the whole agricultural lands all over the Delta. The excessive use of fertilizers and pesticides in agricultural operations is mainly responsible for groundwater contamination in the Nile Delta.

The most commonly used fertilizers in Egypt are nitrogen, phosphorous, and potassium. These applied dose of fertilizers are based on the crops patterns and the method of irrigation; flood irrigation is the most popular method used; fertilizers applied at the ground surface of agricultural lands pass through the unsaturated zone and most of the transformation processes occur in this zone in addition to the plant uptake and the rest amount of fertilizer reaches the groundwater.

The modeling of fertilizers fate and transport in groundwater can be classified into the following two broad categories: (1) studies that incorporated soil transformation models to determine leaching to groundwater [1–4] and (2) studies that did not encompass soil transformation models in the development of fertilizers fate and transport models of groundwater [5–8].

The aim of this chapter is to give the reader a comprehensive background about the Nile Delta and the use of fertilizers in agricultural systems, and also to provide numerical methods and computer codes for modeling the fertilizers in the Nile Delta. After reading this chapter, the reader can understand the principals of contaminants transport and how to choose the best method for numerical simulation as well as the governing equations.

2 Groundwater Aquifers

Groundwater is contained in geological formations called aquifers which are sufficiently permeable to transmit. Sands and gravels, which are found in alluvial deposits, dunes, coastal plains, and glacial deposits, are the most common aquifer materials. The more porous the material is, the higher the yielding capacity. Sandstone, limestone with solution channels, and other karst formations are also good aquifer materials.

2.1 Types of Aquifers

The two main types of aquifers are confined and unconfined. A confined aquifer is a layer of water-bearing material overlaid by a relatively impermeable material. If the confining layer is essentially impervious, it is called an aquiclude. If it is permeable enough to transmit water vertically from or to the confined aquifer, but not in a horizontal direction, it is called an aquitard. An aquifer bound by one or two aquitards is called a leaky or semiconfined aquifer.

2.1.1 Confined Aquifers

Confined aquifers are completely filled with groundwater and they do not have a free water table. Also the pressure is greater than atmospheric pressure. The pressure condition in a confined aquifer is characterized by a piezometric surface, which is the surface obtained by connecting equilibrium water levels in tubes or piezometers penetrating the confined layer.

2.1.2 Unconfined Aquifer

The unconfined aquifer is a layer of water-bearing material without a confining layer at the top of the groundwater, called the groundwater table, where the pressure is equal to atmospheric pressure. The groundwater table which is called the free or phreatic surface is free to rise or fall. The groundwater table height corresponds to the equilibrium water level in a well penetrating the aquifer. Above the water table is the vadose zone, where water pressures are less than atmospheric pressure. The soil in the vadose zone is partially saturated, and the air is usually continuous down to the unconfined aquifer [9]. Figure 1 shows these different types of aquifers after Liu and Liptak [10].

Fig. 1

(a) Confined aquifer, (b) phreatic aquifer, (c) perched aquifer, and (d) leaky aquifer [10]

2.2 Physical Properties of Aquifers

As stated before, the aquifer is considered an underground storage reservoir for water. It also acts as a conduit through which water is transmitted and flows from a higher to a lower level of energy. An aquifer is characterized by the three physical properties: hydraulic conductivity, transmissivity, and storativity.

2.2.1 Hydraulic Conductivity

Hydraulic conductivity, or thermal conductivity, is a physical measure of how readily an aquifer material (soil) transmits water through it. Mathematically, it is the proportionality between the rate of flow and the energy gradient as expressed in Eq. (1). Therefore, it depends on the properties of the aquifer material and the fluid flowing through it.

$$ K= k\frac{\gamma}{\mu} $$

(1)

where K is the hydraulic conductivity (called the coefficient of permeability in soil mechanics), k is the intrinsic permeability, γ is the specific weight of fluid, and μ is the dynamic viscosity of fluid. For a given fluid under a constant temperature and pressure, the hydraulic conductivity is a function of the properties of the aquifer material.

2.2.2 Transmissivity

Transmissivity is the physical measure of the ability of the aquifer of a known dimension to transmit water through it. In an aquifer of uniform thickness d, the transmissivity T is expressed as:

$$ T= K^{\prime } d $$

(2)

where K′ represents the average hydraulic conductivity. When the hydraulic conductivity is a continuous function of depth, the equation is expressed as:

$$ K^{\prime }=\frac{1}{d}\ {\int}_0^d{k}_z{d}_z $$

(3)

2.2.3 Storativity

Storativity, also known as the coefficient of storage or specific yield, is the volume of water yielded or released per unit horizontal area per unit drop of the water table in an unconfined aquifer or per unit drop of the piezometric surface in a confined aquifer. Storativity S is expressed as:

$$ S=\frac{1}{A}\ \frac{d Q}{d\phi} $$

(4)

where dQ is the volume of water released or restored and dϕ is the change of water table or piezometric surface [11].

2.3 Fundamental Equations of Groundwater Flow

2.3.1 Darcy Law

The theory of groundwater flow originates with Henry Darcy who published the results of his experimental work in 1856. He found that the total discharge Q was proportional to cross-sectional area A, inversely proportional to the length Ds, and proportional to the head difference ϕ ₁ – ϕ ₂ as expressed mathematically in the form called Darcy’s equation:

$$ Q= KA\ \frac{\phi_1-{\phi}_2}{\varDelta s} $$

(5)

where K is the hydraulic conductivity and the quantity Q/A is called specific discharge q. If ϕ ₁ − ϕ ₂ = Δϕ and Δs = 0, the equation becomes:

$$ q=- k\frac{d\phi}{d s} $$

(6)

This equation states that the specific discharge is directly proportional to the hydraulic gradient. The specific discharge is also known as Darcy’s velocity. Note that q is not the actual flow velocity (seepage velocity) because the flow is limited to pore space only. The seepage velocity v is then expressed as:

$$ v=\frac{Q}{n\bullet A}=\frac{q}{n} $$

(7)

where n is the porosity of the soil and the seepage velocity v is always larger than q.

Practically, the flow is seldom one-dimensional. The simple form of equation of Darcy’s law is not suitable for solving problems. A generalized form must be used, assuming the hydraulic conductivity K to be the same in all directions as:

$$ {q}_x=- K\frac{\partial \phi}{\partial x}\bullet {q}_y=- K\ \frac{\partial \phi}{\partial y}\bullet {q}_z=- K\ \frac{\partial \phi}{\partial z} $$

(8)

For an anisotropic material, these equations can be written as:

$$ {q}_x=-{K}_{x x}\frac{\partial \phi}{\partial x}-{K}_{x y}\frac{\partial \phi}{\partial y}-{K}_{x z}\frac{\partial \phi}{\partial z} $$

$$ {q}_y=-{K}_{y x}\ \frac{\partial \phi}{\partial x}-{K}_{y y}\ \frac{\partial \phi}{\partial y}-{K}_{y z}\ \frac{\partial \phi}{\partial z} $$

$$ {q}_z=-{K}_{z x}\ \frac{\partial \phi}{\partial x}-{K}_{z y}\ \frac{\partial \phi}{\partial y}-{K}_{z z}\ \frac{\partial \phi}{\partial z} $$

(9)

2.3.2 Equation of Continuity

Darcy’s law provides three equations of motion for four unknowns (q _x , q _y , q _z , and ϕ). The flow phenomenon must satisfy the fundamental physical principle of conservation of mass. When an elementary block of soil is filled with water, no mass can be gained or lost regardless of the pattern of flow. The conservation principal which is shown in Fig. 2 requires that the sum of the three quantities (the mass flow) is zero, hence when divided by Δx. Δy. Δz:

$$ \frac{\partial \left(\rho {q}_x\right)}{\partial x}+\frac{\partial \left(\rho {q}_y\right)}{\partial y}+\frac{\partial \left(\rho {q}_z\right)}{\partial z}=0 $$

(10)

Fig. 2

Conservation of mass (after [10])

When the density is a constant, then the equation is reduced to:

$$ \frac{\partial {q}_x}{\partial x}+\frac{\partial {q}_y}{\partial y}+\frac{\partial {q}_z}{\partial z}=0 $$

(11)

This equation is called the equation of continuity.

By substituting Darcy’s law Eq. (8) into the equation of continuity, Eq. (11) yields:

$$ \frac{\partial^2\phi}{{\partial X}^2}+\frac{\partial^2\phi}{{\partial y}^2}+\frac{\partial^2\phi}{{\partial z}^2}=0 $$

(12)

or

$$ {\nabla}^2\phi =0 $$

(13)

3 Principles of Groundwater Contamination

A groundwater contaminant is defined as any physical, chemical, biological, or radiological substance or matter in groundwater. The contaminants can be introduced in the groundwater either by naturally occurring activities, such as natural leaching of the soil and mixing with other groundwater sources, or by planned human activities, such as waste disposal, mining, and agricultural operations.

The most dominant human activities that cause groundwater contamination are waste disposal, storage and transportation of commercial materials, mining operations, and agricultural operations. Fertilizers are the primary cause of groundwater contamination beneath agricultural lands. Both inorganic (chemically manufactured) and organic (from animal or human waste) fertilizers applied to agricultural lands provide nutrients such as nitrogen, phosphorous, and potassium that fertilize the land and stimulate plant growth.

A portion of these nutrients usually leaches through the soil and reaches the groundwater table. Phosphate and potassium fertilizers are readily adsorbed on soil particles and seldom constitute a pollution problem. However, only a portion of nitrogen is adsorbed by soil or used by plants, and the rest is dissolved in water to form nitrates in a process called nitrification. Nitrates are mobile in groundwater and have the potential to harm infant human beings and livestock if consumed on a regular basis [12]. When a contaminant is introduced in the subsurface environment, its fate and concentration are controlled by a variety of physical, chemical, and biochemical processes that occur between the contaminant and the constituents of the subsurface environment.

3.1 Organic Contaminants

The reactions that can change the concentration of an organic contaminant in groundwater can be grouped into five categories [13, 14]. These categories include: hydrolysis of the contaminant in water, oxidation–reduction, biodegradation of the contaminant by microorganisms, adsorption of the contaminant by the soil, and volatilization of the contaminant to the air present in the unsaturated zone. The relative importance of each of these reactions depends on the physical and chemical characteristics of the contaminant and on the specific conditions of the subsurface environment.

3.1.1 Hydrolysis

Hydrolysis is a chemical reaction in which an organic chemical reacts with water or a hydroxide ion (OH). The hydrolysis of organic chemicals in water is generally considered first-order with respect to the organic chemical’s concentration; thus, the rate of hydrolysis can be calculated with the following equation [15]:

$$ k\bullet c=-\frac{dc}{dt} $$

(14)

or

$$ k=\frac{2.303}{t} \log \left(\frac{c_0}{c}\right) $$

(15)

where k is rate constant, t is the time, C ₀ is the initial concentration (ppm), and C is concentration at time t (ppm). The time needed for half of the concentration to react, half-life, can be calculated if k is known with the use of the following equation:

$$ {t}_{1/2}=\frac{0.693}{k} $$

(16)

where t _1/2 is equal to the half-life.

3.1.2 Oxidation–Reduction

Oxidation–reduction reactions greatly affect contaminant transport and are usually closely related to the microbial activity and the type of substrates available to the organisms. The occurrence of oxidation in the subsurface is a function of the electrical potential in the reacting system.

3.1.3 Biodegradation

Biodegradation of an organic chemical in soil is the modification of the chemical by soil microorganisms to produce microbial cells, carbon dioxide, oxygen, and water. The most predominant microorganisms in soil include bacteria and fungi. The microorganism population in soils is generally the greatest in the surface layers where temperature, moisture, and energy supply are favorable for their growth. As the depth increases, the number of aerobic microorganisms decreases; however, anaerobic microorganisms can exist depending on the availability of nutrients and organic material. Biodegradation of many organic chemicals is generally first-order with respect to the organic chemical’s concentration [16].

3.1.4 Adsorption

Adsorption is the bonding of an organic chemical to the soil mineral surfaces (clay). Adsorption is important in the movement of organic chemicals in groundwater because it decreases the mobility and retards the migration of the organic chemical in the groundwater. In addition, the adsorption of organic chemicals depends on the organic matter content of the soil. The relationship between the organic content of soil and the adsorption coefficient of organic chemicals is generally linear for soils with an organic carbon content greater than 0.1 [17]. At equilibrium, the adsorption coefficient can be described with the linear Freundlich isotherm equation as:

$$ {k}_d=\frac{c_s}{c_w} $$

(17)

where K _d is the distribution coefficient, C _s is the concentration adsorbed on soil surfaces (mg/g), and C _w is the concentration in water (mg/ml).

3.1.5 Volatilization

Volatilization is the loss of chemicals in vapor form from the soil water (liquid phase) or the soil surfaces (solid phase) to the soil air (gas phase) of the unsaturated zone. The volatilization from the solid phase to the gas phase is relatively small and usually neglected. The extent of volatilization of an organic chemical from water to the soil air can be determined by Henry’s law; the vapor pressure of a chemical is proportional to its concentration [18] as:

$$ {C}_a= H\bullet {C}_W $$

(18)

where C _a is the concentration of the chemical in air, H is Henry’s law constant, and C _w is the concentration of the chemical in water. Henry’s law constant for a chemical can be calculated with the following equation:

$$ H=\frac{P_V\bullet {M}_W}{760\bullet S} $$

(19)

where P _v is the vapor pressure of the chemical in mmHg, M _w is the molecular weight of the chemical, and S is the solubility in mg/l.

The volatilization of organic chemicals in groundwater is affected by several soil characteristics. Volatilization decreases as the soil water content increases or as the soil porosity decreases. Soils with high clay content tend to have a high water content and hence low volatilization [19].

3.2 Inorganic Contaminants

Inorganic constituents in the subsurface environment can be classified into different categories; nutrients are the main concern from these categories. Nutrients such as nitrogen, phosphorous, and sulfur are essential for plant and microorganism growth. They are applied to the land surface to increase the fertility. These nutrients can have appreciable concentrations that may leach into the ground and adversely affect the quality of groundwater.

3.2.1 Nitrogen

Nitrogen (N) is found in waste, soil, and the atmosphere in various forms such as ammonia, ammonium, nitrite, nitrate, and molecular nitrogen. Nitrogen is converted to ammonium (NH₄ ⁺) by a process called ammonification. Due to its positive charge, ammonium can be held in the soil on cation exchange. Ammonium can also be converted temporarily to nitrite (NO₂ ⁻) and then to nitrate (NO₃ ⁻) by aerobic organisms through a process called nitrification. Ammonification and nitrification normally occur in the unsaturated zone where microorganisms and oxygen are available, but nitrate can be readily leached from the soil into groundwater. Nitrate is highly mobile in groundwater because of its negative charge.

3.2.2 Phosphorous

Phosphorous (P) is found in organic waste, fertilizers, and pesticides. Although phosphorous is not a harmful constituent in drinking water, its presence in groundwater is environmentally significant if the groundwater discharges to a surface water body where phosphorous can produce algae growth and cause eutrophication of the aquatic system [20].

3.2.3 Sulfur

Sulfur (S) is found in appreciable amounts in waste streams from sugar refining, petroleum refining, and copper and iron extraction [21]. Aerobic bacteria can oxidize the reduced forms of sulfur to form sulfate which can be highly adsorbed to soil when the cation adsorbed on the clay is aluminum, moderately adsorbed when the cation is calcium, and weakly adsorbed when the cation is potassium.

4 Fertilizers in Nile Delta

The improvement of the efficiency of use of Nile water is the major component of the strategy for agricultural development including increasing the productivity per unit of water. Egypt currently consumes 1.25 million tons of fertilizer with an N:P₂O₅:K₂O ratio of 1:0.12:0.05 [22].

4.1 Farming Systems and Agroecological Zones

4.1.1 Old Land

This land is located in the Nile Valley and the Delta regions. It covers a total area of 2.25 million ha and is characterized by alluvial soils (clay to loamy). The Nile is the main source of water for irrigation [22].

4.1.2 New Land

This land is located on both the east and west sides of the Delta and scattered over various areas in the country. It covers 1.05 million ha. Reclamation of this land began in the early 1950s and is continued until now. Nile water is the main source of irrigation water but in some desert areas underground water is the only source of irrigation water.

4.1.3 Oases

Oases are characterized by sandy and calcareous soils. They cover a total area of 40,000 ha and the underground water is the main source for irrigation.

4.1.4 Rainfed Areas

These include approximately 0.17 million ha of land located in the north coastal areas, where rainfall fluctuates between 100 and 200 mm annually. There is no effective rainfall in Egypt except on this narrow strip along the north coast and Egypt’s agriculture is almost totally dependent on flood irrigation from the Nile.

4.2 Agricultural Production Systems

The rapid increase of the population in Egypt together with a limited cultivated area leads to steady decline in the area of land per capita and also the availability of water per capita (from 0.2 ha in 1907 to 0.05 ha at the beginning of the year 2004). Thus, the need for additional production of various crops becomes essential. In order to achieve a significant increase in crop production, efforts were focused on measuring many factors as the balanced fertilization of different crops and the adoption of suitable fertilizer practices.

4.3 Crop Production System

The total cultivated area increased from 4.7 million ha in 1982 to 6.5 million ha in 2003 due to the increase in cropping intensity to 180%. This was made possible by the cultivation of earlier maturing varieties of various crops, permitting the possibility of harvesting three crops per year. The aim is to reach a cropping intensity of 220% by 2020. This target requires new varieties that combine earliness with higher yields [22].

4.3.1 Cereal Crops

In the Nile Delta, Egypt, the total production of cereal crops amounted to 20.1 tons in 2000. Wheat production increased from 2 million tons in 1982 to 6.8 million tons in 2003. Maize production increased from 3.35 million tons in 1982 to 6 million tons in 2002 due to the cultivation of maize hybrids that now cover almost 70% of the area grown to maize. Rice production increased from 2.4 million tons in 1982 to 6.1 million tons in 2002 because of the cultivation of short duration, high yielding varieties.

4.3.2 Sugar Crops

The average yield of sugar cane has increased from 84.7 tons/ha in 1982 to 121 tons/ha in 2001 and that of sugar beet from 31.5 tons/ha in 1982 to 51 tons/ha in 2002.

4.3.3 Horticultural Crops

Fruits and vegetables are produced in sufficient quantities to meet domestic demand and to provide some surplus for export. Vegetables are grown on about 560,000 ha and contribute 10.5% of the total value of horticultural crops. The main vegetable crops are potatoes, tomatoes, cabbage, onions, beans, peas, melons, watermelons, garlic, peppers, cucumbers, sweet potatoes, and leaf vegetable crops.

4.4 Cropping Patterns

In the Nile Delta, there are several different crop rotations which are followed depending on crops and the soil type. The present development has been applied and the aim of this strategy is to optimize the cropping pattern and the use of agricultural and water resources. By 2017, it is planned that the cropping pattern should involve:

• A gradual increase in the area of wheat agriculture from about 1 million ha in 1997 to about 1.4 million ha in 2017. That means the production of wheat will raise to about 9 million tons annually by the year 2017.

• The area of cotton agriculture would be kept constant at about 420,000 ha to meet the demand for local consumption.

• A total production of paddy rice of about 4 million tons annually should increase to 5 million tons annually by the year 2017, by planting the whole area with short duration, high yielding varieties, which have lower water requirements. MALR has new varieties that require only 120 days from planting to harvest, giving an average yield of 9.5–13.1 tons/ha, compared with 8.3 tons/ha from old varieties. The water consumption/evapotranspiration of the new varieties should be around 14,000 m³/ha, compared with 21,000–24,000 m³/ha for the old varieties. The productivity of old land is relatively high but additional yield gains could be achieved with improved seed quality, and better land and soil management. The area under cultivation should increase to about 4.7 million ha by the year 2017 that means an increase of 1.2 million ha, according the objectives of the agricultural strategy [23].

4.5 Fertilizer Requirements and Crop Needs

Efforts continue to improve crop productivity and quality. The development of better agricultural practices and new high yielding varieties are some of these measures aimed to increase the agricultural production. Appropriate fertilization is one of the most important agricultural practices for achieving this objective. Evaluation of the best source of nutrients, optimum rates of fertilization, suitable timing, and proper fertilizer placement are necessary for efficient fertilizer management.

In Egypt, there are many traditional practices that are commonly implemented and which play a major role in restoring and maintaining soil fertility. Among these practices are:

• Planting berseem clover as a winter fodder crop before the cotton crop, providing a green manure by ploughing in after taking one or two cuts

• Incorporating farmyard manure (FYM) into the soil during seedbed preparation. This is usually done before the planting of cotton

• Including in the crop rotation a legume crop such as: fava bean and soybeans, which have a positive effect on soil fertility and provide part of the nitrogen requirement

The main types of fertilizers used are:

• Nitrogen

  • Urea (46.5% N)

  • Ammonium nitrate (33.5% N)

  • Ammonium sulfate (20.6% N)

  • Calcium nitrate (15.5% N)

• Phosphate

  • Single superphosphate (15% P₂O₅)

  • Concentrated superphosphate (37% P₂O₅)

• Potassium

  • Potassium sulfate (48–50% K₂O)

  • Potassium chloride (50–60% K₂O)

The recommendation of fertilizer use is based on the experiments carried out by the Ministry of Agriculture. In practice, farmers use different rates of fertilizers for the same crop. The two main factors for estimating the fertilizer requirements are the indicative cropping pattern and the economic optimum rate of fertilizer for each crop under different agroclimatic conditions. Figure 3 shows the estimation of the fertilizer requirements of new and old lands, respectively, up to 2017.

Fig. 3

Estimated fertilizer requirements for new and old land [24]

In addition to these two main factors, the following must be taken into consideration:

• Expansion of the newly reclaimed area

• Crop rotations and their impact on crop responses to fertilizers

• Soil and plant tissue analysis

• Residual effect of the fertilizers and the organic manures

• Improvements in the irrigation and drainage systems

• Nutritional balances for the various crops

• Crop intensification, whether by increasing the number of plants per unit area or by intercropping

It is necessary to differentiate between removal, and uptake. Nutrient removal is the amount of a nutrient removed from the field (soil) by a given yield. Nutrient uptake is the maximum amount taken up by a plant during the vegetative period. Normally uptake is higher than the removal [25]. Thus, the input of nutrients should be equal to the amount removed and/or taken up by the crops. If the quantities from these natural sources are not sufficient for the crop to reach the target yield, the difference should be added as fertilizer. Insufficient amounts of nutrients result in loss of yield. The excessive amounts of the applied fertilizers possibly cause environmental hazards, and reduction of crop yield.

The consumption of nitrogen and phosphate containing fertilizers has increased during the last three decades. The recommended rates of N, P₂O₅, and K₂O for all the crops, on a national level, are issued by MALR each year. The rates of fertilizers application differ according to the species and variety of crops, soil type as well as the area allocated to each crop in that year.

4.6 Methods of Fertilizer Application

Previous studies have been carried out to determine the most suitable time and proper method of fertilizer application for various crops in the Nile Delta [26].

Rice

The Rice Research and Training Center (RRTC) conducted a work for spread seeded rice, and the results indicated that the most effective treatment is the split application of fertilizer nitrogen in three equal doses: one third applied before planting, one third at the mid tillering stage, and one third at panicle initiation.

Wheat

Several studies were carried out to determine the most suitable time of nitrogen application for producing the highest yield of grain and protein. In a coordinated field trial, using N¹⁵ labeled fertilizer, it was found that splitting the amount of nitrogen into three equal doses to be applied at planting, early tillering, and booting stages of growth were more effective than N fertilizer applied in two equal doses at planting and tillering or in one single dose at planting.

Maize

Data obtained using N¹⁵ labeled fertilizer showed that the split application of N fertilizer in three equal doses was more effective than N fertilizer applied in two equal doses.

Cotton

About 22 field trials were conducted to study the most effective method and the suitable time of nitrogen application. The results indicated that:

• Deep side dressing after thinning was the most effective treatment when compared with topdressing after thinning or banding in the bottom of the ridge.

• Splitting the nitrogen dose into two equal doses, the first before the second watering (after thinning) and the second before the fourth watering was the most efficient treatment.

• Data from different field experiments showed that the application of phosphate fertilizer in one single dose before planting or before the first or second watering were almost equal in their impact on crop production.

Nitrogen is considered to be the most critical factor in crop production regarding to the Egyptian agricultural conditions. The rate of nitrogen application in Egypt is one of the highest rates in the world. As a result, nitrogen contamination of drainage water reaches an average of 1.5 ppm N in the drains of the Nile Delta area. These are because of the heavy application of nitrogenous fertilizers which was usually practiced by Egyptian farmers. Such losses of nitrogen are a substantial financial waste and pollution of the environment with nitrate. The recommended rates of nitrogen, phosphorus, and potassium of fertigation are shown in Table 1.

Table 1 Recommended rates of fertilization [24]

Applying fertilizers through the irrigation system has several advantages:

• Placement of mobile nutrients such as nitrogen can be regulated in the soil profile by the amount of water applied.

• Applied nutrients are readily available for rapid plant uptake.

• Crop damage during fertilizer application is minimized.

The disadvantages of fertilizer application through the irrigation system are:

• Localized fertilizer placement such as banding cannot be achieved in a sprinkler irrigation system. To a limited extent, it can be achieved with drip irrigation.

• Water source contamination can be significant if the injection system is not properly installed or is poorly maintained.

5 Transport of Contaminants in Groundwater

When a contaminant is introduced in groundwater, it spreads and moves with the groundwater as a result of advection which is caused by the flow of groundwater, dispersion which is caused by mechanical mixing and molecular diffusion, and retardation which is caused by adsorption. The mathematical relation between these processes can be written as follows [27]:

$$ \frac{\partial }{\partial {x}_i}\ \left[{D}_{i j}\ \frac{\partial C}{\partial {x}_j}\right]-\frac{\partial }{\partial {x}_i}\left({C\bullet v}_i\right)-\frac{C^{\prime } W^{\prime }}{n}= R\frac{\partial C}{\partial t} $$

(20)

$$ {v}_i=\frac{-{K}_{i j}}{n}\frac{\partial h}{\partial {x}_j} $$

(21)

$$ R=\left[1+\frac{\rho_b{K}_d}{n}\right] $$

(22)

where C is the contaminant concentration, v _i is the seepage or average pore water velocity in the direction x _i , D _ij is dispersion coefficient, K _ij is hydraulic conductivity, C′ is solute concentration in the source or sink fluid, W′ is volume flow rate per unit volume of the source or sink, n is the effective porosity, h is the hydraulic head, R is the retardation factor, and x _i is the Cartesian coordinate.

The following discussion uses a simplified two-dimensional representation of the equation to describe the transport of contaminants in groundwater. In a homogeneous, isotropic medium having a unidirectional steady-state flow with seepage velocity, Eq. (20) can be rewritten as:

$$ {D}_L\frac{\partial^2 C}{\partial {x}^2}+{D}_T\frac{\partial^2 C}{\partial {y}^2}- V\frac{\partial C}{\partial x}= R\frac{\partial C}{\partial t} $$

(23)

where C = contaminant concentration, V = seepage or average pore water velocity, D _L  = longitudinal dispersion coefficient, D _T  = transversal dispersion coefficient, and R = retardation factor.

5.1 Advection

A contaminant moves with the flow of groundwater according to Darcy’s law as:

$$ Q=- K\bullet A\frac{h_2-{h}_1}{L} $$

(24)

where Q = groundwater flow rate, A = cross-sectional area of flow, (h ₂ – h ₁) = head loss between point 1 and point 2, L = distance between point 1 and point 2, and K = hydraulic conductivity.

The actual seepage or average pore water velocity can be calculated as:

$$ V=\frac{Q}{n\bullet A}=-\frac{K}{n}\frac{h_2-{h}_1}{L} $$

(25)

where n is the effective porosity. The average pore water velocity calculated in Eq. (23) is a conservative estimate of the migration velocity of the contaminant in groundwater. Therefore, when only advection is considered, a contaminant moves with the groundwater flow at the same rate as water, and no diminution of concentration is observed. In reality, however, the movement of the contaminant is also influenced by dispersion and retardation.

5.2 Dispersion

Dispersion is the result of two processes, molecular diffusion and mechanical mixing. Molecular diffusion is the process whereby molecules move under the influence of their kinetic activity in the direction of their concentration gradients. Under this process, constituents move from regions of higher concentration to regions of lower concentration; the greater the difference, the greater the diffusion rate. Molecular diffusion can be expressed by Fick’s law as:

$$ F=-{D}_f\frac{dC}{dx} $$

(26)

where F is the mass flux per unit area per unit time, D _f is the diffusion coefficient, C is the contaminant concentration, and dC/dx is the concentration gradient.

Mechanical mixing is the result of velocity variations within the porous medium. The velocity is greater in the center of the pore space between particles than at the edges. As a result, the contaminant spreads gradually to occupy an ever increasing portion of the flow field. Mechanical mixing dispersion can occur both in the longitudinal direction of the flow as well as in the transverse direction. The mechanical mixing component of dispersion can be assumed proportional to the seepage velocity as:

$$ {D}_{11}={a}_L\bullet V $$

$$ {D}_{22}={a}_T\bullet V $$

(27)

where D ₁₁, D ₂₂ are longitudinal and transversal mechanical mixing components of dispersion, a _L , a _T are longitudinal and transversal dispersivity, and V is the average linear pore water velocity.

Finally the hydrodynamic dispersion coefficients can be written as:

$$ {D}_L={D}_{11}+{D}_f $$

$$ {D}_T={D}_{22}+{D}_f $$

(28)

The dispersivity coefficients a _L and a _T are characteristic of the porous medium. Representative values of dispersivity coefficients can be determined from breakthrough column tests in the laboratory or tracer tests in the field [28]. Figure 4 shows how dispersion can cause some contaminants to move faster and slower than the average groundwater velocity.

Fig. 4

Effect of dispersion–advection on concentration distribution (after [10])

5.3 Retardation

Retardation is due to the adsorption mechanism. The retardation coefficient can be calculated based on the adsorption coefficients of the contaminant and the characteristics of the medium as:

$$ R=\left[1+\frac{\rho_b{K}_d}{n}\right] $$

(29)

where K _d is the adsorption coefficient. The values p _d and n are the bulk density and porosity of the soil. Figure 5 illustrates the effect of advection, dispersion, and retardation on the mobility of a contaminant in groundwater.

Fig. 5

Effect of advection, dispersion, and retardation on the mobility of a contaminant in groundwater (after [10]). (a) Distance from continuous contaminant source. (b) Distance from slug-release contaminant source

6 Numerical Models and Computer Codes

Basic information on such techniques and on the use of computer programs to solve (run, or simulate) flow and solute transport problems in practice will be provided in this section. While an analytical solution seeks to determine the spatial and temporal distribution of the problem’s state variables, as continuous functions of space and time, a numerical solution provides information on these variables only at a selected set of points in space and time. Information at all other points of interest is obtained by interpolation. In this way, the problem is transformed from one described by a mathematical model, written in terms of a small number of variables, to one described by a numerical model, written in terms of many discrete values of these variables, defined at specified points. The small number of partial differential equations (PDEs) that contain the continuous variables is replaced by a large number of linear algebraic equations that contain the discrete variables.

6.1 Numerical Models

6.1.1 Finite Difference Methods

The first step in most numerical methods is to replace the mathematical model, composed of PDEs, accompanied by initial and boundary conditions, written in terms of continuous state variables like h(x, t) and c(x, t), by a numerical model, written in terms of discrete variables.

Figure 6a demonstrates a grid for a two-dimensional plan domain. The grid is obtained by dividing the axes into segments, and drawing lines parallel to the axes. The segments on the axes may be equal (uniform grid) or different (variable grid). In general, lines are made closer in areas where we wish to obtain more detailed information on the behavior of the state variable. Figure 6b shows such a variable grid.

Fig. 6

A grid for the grid-centered finite difference method (FDM): (a) equal spacing, (b) variable spacing (after [9])

Second approach for the development of a finite difference scheme is to use a cell-centered as shown in Fig. 7, rather than a grid-centered approximation. Particularly, the cell-centered approach is adopted in the widely used computer code, Modular Finite-Difference Groundwater Flow Model (MODFLOW), developed by the US Geological Survey (USGS). The cell-centered approach is based on the mass balance of the cell.

Fig. 7

Cell-centered finite difference approach (after [9])

The cells formed by the FDM grid have either a rectangular 2D or a cubical 3D shape. It is usually difficult to use these shapes to fit an irregular geometry of the boundary of a considered domain. A strength of the FDM, in contrast to other numerical methods, such as the Finite Volume and Finite Element Methods (FEM), is that the nodes are arranged in a regular pattern. Figure 8 gives an example of how a solution domain is approximated by the cell-centered FDM. All cells with (cell-centered) nodes falling within the domain are considered domain cells. As in many codes, MODFLOW, all domain cells are designated as variable head cells, meaning that the head values are unknown in such cells.

Fig. 8

The approximation of a solution domain and the designation of boundary conditions by the cell-centered finite difference approach (after [9])

6.1.2 Finite Element Methods

Because the FEM uses triangular and various irregularly shaped elements, the subdivision of a considered domain can be unstructured, meaning that the nodes forming the elements can be arbitrarily scattered in the domain in sparse or concentrated patterns to form elements of various sizes. This flexibility is useful not only for irregularly shaped domains, but also for concentrating elements in regions where larger variations exist in the considered variable, and where a better accuracy is required. The rectilinear grid based FDM has some difficulty to conform to these requirements.

6.1.3 Boundary Element Methods

The advantage of the boundary methods is that the number of unknowns is much smaller, thus, both the computer storage requirement and the computational effort are significantly reduced. Another advantage of the boundary methods is the preparation of the solution mesh. The reduction in spatial dimensions in the formulation of a boundary method (recalling that a three-dimensional domain has a two-dimensional boundary) can make the mesh preparation easier.

The most critical advantage of the boundary methods, however, lies in their flexibility in dealing with moving boundary problems. In domain methods, whenever the boundary location is moved, the interior mesh needs to be adjusted, as elements and nodes can be crossed. The major disadvantage of boundary methods is that they cannot be applied to all types of governing equations. The boundary methods require information on some solution of the governing equation, such as a general solution, or a fundamental solution. In general, these solutions are available only for linear governing equations with constant coefficients (i.e., homogeneous materials).

6.2 Computer Codes

Once a numerical model has been constructed, and a numerical method has been chosen to enable (approximate) the solution of the PDEs included in a mathematical model that represents a given physical problem, a computer code (or program) is used to execute the large number of repetitive calculation steps involved in the solution of the numerical model. Among the most notable sources for such codes are government agencies, such as the USGS, the US Environmental Protection Agency (USEPA), the US Army Corps of Engineers (USACE), the various US Department of Agriculture (USDA) laboratories, and the National Laboratories.

6.2.1 MODFLOW

MODFLOW is a computer program that simulates three-dimensional groundwater flow by using a cell-centered FDM. MODFLOW is one of the most widely used computer codes for groundwater flow simulation. Also, it has been developed with a modular structure, meaning that the source code is easier to understand, and users can develop their own subroutines to link with the main program. Particularly, in MODFLOW-2000 and in later versions, users can add multiple non-groundwater flow equations, such as the contaminant transport equation, to enhance its modeling capability.

6.2.2 MT3DMS

Modular 3D Multi Species Transport Model for Simulation of Advection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems (MT3D) interfaces directly with MODFLOW for the flow solution. For solute transport, it utilizes an Eulerian–Lagrangian scheme, based on a forward tracking method of characteristics [29]. MT3D was later extended and released by the USACE, Engineering and Research Development Center [30]. MT3DMS is an extended version, where the “MS” stands for multispecies transport.

6.2.3 Groundwater Modeling System

Groundwater Modeling System (GMS) is a software preprocessor, postprocessor, and graphic user interface (GUI) implementation of a number of public domain groundwater modeling computer codes, which include FEMWATER, MODFLOW, MODPATH, MT3DMS, RT3D, UTCHEM, and PEST. It was developed by the US Army Engineer Research and Development Center for use by governmental agencies. It is available as commercial software.

6.2.4 Soil and Water Assessment Tool

Soil and Water Assessment Tool (SWAT) [31, 32] is a basin scale, continuous time model designed to predict the impact of management on water, sediments, and agricultural chemical yields in watersheds. Major model components include weather, hydrology, soil temperature, plant growth, nutrients, pesticides, bacteria and pathogens, and land management.

6.2.5 Finite Element Subsurface Flow and Transport Simulation System

Finite Element Subsurface Flow and Transport Simulation System (FEFLOW) is a commercial software package based on the FEM. It simulates three-dimensional, density-dependent, saturated–unsaturated flow, chemical mass transport, and solid and fluid heat transport in porous media.

6.2.6 SUTRA

SUTRA is a finite element code that solves groundwater flow and transport problems under saturated and unsaturated conditions. It is a model for 2D or 3D saturated–unsaturated, variable-density groundwater flow, with solute or energy transport. Particularly, it models variable density, and, hence, has been widely used for simulating saltwater intrusion.

6.2.7 HYDRUS

HYDRUS 1D and 2D are public domain software packages developed for the US Salinity Laboratory. HYDRUS-3D is a commercial software that is used for modeling of movement of water, heat, and multiple solutes in variably saturated media. The program is an FEM that solves Richards’ equation (for saturated–unsaturated water flow) and Fickian-based advection–dispersion equations (for heat and solute transport).

The flow equation incorporates a sink term to account for water uptake by plant roots. The solute transport equations consider advective–dispersive transport in the liquid phase, and diffusion in the gaseous phase. The equations also include provisions for nonlinear and/or nonequilibrium reactions between the solid and liquid phases, linear equilibrium reactions between the liquid and gaseous phases, zero-order production, and first-order degradation reactions.

6.2.8 SEAWAT

SEAWAT is a computer program for simulation of three-dimensional variable density groundwater flows. SEAWAT is a USGS code that combines MODFLOW and MT3DMS into a single computer program for the purpose of simulating saltwater intrusion [33]. It is a finite difference, Eulerian–Lagrangian code, in contrast to SUTRA, which is a finite element code.

7 Case Study

El-Menoufia Governorate occupies the southern Nile Delta, extending from 30° 50′ E to 31° 15′ E and 30° 20′ to 30° 40′ N. The area is bounded to the west by the Rosetta branch of the Nile River, and to the east by the Damietta branch. Transmissivity in the Nile Delta ranges from 2,000 to 3,000 m²/day, effective porosity ranges from 12 to 19 %, and total porosity ranges from 25 to 40%. Figure 9a, b shows the hydrogeological map of the studied area. The estimated longitudinal and lateral dispersivities for the Nile Delta aquifer are 100 and 10 m, respectively. The average depth of the groundwater table is generally 3–5 m, Fig. 10. The constant head boundary of the Nile Delta is shown in Fig. 11.

Fig. 9

(a) Hydrogeological section from south to north. (b) Key map for cross section (A–A′) (after [34])

Fig. 10

Average depth of groundwater (after [35])

Fig. 11

Constant head boundaries in the Nile Delta (after [36])

7.1 General Considerations

The study area is covered by Quaternary Nile deposits, including silt, clay, sandy clay, sands, and gravels. The ground surface topography of El-Menoufia is flat and crops are cultivated in a mixed pattern following two- or three-year crop rotation. The main crops consists of berseem (Egyptian clover), wheat in the winter (starting October–November), and corn and cotton in the summer (starting May–June). Irrigation is mainly by the traditional flooding method, which occurs frequently (3 and 2 times per month in the summer and winter, respectively). Commonly used fertilizers are urea (CH₄N₂O), potassium sulfate (K₂SO₄), calcium nitrate (Ca [NO₃]₂), and ammonium phosphate ([NH₄]₃PO₄). Fertilizers are supplied to farmers through the Agricultural Cooperative Society (ACS), and these application rates are shown in Table 2.

Table 2 Fertilizer dose (kg/ha) and duration (after [7])

7.2 Modeling Groundwater Flow

Simulations for groundwater and contaminants were conducted for the saturated zone of the Nile Delta aquifer. NO₃ ⁻ inputs to the groundwater table were estimated according to ACS records. MODFLOW and MT3DMS were chosen to build the required simulation models. The spatial distribution of groundwater heads and NO₃ ⁻ concentrations in the Nile Delta were used in the calibration of different sets of model parameters. Firstly, the determination of model parameters was begun by using the steady-state flow to calibrate hydraulic conductivity, while recharge was based on groundwater heads and water budget values. Secondly, the transient transport model was calibrated for the denitrification rate constant, which controls NO₃ ⁻ levels. The MT3DMS model was calibrated against measured concentration profiles at 40 m deep.

At the top of the aquifer, there is a 30 m thick clay-silt cap. The only significant recharge comes from the infiltration of irrigation water and seepage from irrigation canals. The high intensity and continuity of precipitation events play an important role in soil water changes but in Nile Delta, rainfall is extremely low ~20 mm/year so it is not significant. The lateral boundaries of the modeling area were defined as the Rosetta branch on the west and the Damietta branch on the east, which were considered as fixed head boundary conditions. The southern boundary of the study area is parallel to the head gradient of the groundwater; therefore, the southern side of the modeling area was set as a flux boundary with a variable inflow rate.

The values of horizontal hydraulic conductivities for the silt clay, sand gravel, and sand clay were 0.20 m/d, 100 m/d, and 10 m/d, respectively. The values of vertical conductivity were set as 10% of the horizontal conductivities. Fifty-five pumping wells that exist in the study area were included in the simulations. The screen depths of these wells vary from 40 to 50 m for drinking water wells, and from 60 to 70 m for irrigation wells (Fig. 12).

Fig. 12

Location map of groundwater production and observation wells

7.3 Modeling NO₃ ⁻ Transportation Processes

The calibration of the MT3DMS model parameters was accomplished by matching the measured contaminants concentrations at 40 m from ground surface with those calculated at the end of the calibration year in 2014. The values of bulk density and porosity for the entire domain were 1.5 kg/m³ and 0.3, respectively. For nonpoint source contamination, the effects of longitudinal and transverse dispersion were of lesser importance because there is no transition zone between the contaminated and non-contaminated areas; therefore, the longitudinal transverse dispersivity was assigned a constant value of 120 m and the ratios of transverse and vertical to longitudinal dispersivity were taken as 0.05 and 0.005, respectively. Molecular diffusion for NO₃ ⁻ was D ₀ = 1.6416 × 10⁻¹⁰ m²/d.

The estimated NO₃ ⁻ loading values of the ground surface for summer (cotton and corn) and winter (wheat and berseem) were 270 and 187 kg N/ha, respectively. After the application of fertilizers, many biological transformations occur in both the root and vadose zones. A significant volume of fertilizer is absorbed by crop roots and the nutrient leaching amount was considered equal to the amount applied at the surface minus crop uptake, taking into consideration the transformations of nutrients in the vadose zone. The locations of the eight monitoring wells in the study area are shown in Fig. 12 and the concentrations of nitrate in groundwater samples from these wells in year 2014 are tabulated in Table 3.

Table 3 Nitrate concentration for the groundwater samples in 2014 (ppm)

In this study area, the plant uptakes in summer and winter were taken to equal 142 and 146 kg N/ha, respectively. The estimated NO₃ ⁻ N loading to groundwater in summer and winter were 128 and 41 kg N/ha, respectively. The estimated annual leaching amount of NO₃ ⁻ to the water table was about 35% of the annual NO₃ ⁻ fertilizer application.

7.4 Results and Discussion

Results for groundwater modeling show that the head of groundwater remains constant throughout the years because of the dynamic steady-state equilibrium of groundwater in the aquifer. Also, the flow direction of groundwater in the Nile Delta aquifer is towards the northwest. The resulting infiltration rate from distributed canals and drains is small compared with that from the Rosetta and the Damietta branches because they pass through the high resistance (low vertical permeability of top clay) layer. In addition, simulated water level differs by about 40 cm from the observed water level and errors are generally spread across the model area. The results indicated that any change in the recharge rate will affect the model results significantly rather than the change in the hydraulic conductivities. The simulated versus measured groundwater heads are shown in Fig. 13.

Fig. 13

Contour map of groundwater levels (in meters) in El–Menoufia area (red contours after MODFLOW calculations, and blue contours [36])

For nitrate contamination, Fig. 14 shows the spatial distribution of NO₃ ⁻ contamination in whole Nile Delta in year 2014 at depth 40 m below the ground level. Results showed that the NO₃ ⁻ concentrations at the screen’s elevations of the drinking water supply did not exceed the maximum contamination level of 45 mg NO₃/L. Moreover, there is no significant difference between the simulated and measured NO₃ ⁻ concentrations at 40 m depth. Contamination by NO₃ ⁻ in the study area is shown in Fig. 15 which is related to the high extraction rate from production wells.

Fig. 14

Distribution of NO₃ ⁻ in Nile Delta in year 2014

Fig. 15

NO₃ ⁻ (mg/l) at 40 m depth in year 2014

The comparison (which is shown in Figs. 16 and 17) is between the nitrate concentration in the eight observation wells and the calculated values from the model in year 2014. The max deviation in nitrate concentration between observation and simulated did not exceed 0.22 mg/l, and the other deviations range between 0 and 0.21 mg/l. The value of R² is equal to 0.98.

Fig. 16

Observed and simulated NO₃ ⁻ (mg/l)

Fig. 17

Comparison of observed and simulated NO₃ ⁻ values

8 Conclusion and Recommendation

Traditional practices for groundwater extraction by hand pump (at lower elevations) must be avoided. The abstractions with these pumps are from shallow depths (ex. 15 m), and by this way the vulnerability of groundwater to pollution will be increased. Existing extraction wells should be used according to regulated pumping rates and discharge. In addition, new water supply wells must be drilled to deeper depths in the next decades to avoid groundwater contamination by NO₃ ⁻ in the upper layers. It is a must to give just the required dose of fertilizers which plants need. Finally, chemical analyses of groundwater samples should be taken periodically; including the analysis of NO₃ ⁻, K₂SO₄, (NH₄)₃PO₄, and total dissolved solids, in particular for agricultural lands.