**5. Summary and Conclusions**

This research showed the potential benefits of the solar-powered water-lifting system (MajiPump) and CA technologies on water productivity and crop yields under on-farm conditions of smallholder farmers in Ethiopia. The capacity of two MajiPumps used in this study (MP400 and MP200) were found to extract water up to a maximum depth of 10 m using MP200 with 150 W rigid panel, 14 m using MP400 with 200 W flexible panel, and to 18 m using MP400 with 200 W rigid panel from shallow groundwater wells. The corresponding flow rate discharge capacity for these pumps and panel sizes were in the range of 7.8 L/min to 24.6 L/min, 3 L/min to 15 L/min, and 3.6 L/min, to 22.2 L/min, respectively.

Water and crop productivity were significantly increased under the CA farming system when compared with CT, both using farmers' common overhead irrigation (hose system). Water productivity was improved by 9% to 256%, and crop productivity was improved by 15% to 170% depending on the types of crops, and seasons of production (i.e., dry irrigated and rainfed). This shows the CA farming system has increased significant benefits (watersaving and crop yield increment) to farmers even using traditional overhead irrigation. However, the use of drip irrigation with the CA system further improved water and crop productivity as compared to the combination of the CA system with overhead irrigation. Besides, a significant increase in water productivity was observed in the combined use of MajiPump and CA when compared with the pulley water-lifting system. We conclude that the solar MajiPump with CA and drip irrigation is a promising approach to expand small-scale irrigation that can improve some key vegetable and grain crops of smallholder farmers in Ethiopia [7].

**Author Contributions:** T.T.A. contributed to the experimental design, data analysis and interpretation, and drafted the manuscript; T.F.A. contributed to the experimental design, data acquisition and analysis; A.Y.Y. contributed to experimental design, data collection and analysis; S.A.B. contributed to the data analysis and interpretation, revised the manuscript; Y.M.D. contributed to data collection and revising the manuscript; S.T.H. contributed to data collection and revising the manuscript, S.A.T. contributed to the data analysis and revising the manuscript; M.R.R. contributed to revising the

manuscript; P.V.V.P. contributed to revising the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Appropriate Scale Mechanization Consortium of Feed the Future Innovation Lab for Collaborative Research on Sustainable Intensification (Cooperative Agreement No. AID-OAA-L-14-00006, Kansas State University) funded by United States Agency for International Development (USAID). The opinions expressed herein are those of the author(s) and do not necessarily reflect the views of the USAID or Kansas State University.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Acknowledgments:** We would like to acknowledge the Ethiopian National Meteorological Agency (ENMA) for providing quality data for this research. Contribution no. 21-122-J from Kansas Agricultural Experiment Station.

**Conflicts of Interest:** The authors declare no conflict of interest.

## **References**

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# **Taxonomy and Ecology of Marine Algae**

#### Edited by Bum Soo Park and Zhun Li

Printed Edition of the Special Issue Published in *Journal of Marine Science and Engineering*

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**9.2 Adsorption isotherm**

Since the process of adsorption of natural gas on carbon nanotubes is similar to the adsorption of gas by ANG method, it was considered as a possible type of interaction between nanotubes and natural gas. The adsorption equilibrium depends on the pressure, temperature, and geometry of the adsorbent, which makes adsorption isotherms to be used to obtain the adsorption equilibrium. The Sips equation has the highest consistency with the experimental data to explain the adsorption of natural gas in nanotubes; thus, it can be used to describe the behavior of the adsorption process. The equation of the Sips adsorption isotherm is shown below:

$$\mathbf{q}\_{\mathbf{e}} = \frac{\mathbf{q}\_{\mathbf{m}} (\mathbf{b}\rho)^{\frac{1}{n}}}{\mathbf{1} + (\mathbf{b}\rho)^{\frac{1}{n}}} \tag{1}$$

$$\frac{1}{\mathbf{n}} = \frac{1}{\mathbf{n}\_o} + \alpha \left(\mathbf{1} - \frac{\mathbf{T}}{\mathbf{T}\_o}\right) \tag{2}$$

where b is adsorption/desorption constant (Pa�1 ), n is adsorbate/adsorbent interaction parameter, p is pressure (Pa), qe is adsorption equilibrium(mmol/gr), qm is maximum adsorption (mmol/gr), T is temperature (K), To is reference temperature (K), and bo,no, and α are constant parameters of adsorption isotherm. Eq. (2) proves that the amount of equilibrium adsorption in the original equation is pressure-dependent, and the dependence of the Sips model on parameters b and n on temperature is proved. In addition, the reference temperature is 283.15 K. The other parameters are different depending on the type and structure of the adsorbent, which are shown in **Table 1**.

$$\mathbf{b} = \mathbf{b}\_o \exp\left[\frac{\mathbf{Q}}{\mathbf{R} \mathbf{T}\_\mathrm{O}} \left(\frac{\mathbf{T}}{\mathbf{T}\_o} - \mathbf{1}\right)\right] \tag{3}$$

where Q is isosteric heat adsorption during the half-life of adsorption (kJ/mol), R is universal gas constant (j/mol K), T is temperature (K), and To is reference temperature (K). Absorption is heat, and when the temperature of the adsorption medium increases, isothermal heat has a negative effect on the process and reduces the adsorption capacity. The Clausius-Clapeyron equation is used to calculate isothermal heat. Each of the adsorption equations can be used to calculate the adsorption heat:

*Natural Gas - New Perspectives and Future Developments*

#### **Table 1.**

*Constant parameters of equations [1].*

$$Q\_{st} = RT^2 \left(\frac{\delta ln\rho}{\delta T}\right)\_q \tag{4}$$

$$Q\_{st} = Q - amRT\_o \ln\left(b\_p\right) \tag{5}$$

where Qst is isosteric heat adsorption. Simultaneously with environmental conditions, equilibrium time has a great impact on the process. The kinetic equation (6) is used to obtain the absorption capacity at a given time. This is because after reaching the equilibrium point, the process of gas adsorption by nanoparticles stops, and this time is called the end time of the process:

$$\frac{t}{q\_t} = \frac{1}{k^2 q\_\epsilon^2} + \frac{t}{q\_\epsilon} \tag{6}$$

where qe is adsorption equilibrium (mmol/gr), qt is adsorption capacity (mmol/gr), t is time (min), and k2 is the experimental parameter that varies upon a change in the pressure, and its relationship is obtained by the interpretation of experimental data [1].

#### **9.3 Mass equation**

Natural gas can be stored on carbon nanotubes in the following two ways:

After writing the mass balance according to the hypotheses, the following equation was obtained:

$$\frac{dm\_{\rm g}}{dt} = \pm m\_{\rm g}^{\cdot} - m\_{\rm s} \frac{da}{dt} \tag{7}$$

$$\mathfrak{a} = \mathbf{M}\_{\mathfrak{g}} \times \mathfrak{q}\_{\mathfrak{t}} \tag{8}$$

$$\frac{da}{dt} = \mathbf{M}\_{\mathbf{g}} \times \frac{dq\_t}{dt} \tag{9}$$

*Storage of Natural Gas by CNTs DOI: http://dx.doi.org/10.5772/intechopen.103814*

$$\frac{da}{dt} = \mathcal{M}\_{\text{g}} \frac{dq\_t}{dt} = \mathcal{M}\_{\text{g}} \left[ \frac{q\_t}{t} - \frac{q\_t^2}{q\_e^t} \right] \tag{10}$$

where ṁg is inlet (outlet) gas flow (gr/s), mg is the amount of gas stored in the vessel as gas phase (gr), ms is loaded mass of nanoparticles in the vessel (gr), a is adsorbed gas relative to adsorbent mass (gr gas/gr adsorbent), and Mg is molecular weight (gr/mol) [1].

#### **9.4 Energy equation**

To investigate the thermal behavior of the vessel, the energy equation in one dimension and the radial direction were used based on Eq. (11):

$$r\left(\varepsilon\rho\_{\rm g}\mathbf{C}\_{\rm g} + \rho\mathbf{C} + \rho\_{\rm a}a\mathbf{C}\_{\rm a}\right)\frac{\delta T}{\delta t} + r\rho\_{\rm g}\theta\mathbf{C}\_{\rm g}\frac{\delta T}{\delta r} = \frac{\delta}{\delta r}\left(r\lambda\frac{\delta T}{\delta r}\right) + \theta\mathbf{Q}\_{\rm st}\rho\frac{\delta a}{\delta t} \tag{11}$$

where C is the specific heat kJ/kg. K, r is radius (m), *v* is velocity of fluid (m/s), α is the relationship between viscosity and permeability, ε is overall porosity, λ is overall thermal conductivity (W/mK), and ρ is density (kg/m3 ). Using the Darcy equation, the mass velocity of the fluid inside the porous medium can be obtained. Because the Reynolds range was small during the process, the Darcy equation is used:

$$
\theta = -\frac{1}{a}\Delta \tag{12}
$$

$$a = \frac{150\mu}{4} \frac{\left(1 - \varepsilon\_b\right)^2}{\varepsilon\_b^3 R\_p^2} \tag{13}$$

where Δρ is pressure difference (Pa), εb is bed porosity. These laboratoryobtained equations correspond to the experimental results in the main fields for spherical nanoparticles, and their equivalent diameter must be used for nonspherical nanoparticles. Eq. (14) can be used to obtain the equivalent radius of the nanotubes:

$$R\_p = \frac{1}{2} \left( \frac{L}{\ln\left(\frac{2L}{d}\right)} \right) \tag{14}$$

where Rp is the radius of the particle (m), d is external diameter of nanotubes (nm), and L is nanotube length (nm) [1].

#### **9.5 Initial and boundary conditions**

To answer the energy equation, we must first determine the boundary values. For this purpose, the boundary conditions of the system, in the initial network and based on the Eq. (15), was calculated:

$$\frac{\delta T}{\delta r}(r\_i, t) = 0 \tag{15}$$

Two thermal resistors named R1 and R2, which show the conductivity and convection resistance, respectively, are used between the end points (vessel wall) and the fluid. The resistors are closed in series, and the resistance of each of them can be obtained by merging with each other. As **Figure 6** shows, the heat conduction and convection in the wall are balanced, and the thermal equilibrium is applied to the Eq. (16):

$$
\lambda\_{\rm eff} \frac{\delta \mathbf{T}}{\delta \mathbf{r}}(\mathbf{r\_o}, \mathbf{t}) = \mathbf{U}(\mathbf{T\_{r\_o}} - \mathbf{T\_f}) \tag{16}
$$

$$\mathbf{U} = \frac{\mathbf{1}}{\mathbf{R}\_s} \tag{17}$$

$$\mathbf{R\_s = R\_1 + R\_2} \tag{18}$$

$$\mathbf{R\_1} = \frac{\mathbf{r\_o} \ln \left(\frac{\mathbf{r\_w}}{\mathbf{r\_o}}\right)}{\lambda\_\mathbf{w}} \tag{19}$$

$$\mathbf{R\_2} = \frac{1}{\mathbf{h\_o}}\tag{20}$$

where ho is convection heat transfer coefficient of surrounding fluid of vessel (w/m.K). ro is external radius of the vessel (m), Rs is equivalent resistance, rw is inner radius of vessel (m), Tf is bath temperature of vessel (K), U is the overall heat transfer coefficient (W/m2 .k), λeff is effective heat transfer conduction coefficient (W/m.K), and λw is the thermal conductivity of the vessel's wall (W/m.K) [1].

#### **9.6 Nanotube's properties**

The smallest inner diameter of the nanotube has been reported to be 0.4 nm, and the distance between the nanotubes is equal to 0.34 nm. Hence, to obtain the number of the nanotube wall, Eq. (21) is used. As the nanotube diameter increases, the number of wall increases:

$$N\_{wall} = \frac{1}{d\_d}(d\_{\text{ext}} - d\_{\text{int}}) + \mathbf{1} \tag{21}$$

**Figure 6.** *Thermal boundary conditions in external environment of vessel [1].*

*Storage of Natural Gas by CNTs DOI: http://dx.doi.org/10.5772/intechopen.103814*

where NWall is the number of nanotubes wall, dd is the distance between the walls (nm).

$$\rho = \frac{4000}{1315} \left[ \frac{N\_{\text{wall}}}{d\_{\text{ext}}} - \frac{2d \sum\_{i=0}^{N\_{\text{wall}}^{-1}} i}{d\_{\text{ext}}^2} \right] \tag{22}$$

dext is external diameter of the nanotube (nm), and dint is internal diameter of the nanotube (nm). The weight and density of nanotubes depend on the internal and external diameter of nanotubes and the number of walls.

The properties of methane, natural gas, and carbon nanotubes are given in **Tables 2** and **3**. Nanotubes made of silicon can be called a competitor to carbon nanotubes, because there are many similarities between carbon and silicon. In this experiment, which is performed in a laboratory environment, pure methane gas is used, but on a large and industrial scale, natural gas must be used. By looking at **Table 4**, the natural gas composition used in this experiment can be obtained [1].


**Author details**

Heoncheol Lee

Department of IT Convergence Engineering, School of Electronic Engineering, Kumoh National Institute of Technology, Gumi, Gyeongbuk, South Korea

\*Address all correspondence to<EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


2.2.4. Topographic Data

Some research indicated that using topographic variable data, such as the digital elevation model (DEM) produces major classification enhancements [32,53]. Therefore, shuttle radar topography mission (SRTM) one-arcsecond DEM tiles were resampled to a 10-m spatial resolution by the bilinear interpolation. Additionally, during the test phase of the research, slope and aspect were derived from the SRTM DEM, but their presence as input features brought noise in the dataset, which led to lower classification accuracy. Therefore, the aforementioned features (i.e., slope and aspect) were not further considered as input features for vegetation mapping.


**3. Line impedance emulator modeling**

The GsC power circuit single phase representation is depicted on **Figure 5**, where *Lg* denotes the grid impedance. According to this figure, the GsC electric equation in the *abc* reference frame is given by Eq. (1).

$$U\_i = V\_\text{g} - L\_\text{g} \frac{di\_\text{g}}{dt} \tag{1}$$

*i*1 ¼ *Vi* � *Vc sL*1

*Line Impedance Emulator: Modeling, Control Design, Simulation and Experimental Validation*

*Vc* ¼ *ic sCf*

*i*2 ¼ *Vc* � *VE sL*2

**Figure 8** shows the GsC control. It incorporates two control loops. The internal loop controls in the *abc* reference frame the grid currents *ig*(*abc*) and it is based on

**4. Line impedance emulation control**

**4.1 Grid side converter control**

**Figure 6.**

**Figure 7.**

**Figure 8.**

**135**

*Block diagram of GsC control.*

*EsC power circuit single phase representation.*

*DOI: http://dx.doi.org/10.5772/intechopen.90081*

*LCL-EsC simplified block diagram.*

*i*1 ¼ *i*2 þ *ic* (3)

(2)

(4)

(5)

The EsC power circuit single phase representation is given by **Figure 6**. Based on this Figure, the equations related to the EsC are given by Eq. (2), Eq. (3), Eq. (4) and Eq. (5). The obtained single phase simplified block diagram of the LCL-EsC is depicted on **Figure 7**.

**Figure 5.** *GsC power circuit.*

*Line Impedance Emulator: Modeling, Control Design, Simulation and Experimental Validation DOI: http://dx.doi.org/10.5772/intechopen.90081*

#### **Figure 6.**

*EsC power circuit single phase representation.*