Presentazione di PowerPoint

Feasibility study to reduce Hospital’s
load of wood biomass in Burundi
Fabio Riva
Prof.ssa Emanuela Colombo
Ing. Matteo Rocco
Dott. Gianmario Stefanelli
2
Summary
“Affordable and reliable
modern energy services
are essential for
alleviating poverty,
improving health and
raising living
standards”
Ban Ki-moon
18 February 2014
TO INCREASE ACCESS TO MODERN ENERGY IN
BURUNDI
Ultimate
goal
General
context
Goals
of the
thesis
- Access to energy
- Burundi
- Energy sources assessment
- Technologies analysis
- Decision process
Fabio Riva
3
Access to energy
1.3 billion people are without
access to electricity
no access to WATER and
IMPROVED SANITATION
FACILITY, EDUCATION
source: WEO2013 – Energy For All
Fabio Riva
4
Access to energy
2.6 billion people are without access to clean cooking facilities
source: WEO2013 – Energy For All
Fabio Riva
5
Access to energy
Impact on Health:
- 4.3 million people a year die prematurely from illness attributable
to the household air pollution caused by the inefficient use of solid
fuels (WHO 2014)
Social impact:
-
wood collection is highly time-consuming. Especially for
women and children, this limits their time available for education (FAO
2012)
Environmental impact:
more pressure on deforestation and desertification of lands (Allen
and Douglas 2010 – WHO 2006)
Fabio Riva
Burundi – a general and energy assessment
6
<1% of the population have access to Modern Cooking
source: IIASA UNIDO 2012
70.8% of TPES is met by FUEL WOOD
source: IRENA 2009
A GREAT PRESSURE ON DEFORESTATION
2.02% deforestation rate, the highest in Africa
source: WB 2013
Population (million)
10.16
GDP per capita (US$)
Life expectancy at birth (years)
Enrolment in secondary school (%)
251.0
53
28%
Human Development Index
-
0.355
Fabio Riva
soil erosion
siltation
social problems
7
Analysis of the problem
MUTOYI MISSION
V.I.S.P.E. NGO
- Problem Tree source: European Commission – Project Cycle Management Guidelines
Fabio Riva
8
Goals of the thesis
Three main goals
Finding energy
substitutions to
traditional fuels
in Burundi
Determination of
the appropriate
technological setup
Analysis of the
benefits of
technologies
and final
decision
Analysis of the
available and
affordable energy
resources in Burundi
Analysis of the
context
Prefeasibility study
and test of
homemade solar
cookers
Trnsys simulation
Economic,
environmental and
energy analysis
First approach
Decision making
process
Fabio Riva
9
1. Energy sources analysis
Fossil fuels:
Wind energy:
-
Not affordable (excessive cost of
diesel)
-
Weak supply chain (es: no gas
grid)
-
Low wind speed on the hill of
Mutoyi†
Only used for
emergency
Not suitable for
electric generation
†source: NASA Database
Fabio Riva
10
1. Energy sources analysis
Solar energy:
-
2,000 kWh/m2year
-
140,000 m2 of solar heat
collectors from 2003 †
Biomass:
-
No electrical applications
-
It is required to improve the
efficiency of the devices which
use traditional fuels
Hydroelectricity: -
-
Suitable thermal
applications
Improved Cook
Stoves (ICSs)
pollutant emissions
fuel usage, land degradation
+
health
children and women empowerment
85% of Total Installed Capacity
Suitable applications
during the night
(31.5 MW on 37MW)††
Future 700 kW plant that will
supply Vispe with free
electricity
Night surplus
Fabio Riva
†
source: UNDP 2012
†† source: African Development Bank 2009
1. Energy sources analysis
11
source: Burundian Ministry of Energy and Mines
 Night electric surplus : - Not imported energy
- Actual weak electric grid NOT overloaded during the night
Fabio Riva
2. Determination of the appropriate technological set-up
12
Analysis of the context – current technologies
1. PaMu center
-
Lunch for the hospital
Construction
materials
Thermal
efficiency
• Metal plate, bricks
• 8 - 12%
2. Hospital
- Tea and milk for patients
Construction
materials
Thermal
efficiency
• Metal, insulating
materials, bricks
• 30 - 42 %
3. Patients' relatives kitchen
- Dinner for patients
Construction
materials
• stones, mud
Thermal
efficiency
• 10-18 %
CO emissions
• 0 mg/gFUEL
CO emissions
• 0 mg/gFUEL
CO emissions
• 35 - 80 mg/gFUEL
PM emissions
• 0 mg/gFUEL
PM emissions
• 0 mg/gFUEL
PM emissions
• 1-2 mg/gFUEL
Literature research about stoves studies and testing energy efficiencies:
1.
2.
3.
Fuel use and emissions performance of fifty cooking stoves in the laboratory and related benchmarks of performance [Aprovecho Center 2010]
Solid-fuel household cook stoves: Characterization of performance and emissions [U.S. Environmental Protection Agency 2008]
Stove Performance Inventory Report [Berkeley Air Monitoring Group 2012]
Fabio Riva
2. Determination of the appropriate technological set-up
13
Analysis of the context – physical properties
Need for a realistic value for the LHV
wood diffused in Burundi and used at Mutoyi: Eucalyptus
•
LHVdry = 18 MJ/kg†
•
XH2O is directly related to the humidity and
temperature of the surrounding air
†
𝐿𝐻𝑉 = 𝐿𝐻𝑉𝑑𝑟𝑦 1 − 𝑥𝐻2𝑂 − 𝑥𝐴𝑆𝐻
− 𝑥𝐻2𝑂 𝛥𝐻𝑒𝑣𝑎 = 𝟏𝟓 − 𝟏𝟔 𝑴𝑱/𝒌𝒈
†sources: BM Jenkins, LL Baxter, TR Miles Jr
et al., “Combustion properties of biomass,” Fuel processing technology
Phyllis database (Energy Research Centre of the Netherlands). https://www.ecn.nl/phyllis2/
Fabio Riva
2. Determination of the appropriate technological set-up
Analysis of the context – water and
wood needs
14
Monthly average of daily number of patients
! no data apart August 2013
Proxy is needed
 PaMu center:
1.
2.
Needs constant during the year
Needs change proportionally to the number of
patients
 Hospital:
•
•
𝟎. 𝟔 𝒍𝒊𝒕𝒆𝒓𝒔 𝒑𝒆𝒓 𝒑𝒂𝒕𝒊𝒆𝒏𝒕𝒔 ∗ 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒑𝒂𝒕𝒊𝒆𝒏𝒕𝒔 → EII is known for each month
𝑬𝑰 = 𝑬𝑰𝑰 + 𝑬𝑳𝑶𝑶𝑺+𝑩𝑶𝑰𝑳
dividing by EII
𝒙=𝟏+𝒛
z equal to the value of August 2013 for each
month  evaluating x for each month and EI
𝑬𝑰 = 𝒙 ∗ 𝑬𝑰𝑰
𝒎𝒘𝒐𝒐𝒅 = 𝑬𝑰 𝑳𝑯𝑽
 Patients’relatives:
NO DATA
Fabio Riva
with EI = primary energy of wood
EII = secondary energy of
water
ELOSS + BOIL = sum of boiling
and lost energy
mwood = mass of wood
LHV = Low Heating Value of
wood
2. Determination of the appropriate technological set-up
15
Analysis of the context – considerations
 Achievements
1-2. PaMu center and the Hospital: technological improvements must avoid a replacement of
the stoves  TECHNOLOGICAL IMPLEMENTATION FOR
PREHEATING PURPOSES
3. Patients’ relatives’ kitchen:
the Open Fire stoves could be replaced
Fabio Riva
16
2. Determination of the appropriate technological set-up
Analysis of the context – appropriate technological set-up
Available and
affordable
energy
resources
PaMu center and
Hospital
Patients’relatives’
kitchen
Local needs
and
technologies
A.
B.
C.
D.
E.
F.
Individuation of
the new
appropriate
technological
set-up and
dimensioning
Electrical water heater
Heat Pump water heater + electrical resistances
Heat Pump water heater
Electrical water heater + solar
Heat Pump water heater + solar
Solar collectors and storage
1. Improved Cook Stoves
! Acceptability
2. Solar Stoves
Fabio Riva
Prefeasibility study
2. Determination of the appropriate technological set-up
17
Prefeasibility study and test of homemade solar cookers
Dangerous
Expensive
PANEL STOVE
BOX STOVE
1. CO, PM, SO2, fly ash, smoke
savings
2. CO2 reduction
3. Firewood reduction
4. Wood cost savings
5. Time saved
6. Easily and cheaply self-built
Fabio Riva
1.
2.
3.
4.
5.
6.
PARABOLIC STOVE
Time of day limits
It takes longer
Disruption by weather changes
Conflict with traditional three stone fire
Food outside the home
Manufacturers unknown
2. Determination of the appropriate technological set-up
18
Prefeasibility study and test of homemade solar cookers
Self construction and Optimization of solar cookers
Celestino Ruivo Panel Cooker
Engineer and Doctor of the University of Algarve
Just optimized
1+co s(𝛽
si n(𝛽
= ta n( 270 − 2𝛽 − 𝛼𝑠 )
with
Box cooker
Fabio Riva
αs = solar altitude
β = tilt of the mirror
2. Determination of the appropriate technological set-up
19
Prefeasibility study and test of homemade solar cookers
“Standard procedure for Testing and Reporting Solar Cooker Performance” (ASAE)
Experimental campaign
1. Variables:
Loading:
7 kg potable water per square meter intercept area
Insolation:
Direct Normal Irradiation (DNI) >450W/m2
Time:
10:00 – 14:00
11-15-16-17-18 July 2014
DEPARTMENT OF ENERGY
2. Recording at intervals not to exceed ten minutes: the average water temperature
(oC) of cooking vessels, solar insolation (W/m2), ambient temperature (oC)
3. Calculating cooking power
with
m = load of water during the test
Ii = mean solar insolation
4. Reporting in a graphic Ps as a function of the difference between the water and
the air temperature (𝑻𝒅 = 𝑻𝒘 – 𝑻𝒂 )
5. The Mean Cooking Power is defined as the value of Ps evaluated at a Td equal to
50 oC that represents the integral average of the power on the time
Fabio Riva
T2= temperature of water after
ten minutes
T1= temperature of water at
the start
Tw = temperature of water
Ta = air temperature
2. Determination of the appropriate technological set-up
Prefeasibility study and test of homemade solar cookers
20
Experimental campaign
11-15-16-17-18 July 2014
DEPARTMENT OF ENERGY
Fabio Riva
2. Determination of the appropriate technological set-up
21
Prefeasibility study and test of homemade solar cookers
Experimental campaign
Test of cooking time for Panel Stove
1) 𝑬 = 𝑸𝒘 + 𝑸𝒃
E = total energy required to bring water and beans from 20 oC to 90 oC
11-15-16-17-18 July 2014
DEPARTMENT OF ENERGY
Qw = energy required to bring 400 ml of water from 20 oC to 90 oC
Qb = energy required to bring 300 g of beans from 20 oC to 90 oC
ηPANEL
IBURUNDI
Ps
IBURUNDI = Monthly Averaged Midday Direct
Normal Irradiation
[W/m2]†
beans can be estimated: 61 – 74 min
60 – 72 min
2)
3)
Dividing E by Ps, the monthly mean time required to cooking
Experimental test  Δt ~ [+4%÷+9%]
†source: NASA Database
Fabio Riva
22
3. Analysis of the benefits of Technologies and final decision
Trnsys simulation
Example of dimensioning of heat
pump wateronheater
Temperature
the storage (oC)
Tilt of surface
(Solar Electricity
Heating
Heating
rating
 20°rating
VHandbook)
[L]
200
[kW] at
7°C
[kW] at
20°C
2.1
2.45
Time
Time
Thermal
Heating
Heating
losses
[kWh/24h]
HPPhysical
at 7°C
HP
at 20°C
properties
and
268
minperformances
203 min
0.52
Max
Temp.
HP [°C]
Monthly Electrical
consumptions (kWh)
55
source: ARISTON NUOS EVO SPLIT 200l
Weather and solar
geometry data
(METEONORM)
1. Interpolating the values of the HEATING RATING,
TIME HEATING and COP it is possible to estimate
the real values of them for each month on the base
of the air temperature
2. Dividing the HEATING RATING by the COP we obtain
the ELECTRICAL POWER CONSUMPTIONS
for each
Hourly water needs
month
𝑃𝑒𝑙 =
Fabio Riva
𝑄𝑢
𝐶𝑂𝑃
with Qu = Heating Rating
input
output
3. Analysis of the benefits of Technologies and final decision
23
Energy analysis of technologies
CRITERION 1
PaMu and Hospital solution
𝐸𝐼𝐼 = 𝑚𝐻2 𝑂 ∗ 𝐶𝑝 ∗ 𝑇𝑡𝑒𝑐ℎ − 𝑇𝑎𝑞𝑢𝑖𝑓𝑒𝑟
𝛥𝑚𝑤𝑜𝑜𝑑 =
𝑺𝒘𝒐𝒐𝒅
𝐸𝐼𝐼
𝜂𝑆𝑇𝑂𝑉𝐸
∗
with
1
𝐿𝐻𝑉
EII = secondary energy of water [MJ]
Ttech = max. temper. of technology [oC]
𝛥𝑚𝑤𝑜𝑜𝑑 = wood mass saved [kg]
mwood = wood actually used [kg]
𝜂𝑆𝑇𝑂𝑉𝐸 = efficiency of the stove [-]
𝐿𝐻𝑉 = Low Heating Value [MJ/kg]
𝑆𝑤𝑜𝑜𝑑 = savings of wood [%]
𝜟𝒎𝒘𝒐𝒐𝒅
=
𝒎𝒘𝒐𝒐𝒅
Patients’relatives kitchen
𝐸𝐼𝐼𝑂𝐹 = 𝐸𝐼𝐼𝐼𝐶𝑆  secondary energy balance
with
𝐸𝐼𝑂𝐹 ∗ 𝜂𝑂𝐹 = 𝐸𝐼𝐼𝐶𝑆 ∗ 𝜂𝐼𝐶𝑆
𝑚𝑤𝑜𝑜𝑑𝑂𝐹 ∗ 𝐿𝐻𝑉 ∗ 𝜂𝑂𝐹 = 𝑚𝑤𝑜𝑜𝑑𝐼𝐶𝑆 ∗ 𝐿𝐻𝑉 ∗ 𝜂𝐼𝐶𝑆
𝒎𝒘𝒐𝒐𝒅𝑰𝑪𝑺 − 𝒎𝒘𝒐𝒐𝒅𝑶𝑭
𝜼𝑶𝑭
= 𝟏−
𝒎𝒘𝒐𝒐𝒅𝑶𝑭
𝜼𝑰𝑪𝑺
Swood
Fabio Riva
OF = Open Fire
ICS = Improved Cook Stove
3. Analysis of the benefits of Technologies and final decision
24
Environmental and Economic Analysis
CRITERION 2
Greenhouse emissions
𝑥𝐶𝑂2 = 𝟎. 𝟗𝟓† 𝑘𝑚𝑜𝑙𝐶𝑂2 𝑘𝑚𝑜𝑙𝐶 ∗
44 𝑘𝑔𝐶𝑂2 𝑘𝑚𝑜𝑙𝐶𝑂2
= 3.48 𝑘𝑔𝐶𝑂2 𝑘𝑔𝐶
12 𝑘𝑔𝐶 𝑘𝑚𝑜𝑙𝐶
Eucalyptus Carbon content [%wt]= 46.2
𝑺𝑪𝑶𝟐 = 𝑺𝒘𝒐𝒐𝒅 ∗ 𝒎𝒘𝒐𝒐𝒅 ∗ 𝟎. 𝟒𝟔𝟐 ∗ 𝟑. 𝟒𝟖 ∗ 𝒙𝑪𝑶𝟐
with
mwood = wood actually used [kg]
𝑆𝑤𝑜𝑜𝑑 = savings of wood [%]
Economic analysis
CRITERION 3
Money savings for wood supply = Swood * yearly_cost_of_wood
CRITERION 4
Cost of Electricity =
CRITERION 5
Investment (cost of technology)
E el [kWh]* FBU/kWh††
with
𝑆𝑤𝑜𝑜𝑑 = savings of wood [%]
Eel = Electric energy consumed [kWh]
† source: Mark Bryden, Mike Van, Jayme Vineyard 2005
Nordica MacCarty, Damon Ogle, Dean Still 2008
BM Jenkins, LL Baxter, TR Miles Jr 1998
††
Fabio Riva
source: Burundian Ministry of Energy and Mines
3. Analysis of the benefits of Technologies and final decision
25
Results
PaMu center
CRITERION
1
Electrical
A. water
heater
Heat Pump
B. + electrical
resistances
C. Heat Pump
Electrical
water
D.
heater +
solar
Heat Pump
E.
+ solar
Solar
F. collectors
and storage
CRITERION
2
CRITERION
3
Hospital
CRITERION
4
CRITERION
5
CRITERION CRITERION
1
2
Money
Cost of
Cost of
savings
electricity technology Swood [%]
for wood
[€]
[€]
supply [€]
Swood [%]
SCO2
[ton]
16.9%
-26.4
314
11.5%
16.9%
-17.9
-26.5
213
314
11.5%
-18.0
213
Cook 224
12.0%Improved
-18.9
1.
8.1%Stoves-12.8
151
17.4%
-27.3
324
11.8%
-18.5
220
14.9%
10.1%
11.0%
-23.5
-15.9
-17.4
279
188
206
7.4%
-11.7
139
939
494
SCO2
[ton]
31.5%
-9.6
24.7%
CRITERION 1
31.5%
2x2471
Swood [%]24.7%
-7.5
-9.7
20.4%
16.0%
-6.3
67%
-4.9
33.1%
-10.2
26.0%
-7.9
28.6%
22.5%
20.3%
-8.8
-6.9
-6.2
15.9%
-4.9
1150
180 10% 2x2471
490
4721
73
8300
3
3500
-7.6
COMPLEXITY OF CHOICE
Fabio Riva
CRITERION
3
CRITERION
4
CRITERION
5
Money
Cost of
Cost of
savings
electricity technology
for wood
[€]
[€]
supply [€]
-
705
910
-
391
3413
-
157
3413
-
313
4721
-
44
8300
-
3
2610
26
3. Analysis of the benefits of Technologies and final decision
PaMu center
First approach to a decision
making process
CRITERION
1
Swood [%]
CRITERION
2
CRITERION
3
CRITERION
4
CRITERION
5
Hospital
CRITERION CRITERION
1
2
Money
Cost of
Cost of
savings
electricity technology Swood [%]
for wood
[€]
[€]
supply [€]
First analysis - [ton]
QUANTITATIVE INDICATORS
SCO2
HP: 700kW hydroelectric plants will be realized
Electrical
A. water
heater
Heat Pump
B. + electrical
resistances
C. Heat Pump
Electrical
water
D.
heater +
solar
Heat Pump
E.
+ solar
Solar
F. collectors
and storage
16.9%
-26.4
314
11.5%
-17.9
16.9%
-26.5
Reduction-18.0
in
11.5%
the use of
wood biomass
12.0%
-18.9
8.1%
-12.8
213
314
939
1150
494 Money
2x2471
213
savings for
Investments
the supply of
224
wood
180
2x2471
151
17.4%
-27.3
324
11.8%
-18.5
220
14.9%
10.1%
11.0%
-23.5
-15.9
-17.4
279
188
206
7.4%
-11.7
139
ENVIRONMENTAL
490
4721
ECONOMIC
73
8300
3
3500
SCO2
[ton]
31.5%
-9.6
24.7%
31.5%
-7.5
-9.7
Cost of -7.6
24.7%
electricity
20.4%
-6.3
16.0%
-4.9
33.1%
-10.2
26.0%
-7.9
28.6%
22.5%
20.3%
-8.8
-6.9
-6.2
15.9%
-4.9
CRITERION
3
CRITERION
5
Money
Cost of
Cost of
savings
electricity technology
for wood
[€]
[€]
supply [€]
705
Creation of
Creation
of
Capacity
Capacity
- and 391
Building
Building and
dissemination
dissemination
of
new
newoftechnical
157
technical
know how
know how
-
910
3413
3413
313
4721
-
44
8300
-
3
2610
SOCIAL
- Electrical Water Heater with solar integration
- Electrical Water Heater
Fabio Riva
CRITERION
4
27
3. Analysis of the benefits of Technologies and final decision
PaMu
PaMu center
center
First approach to a decision
making
process
CRITERION CRITERION
CRITERION
CRITERION
11
22
[%]
SSwood
wood [%]
SSCO2
CO2
[ton]
[ton]
CRITERION
CRITERION
33
CRITERION
CRITERION
44
CRITERION
CRITERION
55
Hospital
Hospital
CRITERION CRITERION
CRITERION CRITERION
CRITERION
CRITERION
11
22
33
Money
Money
Cost of
of
Cost of
of
Cost
Cost
savings
savings
electricity
technology
Swood[%]
[%]
for wood
wood electricity technology Swood
for
[€]
[€]
[€]
[€]
supply [€]
[€]
supply
SSCO2
CO2
[ton]
[ton]
Second
analysis
–-26.4
SOCIAL314
INDICATORS and DIFFUSION
Electrical
-26.4
314
31.5%
-9.6
16.9%
31.5%
-9.6
A. water
heater
Heat Pump
B. + electrical
resistances
C. Heat
Heat Pump
Pump
C.
D.
D.
E.
E.
F.
F.
Electrical
Electrical
water
water
heater ++
heater
solar
solar
Heat Pump
Pump
Heat
+
solar
+ solar
Solar
Solar
collectors
collectors
and storage
storage
and
11.5%
16.9%
-17.9
-17.9
-26.5
-26.5
213
213
314
314
11.5%
-18.0
213
-18.0
213
Reductionin
in
Reduction
12.0%
-18.9 Investments
224
the use
use of
of-18.9
the
12.0%
224
wood
wood
biomass
8.1%biomass
-12.8
151
8.1%
-12.8
151
17.4%
-27.3
324
17.4%
-27.3
324
11.8%
11.8%
-18.5
-18.5
220
220
14.9%
14.9%
10.1%
10.1%
11.0%
11.0%
7.4%
7.4%
-23.5
-23.5
-15.9
-15.9
-17.4
-17.4
-11.7
-11.7
279
279
188
188
206
206
139
139
939
939
1150
1150
494
494
2x2471
2x2471
Money
savings for
the
of
180
2x2471
180 supply
2x2471
wood
490
490
4721
4721
73
73
8300
8300
33
3500
3500
24.7%
24.7%
31.5%
31.5%
-7.5
-7.5
-9.7
-9.7
CRITERION
CRITERION
44
Money
Money
Costof
of
Costof
of
Cost
Cost
savings
savings
electricity
technology
forwood
wood electricity technology
for
[€]
[€]
[€]
[€]
supply[€]
[€]
supply
--
705
705
Creation of
391
-391
Capacity
24.7%
-7.6
24.7%
-7.6
Building and
Cost of -6.3 dissemination
20.4%
20.4%
-6.3 – 1150- – 910 =157
8300
+8300
…
electricity
157
of-new
16.0%
-4.9
16.0%
-4.9
technical
33.1% -10.2
-10.2 know how
33.1%
313
-313
26.0%
-7.9
26.0%
-7.9
28.6%
28.6%
22.5%
22.5%
20.3%
20.3%
15.9%
15.9%
-8.8
-8.8
-6.9
-6.9
-6.2
-6.2
-4.9
-4.9
910
910
3413
3413
3413
3413
4721
4721
--
44
44
8300
8300
--
33
2610
2610
Heat pump
waterless
heater +than
solar € 14,000?
Is all of this
worth
Fabio Riva
CRITERION
CRITERION
55
Thank you for your
attention
Grazie VISPE e FLAEI
29
𝛾 = 180 − 90 − 𝛽 = 90 − 𝛽
𝜃 = 𝛾 + (90 − 𝛼𝑠
𝐴𝐶𝐵 = 𝛾 + 𝜃 = 𝛾 + 𝛾 + 90 − 𝛼𝑠 = 270 − 2𝛽 − 𝛼𝑠
𝐴𝐵 = 𝐴𝐵′ + 𝐶𝐵′ ∗ cos(𝛽
𝐵𝐶 = 𝐶𝐵′ ∗ sin(𝛽
with 𝛼𝑠 the minimum value of July equal to 38.18°. Thanks to
trigonometric formula:
𝐴𝐵
= tan(𝐴𝐶𝐵
𝐵𝐶
and finally, considering that 𝐴𝐵′ = 𝐶𝐵′ :
1+co s(𝛽
si n(𝛽
= ta n( 270 − 2𝛽 − 𝛼𝑠 )
30
𝛾 = 180 − 90 − 𝛽 = 90 − 𝛽
𝜃 = 𝛾 − (90 − 𝛼𝑠
𝐴𝐶𝐵 = 𝛾 + 𝜃 = 𝛾 + 𝛾 − 90 + 𝛼𝑠 = 90 − 2𝛽 + 𝛼𝑠
𝐴𝐵 = 𝐴𝐵′ + 𝐶𝐵′ ∗ cos(𝛽
𝐵𝐶 = 𝐶𝐵′ ∗ sin(𝛽
with 𝛼𝑠 the maximum value of August equal to
72.73°. Using the same trigonometric formula
used above:
𝐴𝐵 ′ +𝐶𝐵 ′ ∗co s(𝛽
𝐶𝐵 ′ ∗si n(𝛽
= ta n( 90 − 2𝛽 + 𝛼𝑠 )
2
∗ co s( 𝛽
3
= ta n( 90 − 2𝛽 + 𝛼𝑠
2
∗ si n( 𝛽
3
1+
31
Reduction in
the use of Investments
wood
Money
savings for
the supply
of wood
Electrical Water
Heater
2 (21.15%)
1 (2060€)
2 (263.6€)
HP + Electrical
Resistors
2 (21.15%)
3 (8355€)
2 (263.6€)
HP
4 (14.13%)
3 (8355€)
4 (187.6€)
Electrical Water
Heater + Solar
1 (22.08%)
4 (9442€)
1 (266.5€)
HP+ Solar
3 (19.03%)
5 (16600€)
3 (233.5€)
Only solar and
buffer
5 (13.65%)
2 (6110€)
5 (172.2€)
32
∆𝑚𝑤𝑎𝑡𝑒𝑟𝑖 ∗ 𝐶𝑝 ∗ ∆𝑇
1
1
∗
∗
𝜂𝑆𝑇𝑂𝑉𝐸
𝐿𝐻𝑉 𝑚
𝒃 ∗ ∆𝑚𝑤𝑎𝑡𝑒𝑟𝐴𝑈𝐺 ∗ 𝐶𝑝 ∗ ∆𝑇
1
1
𝑆𝑖 =
∗
∗
𝜂𝑆𝑇𝑂𝑉𝐸
𝐿𝐻𝑉 𝒄 ∗ 𝑚𝑤𝑜𝑜𝑑𝐴𝑈𝐺
𝑆𝑖 =
with
𝒃
𝒄
𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠𝑖
𝒌=
𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠𝐴𝑈𝐺
𝑆𝑖 ∝
𝛥𝑇= temperature gap [oC]
𝛥𝑚𝑤𝑎𝑡𝑒𝑟 = water mass heated [kg]
m = wood actually used [kg]
𝜂𝑆𝑇𝑂𝑉𝐸 = efficiency of the stove [-]
𝐿𝐻𝑉 = Low Heating Value [MJ/kg]
𝑆𝑖 = savings of wood [%]
1 ≤𝑐 ≤𝑘
1 ≤𝑏 ≤𝑐
if 𝑁. 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠𝑖 > 𝑁. 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠𝐴𝑈𝐺

1 𝑏
≤ ≤1
𝑘 𝑐
𝑏≥1
Because 𝑐 ≤ 𝑘
𝑏≤𝑐

𝑏 1
1≤ ≤
𝑐 𝑘
𝑏≤1
Because 𝑐 ≥ 𝑘
𝑏≥𝑐
(𝑘, 𝑏, 𝑐 > 1
if 𝑁. 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠𝑖 < 𝑁. 𝑝𝑎𝑡𝑖𝑒𝑛𝑡𝑠𝐴𝑈𝐺
(𝑘, 𝑏, 𝑐 < 1
33
Wood or charcoal - which is better?
𝑤𝑜𝑜𝑑 ∶ 1 𝑘𝑔 ∗ 15
wood
𝑀𝐽
∗ 15%
10% = 2,25
1,2 𝑀𝐽
𝑀𝐽
𝑘𝑔
LHV
Efficiency of the stove
𝑀𝐽
30% ∗ 28 ∗ 15%
20% = 0,84
1,68 𝑀𝐽
charcoal∶ 1𝑘𝑔 ∗ 20%
𝑘𝑔
conversion
Source: J.D. Keita - Regional Forestry Officer at the FAO Regional Office for Africa, Accra, Ghana
34
Monthly mean higher temperatures that can be reached in the storages [°C]
Solar collectors
and heat pump
Only solar
collectors
Jan
Only
solar
collectors
47.9
Hospital
Solar collectors
and electrical
water heater
75.5
Solar collectors
and heat pump
47.9
PaMu
Solar collectors
and electrical
water heater
75.4
64.4
63.3
Feb
50.1
76.1
65.7
50.1
75.9
64.4
Mar
53.2
77.9
69.3
53.2
77.3
66.9
Apr
54.8
77.8
69.6
54.8
77.1
66.6
May
60.2
79.0
73.3
60.2
78.2
69.4
Jun
65.4
81.8
78.2
65.4
80.4
73.4
Jul
61.7
79.9
74.7
61.7
78.9
70.7
Aug
62.5
80.7
75.8
62.5
79.4
71.6
Sep
56.7
78.7
71.7
56.7
78.0
68.4
Oct
54.6
78.0
71.1
54.6
77.5
67.4
Nov
Dec
45.9
45.8
75.8
75.2
64.2
62.8
45.9
45.8
75.6
75.1
62.8
62.2