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Wschodnioeuropejskie Czasopismo Naukowe (East European Scientific Journal) #9(13)/2016 HSkl 8. Markov A.A., Barinov, V.Yu., Umarov, L.M., Filimonov I.A., Thermal and Visible radiation during the synthesis of zinc sulfide NPNJ'2016 pp. 97-99 , Alushta 2016 (in Russian)
Anderson A. Y.
Postgraduate student, Odessa National Academy of Food Technologies
Kologrivov M.M.
Candidate of engineering sciences, senior researcher, Odessa National Academy of Food Technologies
THERMAL DESIGN OF GEOTHERMAL CIRCULATION SYSTEM
Abstract: The paper studied the thermal processes in a geothermal circulation system for heating oil in accordance with the proposed model. The effect of heat leakage in the injection well on the heat exchange in the "underground boiler" and the working period of its operation are taken into account for the first time. The numerical simulation of the "underground boiler" for the long-term period with and without heat exchange and energy dissipation of the flow in the wells is done.
Keywords: injection well, underground boiler, energy dissipation.
1. Introduction
The development of geothermal energy due to its enormous resource potential and the ability to produce clean energy cheaper than using fuel. Under the geo-thermal circulation system means the totality of engineering structures, technical equipment and processes of heating, processing and delivery to the consumer under the hot coolant of the geothermal source. This system includes a natural or synthetic natural reservoir, operating (a mining) and the injection wells and ground technological complex [1,2]. The condition for the efficient extraction of hot rock energy heat transfer agent is the presence in the "underground boiler" developed heat exchange surface.
At the hearth of reliable methods for calculation of technological parameters of such systems are the study of processes of hydrodynamic and heat exchange assuming non-isothermal filtration of heat transfer agent in the «underground boiler».
On the other hand the main method of transporting highly viscous oil and petroleum products is their "hot swapping". The main aim of heating - reduction viscosity of the product in order to reduce flow resistance and energy consumption through the pipeline.
40
2. Formulation of the problem
Geothermal heating of heavy oil, which is pumped through the main pipeline and heating of petroleum in terminals has features. Heat transfer agent temperature (circulation water) at the outlet of the «underground boiler» varies in the range 60°C - 100°C. When the heat transfer agent flows in wells up to a depth of three kilometers there is a significant change in the water temperature due to heat exchange with the surrounding array. With increasing of operating time there is a noticeable impact on the water temperature which arises from the increasing of flow energy dissipation on the rough surface of the pipe.
In the paper [3] has shown that the greatest change in temperature of the water in the wells takes place in a total period of 12 years of operation. The amount of heat leakage from the energy dissipation in the total heat transfer varies with time to the injection well from 8% to 200%, and for the production from 0.7% to 32%. The error in the estimation of the flow temperature at the outlet of the wells excluding dissipation - up to 2°C.
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2 5
(0 ^ i- с
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I?
2 с
С D
39,5 39 38,5 38 37,5 37 36,5 36 35,5 35
Temperature
excluding
dissipation
2 ,.3 4 . 5. ,6. 7. ,.8 9 10 11 12
Operation period of circulation system, years
Fig. 1. Dependence of the inlet temperature in the underground boiler on the operation period of circulation system
Engineering relations, which are using to find the temperature of the heat transfer agent are advisable to receive, basing on approximate methods that allow you to solve a problem in a certain time range.
The general mathematical model of heating a heat transfer agent is a system of classical equations of viscous flow and heat transfer. This system of equations is
not linear. Such a model is complex and cannot be solved by known analytical methods.
The model in the form of plane-parallel plates and fractures the same shape and size is the idealization of the artificial and the natural fractured reservoir. It is the most legitimate for the scheme of geothermal circulation system based on hydraulic fracturing.
Fig. 2. Physical model of «underground boiler»
Evidence of learning and development of oil and gas from fractured reservoirs show, that the lengths of the individual fractures are not big. Other fractures are interconnected by micro fractures, forming a system with greater resistance to movement of the liquid.
Models of heat transfer in a fractured reservoir based on the representation of it in the form of a layer, the folded form of the right block (plate, cylinder, sphere) of the same size and having a regular stacking.
Solving problems about the filtration of heat transfer agent in fractured rocks due to the necessity of calculating the temperature fields not only in rock blocks composing the filtration zone, but also in its surrounding host rocks. The mathematical formulation of these objectives on the assumption of one-dimensionality of filtration flow, the independence of thermo-physical properties of the heat transfer agent and the rocks on the temperature as well as disregard for the conductive component of thermal conductivity in comparison with the convective transport in the filtration area and the heat transfer in the host rocks along the direction of filtration, compared with its radial component is represented as [4]:
dth dth Xbl •Ki-(1-m) dTbl
bl
R
K? • dTr ду '
дг
(1)
R
■f
Initial conditions - th(x, 0) = T0; (2)
Border conditions - th(0, t) = t0, (3)
where m - active porous; vf - filtration rate; th,Tbi,Tr - average temperature of the heat transfer agent at the cross section of the filtration area, temperature of rock blocks and host rock respectively; Rbi -characteristic size of rock blocks that make up the filtration zone; Rf - characteristic size of filtration zone; hbl,Xr - thermal conductivity of the rock blocks and host rock respectively; T0 and t0 - initial temperature of rock blocks and heat transfer agent respectively; K1 h K2 - shape coefficients of rock blocks and filtration zone (2 for cylinders and 3 for sphere). For the rock blocks in form of plates K1 = 2 • Rbi/h, where h - expansion of fracture.
The greatest difficulty is the definition of temperature gradients. For its calculation you must specify additional assumptions and solve complex time-consuming tasks.
In the paper [5] is developing the assumption that used to describe the process of heat exchange between the filtration flow and rock blocks the interfacial heat transfer coefficient. The amount of heat, captured by filterable heat transfer agent from the rock blocks, proposed to find by the formula:
4
R.
(Г - th),
'f
(4)
where T' - average temperature of rock blocks, ccT - interfacial heat transfer coefficient.
The analysis of various physical and mathematical models set forth in [4,5,6,7,8], it was determined that in all the proposed models inlet temperature of heat transfer agent in the «underground boiler» remains unchanged during the period of its operation. To solve the problem with a variable inlet temperature of the heat transfer agent, the simplest model has been chosen. It's proposed by members of the Institute of Engineering Thermophysics Ukraine National Academy of Sciences [5].
3. Mathematic model of heat transfer in geo-thermal circulation system
According to [5] dimensionless temperature в dof the «underground boiler» can be determined by the formula:
в =
To ^2.H To - t\.H
ri = C' •W Rf where Hub - capacity (height) of underground boiler, m; cch - interfacial heat transfer coefficient, W/m2-K; Cw - heat capacity of heat transfer agent, J/m3-°C; W - flow rate of heat transfer agent, m3/s; Rf
- distance from the injection to production well, m.
*h ( nVubP \
Ti = q(r^j{T-—R2)- (7)
where C!r - heat capacity of host rock, J/m3-°C; p
- fracture porosity of the host rocks, %.
Parameter t0 represents the position of a rectangular edge temperature to the temperature T1H for thermally homogeneous formation, provided that the heat is transferred only by convection [5].
nRf2HUbâh
(6)
Tn = ■
C^W
(8)
In the formula (8) parameter CR is defined by the formula:
cR = c^-p + c;(i - p)
As shown in (5), the outlet temperature from «underground boiler» can be determined by formula:
T2.H = To-9(To- Т1Л)
(10)
In [4,5,6,7,8], when calculating the thermal regime of the geothermal circulation system authors take a number of assumption:
1. The inlet temperature in the «underground boiler» T1H is equal to the inlet temperature in the injection well t10;
2. The outlet temperature from the production well t2,0 is equal to the outlet temperature from the «underground boiler» T2H.
Paper [3] shows how the operation period of a geothermal circulation system influence on the temperature of the heat transfer agent in the injection and circulation well. Analysis showed that the temperature of the heat transfer agent circulating along the wells varies in the initial period of operation of the system due to the difference in temperature between the heat transfer agent and surrounding rocks. With increasing of operating period, the share of thermal dissipation losses is increasing, which also affects the temperature of the heat transfer agent.
Basing on the foregoing we can state that a temperature change in circulating wells must be considered when calculating the thermal circulation system.
In the paper [3] the inlet temperature in the «underground boiler» is determined as:
Tim = ti.o exp(-AH) + (tn -
^•[l- erfÇJr- - Jr-)],when t < t0 (5)
J • [l + erf(Jrl - Jr\)],when t > t0
where t - operation period of circulation system, s; t2.H - temperature of heat transfer agent at the outlet of underground boiler, °C; T1H - temperature of heat transfer agent at the inlet of underground boiler, °C; T0 - temperature of host rock, °C.
Design parameters r-, xi h t0 are determine by following formulas:
•(1
- exp(-AH))
(11)
+ KH + Atdiss Similarly, the outlet temperature from the production well:
T2.0 = t2.Hexp(-AH)
A)
exp(-AH))
(12)
-KH + At,
diss
where t10 - temperature of heat transfer agent at the inlet of injection well, °С; tn - temperature of neutral layer, °С; К - geothermal gradient, °C/m; H -height of wells, m; Atdiss - heat generation from pressure drop, that expressed in increments of heat transfer agent temperature, °С.
A =
2nRwkT
"V/
-"w
(13)
where C^ - heat capacity of heat transfer agent, J/kg-K; kT - unsteady heat transfer coefficient.
Coefficient of unsteady heat transfer kT, which includes the heat-storage properties of rock mass depends on the period of operation of the circulating system. The more the system is operated, the lower the value of K [7]:
K=-
Я,
0,6 T0,2 J L
(14)
where Xr - thermal conductivity of the rock, W/m-K; Rw - radius of the well, C" - heat capacity of rock that surround circulation wells, J/kg-K.
In the formulas (12,13) At^cc - the temperature increment of the dissipation of the energy of the flow, which are determined by the formula:
AP
htdiss — '
CwP-A
"'WHW^^U
(15)
where AP - pressure drop in the injection well, Pa; xu - time, which the unit of heat transfer agent goes through the well, s.
Solving equation (5) and (11) we obtain the calculated the outlet temperature from the «underground
boiler» at the end of the operation period. Using a calculation of expression (12) we get the outlet temperature from the production well.
4. Results of modeling
Numerical simulation of heat transfer agent temperature changes is done by simplified mathematical model that does not account for heat flow to the "underground boiler" from the surrounding rock mass. Modeling is done for the "underground boiler" with a small coefficient of porosity, which corresponds to the worst case. Water is accepted as a heat transfer agent. Baseline data for simulating the operation of geother-mal systems is showed in the table below.
Table 1. Parameters of geothermal circulation system
№ Parameter Symbol Measure Value
1 Depth of circulation wells H m 3000
2 Radius of circulation wells Rw m 0,1
3 Capacity (height) of «underground boiler» Нпк m 300
4 Distance between injection and production wells Rf m 220
5 Porosity of rock in the «underground boiler» V % 0,02
6 Interfacial heat transfer coefficient aT W/m^K 0,1
7 Heat capacity of rocks that surround circulation wells С'' J/kg^K 1000
8 Heat capacity of rocks in the «underground boiler» С.' kJ/m^K 2200
9 Heat capacity of water С' С'' J/kg^K 4200
10 Density of the rock Pr kg/m3 2200
11 Thermal conductivity of the rock Àr W/m^K 2
12 Water density Pw kg/m3 1000
13 Inlet temperature of heat transfer agent in the injection well h.o °С 30
14 Water flow rate w m3/h 100
The calculated dependence (5) - the dimensionless temperature 9 of the heat transfer agent from the operation period of "underground boiler" is shown in Figure 3.
Fig. 3. Dependence of the dimensionless temperature on the operation period of circulation system
Type of curve in Fig. 3 shows the heat transfer during first 8 years of operation. A value 9 of "0" cor-agent temperature, which is significant for the work of responds to the maximum level of water heating to a the "underground boilers." Temperature 9 is almost "0" temperature of the «underground boiler» rocks. With
u
the dimensionless representation of temperature is not possible to analyze the effect of heat transfer and dissipation of energy flow on the work of the circulation system due to the overlay of the curves. It is advisable
to carry out such an analysis of graphs in dimensional temperature.
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О Ш
U —
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£ -а
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** з
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100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20
— 1 1 1 1 Excluding heat transfer and energy dissipation in the injection ell ncluding heat transfer and energy dissipation in the injection ell
0
5
55
10 15 20 25 30 35 40 45 50 Operation period of circulation system, years
Fig. 4. Dependence of the outlet temperature from the «underground boiler» on the operation period
60
Using the calculated values of 9,we receive by the formula (10) dimensional temperature (°C) of the heat transfer agent at the outlet from the «underground boiler» with its three different inlet temperatures in the "underground boiler". The aim of the calculations is a graphical representation of the effect of heat transfer and dissipation of energy flow in the injection well on the work of the «underground boiler».
The biggest change of the water temperature in the injection well due to the heat exchange occurs in the first days of operation of the circulation system. The rocks that surround the well, hot and water is heated efficiently. With increasing of operating time, it is gradually cooling by the cold water injected into the well. But the change in water temperature does not affect the work of the "underground boiler" in the initial period of operation. At any inlet water temperature it will be heated to a temperature of rock mass. In the initial period the effect of energy dissipation on water temperature change is minimal, since a smooth and clean pipe surface has minimal hydraulic resistance.
With the onset of the regular mode of heat transfer is a change of temperature in the whole array of host rocks of the «underground boiler». They begin to cool efficiently and thus lower the outlet temperature of water from the "underground boiler." The duration of this
period depends on the workload and the structure of the host rocks of "underground boiler." In the present case, this period is approximately 20 years. In this period there is a marked, all increasing, separation curves of the heat transfer agent temperature. The fastest decrease the water temperature, which is calculated without taking into account the heat transfer and dissipation of energy in the injection well. The smallest drop in water temperature corresponds to the joint accounting of heat transfer and energy dissipation in the calculations. The curve, which corresponds to only accounting heat influence in the injection well is intermediate.
With further water supply in the "underground boiler" with cooled host rocks it will not be heated effectively. This mode is not working for the circulation system. It should be noted that in this mode, the most significant consideration bundle of curves.
Accounting for the effect of heat transfer and energy dissipation of the flow in injection well lead to an increase in working operation period of the «underground boiler». The results of solving this new problem is not apparent. Numerical modeling and analysis of the above results made it possible to predict the increase in service life of the «underground boiler» according to Fig. 5.
-a с
о
Ш
<u ■o с
<u
E °
0 i-*
1- (U 4- —
<u "(5
4-J
re
<u o.
E
<u
4-J 4->
01 4-J
О
100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 Increasing of operation period of circulation system, days
Fig. 5. Dependence to determine the increase in the operation period of the «underground boiler» due account of heat leakage in the injection well at a given temperature of heat transfer agent at the outlet.
Analysis of image data in Fig. 5 showed that the increase of operation period of the «underground boiler» ranges from the three mounts to two years.
5. Conclusions
A mathematical model, which allows for numerical simulation of the effect of increasing the heat transfer agent temperature at the inlet to "underground boiler" on the effectiveness of its heat in the boiler and increase the working life of the «underground boiler»
the flow temperature by a few degrees during the operation due to heat transfer and energy dissipation of flow.
Effect of heat leakage increases with increasing duration of the operation period of the «underground boiler». Increasing the outlet temperature of the heat transfer agent from the «underground boiler» up to 30°C-40°C, and the increase in working period of the «underground boiler» up to 2 - 3 years.
is developed. Heat leakage in the injection well increase
References
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2. Anderson A.Y., Kologrivov M.M. Fuel oil heating by geothermal energy // Industrial heating, 2015. -T37, -№7. -p. 201-207. (In Russian).
3. Anderson A.Y., Kologrivov M.M. The influence of energy dissipation on the temperature of heat transfer agent in geothermal circulation system // Prospecting and development of oil and gas fields, 2016. -№1(58), -p. 82-89. (In Russian).
4. Pavlov I.A. Hydrodynamics and heat exchange in the rock fractured reservoirs when extracting geothermal energy. Extended abstract of PhD dissertation. Leningradskiy gornuy universitet, Leningrad, 1983. (In Russian).
5. Shcherban' A.N. The heat of the Earth and its recovery. — Kiev: Naukova dumka Publ., 1984. — 264 pp. (In Russian).
6. Dyad'kin Y.D., Pariyskiy Y.M. Extracting and using of Earth heat. — Leningrad: LGI Publ., 1977, — 114 pp. (In Russian).
7. Dyad'kin Y.D., Pariyskiy Y.M., Romanov V.A. Heat exchange in deep wells and filtration zones when extracting heat from hot dry rocks. — Leningrad: LGI Publ., 1974, — 40 pp. (In Russian).
8. Smirnova N.N., Mukhin V.A. Heat mass transfer to the walls of the channel when liquid filtration // Physical processes of mining, 1978. -№5. -p. 83-87. (In Russian).
