Chemical and Petroleum Engineering, Vol. 47, Nos. 9–10, January, 2012 (Russian Original Nos. 9–10, Sept.–Oct., 2011)
METHOD OF CALCULATING HEAT EXCHANGE IN THE WORKING ZONE OF OPEN FLARING DEVICES
O. Yu. Kuleshov and V. M. Sedyolkin
A method is proposed for calculating heat exchange in the working zone of vertical and horizontal types of flaring devices (torches). The method is based on joint numerical solution of several associated problems, such as calculation of the length and dynamics of burning of a free flare, complex heat exchange and radiation characteristics in a multizone conical calculated region that approximates a flare (torch), local radiative heat flows from a randomly positioned multizone torch to elemental areas of a horizontal surface exposed to radiation, etc. The calculation method is approved on the example of a vertical gas field torch.
Burning (continuous or periodic) of hydrocarbon-containing gaseous discharges in open torches (flaring devices) is a technological feature of facilities of oil and gas processing, oil-refining, and petrochemical industries. Notwithstanding the obvious drawbacks of such means of utilization of gaseous wastes, there is no viable alternative to it. Currently, torches for burning gas in free diffusion flare are used most commonly. There are also designs of torches having special burners with partial premixing of a combustible gas and air, swirling and turbulization of the gas stream, etc., which intensifies burning and reduces flare length. But use of such burners is constrained due to low and variable pressure of the discharged gases. The flare burner (or simply stabilizing head) is fixed at the mouth of the torch barrel which may be vertical or horizontal. Horizontal torches are generally used in oil and gas fields. In this case, the torch lies directly along the ground surface, and the working area of the device is banked up. Flare is a powerful source of heat radiation. In designing torches, one has to determine the thermal effect of open flare on the objects lying in the zone of its action in order to ensure safe operation of the equipment and safety of the personnel. Forecasting the thermal state of the permafrost ground (soil) is also a critical problem for the regions of the Extreme North and Siberia. Heat engineering methods of calculation of open flaring devices are based on representation of the flare either as a radiating point or as a fixed vertical or horizontal axisymmetric geometric figure (cylinder, ellipse, etc.) with identical radiation properties as well as on determination of angular coefficients from the whole surface that simulates the flare to the horizontal irradiated surface. Use of such simplifications in calculation of heat load from an open flare gives rise to significant error, which gets bigger the shorter the distance of the flare from the irradiated surface. In a physically validated model of heat radiation of an open flare, account must be taken of its real characteristics, such as length, shape, spatial location with due regard for wind impact and temperature stratification, distribution of concentrations, temperatures, and radiation properties of the combustion products across the flare length, etc. At the same time, the procedure and calculating algorithm must not be so complicated as would hinder their engineering use in programmed analysis systems and designing of open flaring devices. The proposed method of calculation of heat emission of an open flare is based on joint solution of several associated problems and use of appropriate methodological approaches: 1) calculation of length and dynamics of burning of a free flare under various conditions based on semiempirical approach; Engels Technological Institute, Branch of Saratov State Technical University, Engels, Russia. Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, No. 9, pp. 12–14, September, 2011. 0009-2355/12/0910-0591 ©2012 Springer Science+Business Media, Inc.
591
Fig. 1. Geometric zonal model of free flare.
2) calculation of complex heat exchange and radiation characteristics in a radiating and absorbing medium in the combustion region using zonal method; and 3) calculation of radiative heat flows from the flare to the elemental areas of the irradiated surface using numerical integration of radiation over the surface of the flare zones. The calculation region, which simulates the free flare, is depicted by a round truncated cone with an expansion angle that depends on the conditions of the outflow [1, 2], which is divided by planes perpendicular to the axis into a large number of zones so as to take account of the variation in the characteristics of the flare across its length (Fig. 1). The length of a random flare Lf is determined from the length of a model free diffusion flare Lfr d.f with due regard for corrective simplex functions of the criteria characterizing the actual flaring process [2], Lf = L fr d.f ƒ1(K1)ƒ2(K2),
(1)
where K1 is the integral characteristic of the degree of premixing of the gas with air in a section of the flare burner, and K2 is a coefficient that takes account of the influence of swirling and turbulization of the gas stream due to attaching of a swirler to the burner. The procedure for calculating the burn-up of a combustible gas across the flare length in the general case of partial premixing of the gas and air takes into account the presence of kinetic and diffusion burning fronts. Since the length of the kinetic burning zone is relatively small, the first flare zone accounts for the characteristic heat liberation (Fig. 1). The burn-up in the diffusion part of the flare is determined from the universal relationship given in [2] with respect to the gas composition and various operating factors, while the air intake and fuel concentration across the flare length are determined from the relationships given in [1]. Determination of the temperatures and radiation characteristics of the combustion products, differentiated across the flare length, is linked with solution of the problem of radiative-convective heat exchange in the combustion zone. For this, the zonal calculation method described in [3, 4] was used. Dividing of the flare into zones creates an axisymmetric calculation region consisting of conical volumetric (gas) zones (Fig. 1). 592
Let us write the zonal heat balance equations system in the form: N
∑ PijTi4 + B j −1T j −1 − B jT j + C j = 0,
j = [1, N ],
(2)
i =1
where N is the number of flare zones; Ti is the average absolute temperature of the ith flare zone; i, j zones are the source and receiver of energy, respectively; (j – 1) is the zone that precedes the j zone along the gas stream path. The coefficients of radiative exchange Pij between i and j zones that feature in system of equations (2) are calculated from the spectral generalized angular coefficients (GAC) by summing over Z rectangular bands (zones) of quasi-serial model of radiation spectrum of combustion products [3]: Z
Pij = 4Viσ 0
∑ bi ,k χi ,k K ε i ,k (ψ ij , k − δ ij ) ,
(3)
k =0
where Vi is the volume of the ith flare zone; σ0 is the Stefan–Boltzmann constant; Z is the number of radiation spectrum bands; bi, k is the portion of the radiation of an absolutely black body in the kth spectral band at Ti; χi, k is the absorption coefficient of gaseous combustion products in the kth spectral band for the conditions in the ith zone; ψij, k is the GAC of radiation from i zone to j zone in the kth band of the radiation spectrum; δij is the Kronecker delta symbol; Kε i,k is the correction for nonlinearity of the degree of blackness of the gas volume [4]. The GACs between the zone of the calculation region take account of absorption of the separating medium and are calculated by the method of simulative modeling of radiation (Monte Carlo method) [3, 4] in the conical flare system. The coefficients of convective exchange in the stream between the current j and the preceding (j – 1) flare zones, which feature in Eq. (2), are determined by the formula Bj = uj ρj cj,
(4)
where uj is the average velocity of the stream in the jth zone, ρj is the density, and cj is the heat capacity of the combustion products in the jth zone. The free term Cj in Eq. (2) includes the internal heat source associated with burning in the j flare zone and with inflow of surrounding cold air. Solution of system of equations (2) gives the temperatures of the flare zones. The degree of blackness of the flare zone is determined by the equation
εf i
V =4 i Fi
Z
∑ bi ,k χi ,k K ε i ,k ,
(5)
k =0
where 4Vi /Fi is the average length of the radiation path in the flare zone; Vi and Fi are the volume and area of the confining surfaces of the ith flare zone in the shape of a truncated cone. The absorption coefficients of the combustion products in the radiation spectral bands χi, k depend on their composition, including the soot concentration. In the general case, we have χi,k = χg + χ s ,
(6)
where χg and χs are the coefficients of absorption of gaseous combustion products and disperse soot particles, respectively. The summarized (composite) data on soot concentration in the gas flare and radiation properties of disperse combustion products are adduced in [3]. 593
TABLE 1 Parameter
Value
Diameter of burner orifice, m
0.4
Gas flow rate, kg/sec
6.7
Gas temperature, °C
20
Temperature of surrounding air, °C
20
Degree of gas–air premixing
0
Height of torch burner above ground level, m
15
Wind velocity, m/sec
5.5
Direction of wind in horizontal coordinate system, grad
45
In modeling heat radiation of a flare, account is taken of various dispositions of the flare relative to the horizontal plane that simulates the ground surface. For vertical flaring devices having a high shaft (barrel), account is taken of the possibility of displacement of the combustion region due to wind force. In the case of horizontal flaring devices, the flare lies right along the ground surface on a banked-up site and hardly experiences wind impact. In this case, the horizontal flare rests upon the earth embankment, which restricts its length. The local angular coefficients of radiation are calculated from the flare zones to the elemental sites (areas) located at the nodes of the calculation net on the horizontal plane. In this case, for vertical flaring devices, direct numerical integration of radiation is performed over the conoid surface of the flare zones lying at random relative to the irradiated horizontal plane, which allows one to take account of the deflection of the flare caused by the wind. This method is inapplicable for horizontal flaring devices, so the flare zones adjacent to the ground surface extend to the central radiating points on its axis. The local density of the incident radiant heat flux at the nodes of the calculation net is determined by summing up over the flare zones by the equation N
q inc M
=
∑ ε f i Ff iϕi ,M Ti4 ,
(7)
i =1
where ϕi, M is the angular coefficient from the iyh flare zone to the unit site (elemental area) dFM = 1 having the central node M; Ff i is the area of the conoid surface of the ith flare zone. Thus, the proposed method can be used to calculate physically valid radiant heat flows in the zone of action of any type of open flaring devices when the design and operation parameters are random. The obtained data on the distribution of heat flows on the ground surface can be used as the limiting conditions for solving the problem of warming up of permafrost grounds when the flaring device is located in regions of Extreme North and Siberia. The proposed calculation method has been approved for vertical flaring device of the gas industry. The characteristics of the flaring device for burning purge (blow) natural gas in diffusion flare in the case where the flare burner is a section of the flare (torch) shaft are furnished in Table 1. In the above-noted case, the flare length determinable by Eq. (1) is equal to the length of the free diffusion flare Lf = Lfr . d.f The flare length was determined from the degree of burn-out of the fuel, which is 98%. The calculated horizontal irradiated area is associated with the plane of rectangular coordinate system. The wind direction is determined by the angle between the corresponding direction vector and X-axis. The height of the flare burner matches the height of the flare shaft. The design flare parameters are: length 14.8 m, maximum temperature tf max = 779°C, and average degree of blackness εf = 0.5. The reason for the relatively small degree of flare blackness is burning of the natural gas with minimal soot formation. 594
Fig. 2. Distribution of density of incident radiation flux (kW/m2) in the zone of action of vertical flaring device: ⊗) flare shaft; →) wind direction.
The results of calculation of local densities of the flow of incident radiation at the points of horizontal irradiated area are plotted in Fig. 2 in the form of isolines (isograms). Let us note the shift of the maximum heat load of the irradiated area in the direction of the wind. At the fixed wind velocity, the deflection of the flare from the vertical position is 11.5°. The heat load maximum shifts relative to the flare shaft roughly by 10 m, which is 3.3 times more than the design length of the flare on the coordinate plane. The heat load is much less (more than 10 times compared to the maximum) at the base (foot) of the flare shaft (in the design of the flare base on the coordinate plane), the reason for which is that the angle of visibility of the flare is reduced and also that colder gas layers at the foot of the flare shield the radiation emanating from the combustion zone located above them. The maximum density of the radiation flux incident on the ground surface is 0.4 kW/m2, whereas the radiation intensity limit safe for human beings is 1.4 kW/m2. The small heat loads are attributable to significant height of the flare shaft, minor deviation of the flare from the vertical position at the fixed wind velocity, and relatively low temperature and degree of blackness of the flame when methane is burned. A comparison of the calculated data with the data of the investigation of open flaring devices, performed at the Research, Planning, and Design Institute of Gas Production (VNIPIGazdobycha), showed good accuracy of the calculation method, being within the experimental error. The proposed method of calculation of heat exchange in the working zone of open flaring devices is highly efficient, universal, and can be used in computing systems for designing various types of open flaring devices and analysis of their effects on industrial and natural environment with a view to minimizing their harmful effect.
REFERENCES 1. 2. 3.
G. N. Abramovich, T. A. Girshovich, S. Yu. Krasheninnikov, et al., Theory of Turbulent Streams [in Russian], Nauka, Moscow (1984). V. M. Sedyolkin and L. I. Shibaeva, “Calculation of length and burn-out of turbulent diffusion flare,” Raspred. Szhig. Gaza, SPI, Saratov (1975), Iss. 1, pp. 74–84. A. G. Blokh, Yu. A. Zhuravlev, and L. N. Ryzhkov, Heat Exchange by Radiation [in Russian], Energoatomizdat, Moscow (1991). 595
4.
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O. Yu. Kuleshov and V. M. Sedyolkin, “Improving thermal conditions of industrial furnaces based on highly efficient zonal method of calculation of complex heat exchange,” in: Problems of Energy and Resource Saving: Coll. Sci. Works [in Russian], SGTU, Saratov (2010), pp. 197–205.