Estimating Discharge Rates

The initial release rate of hydrocarbon gas through a hole to the atmosphere depends on the pressure inside the equipment, the hole shape/size, and the molecular weight of the gas. 

For a small hole in the containment, there are two possible release conditions  

The adiabatic case is the most common for accident conditions. The process is treated as an isentropicfree expansion of an ideal gas using the equation of state  

Equation (5-14) is combined with Bernoulli s equation. Assuming flow on a horizontal axis and using a coefficient of discharge to account for friction at the orifice, the mass flow rate of an ideal gas through a thin hole in the containment wall is  

If the pressure ratio is above a critical value given below, the exiting mass flow is limited to a critical maximum value. This is sonic or choked flow  

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Source models are used to quantitatively define the release scenario by estimating discharge rates (Section 2.1), total quantity released (or total release duration), extent of flash and evaporation from a liquid pool (Section 2.2), and aerosol formation (Section 2.2). Dispersion models convert the source term outputs to concentration fields downwind from the source (Section 2.3). The relationship between source and dispersion models, and the various model types, is shown schematically in Figure 2.1. As shown in Figure 2.1, source and dispersion models are highly coupled, with the results of the source model being used to select the appropriate dispersion model. 

Assume a continuous release of pressurized, hquefied cyclohexane with a vapor emission rate of 130 g moLs, 3.18 mVs at 25°C (86,644 Ib/h). (See Discharge Rates from Punctured Lines and Vessels in this sec tion for release rates of vapor.) The LFL of cyclohexane is 1.3 percent by vol., and so the maximum distance to the LFL for a wind speed of 1 iti/s (2.2 mi/h) is 260 m (853 ft), from Fig. 26-31. Thus, from Eq. (26-48), Vj 529 m 1817 kg. The volume of fuel from the LFL up to 100 percent at the moment of ignition for a continuous emission is not equal to the total quantity of vapor released that Vr volume stays the same even if the emission lasts for an extended period with the same values of meteorological variables, e.g., wind speed. For instance, in this case 9825 kg (21,661 lb) will havebeen emitted during a 15-min period, which is considerablv more than the 1817 kg (4005 lb) of cyclohexane in the vapor cloud above LFL. (A different approach is required for an instantaneous release, i.e., when a vapor cloud is explosively dispersed.) The equivalent weight of TNT may be estimated by... 

We shall first consider the case of non-flashing liquids. In this situation, there is no critical flow pressure limiting the flow of liquid through a PR valve orifice, as opposed to the case of vapor flow. The discharge rate is a function of the pressure drop across the valve and can be estimated by the following expression ... 

Based on National Urban Runoff Program Report (37), estimated Willamette Basin impervious drainage area at 518 km (200 mi ) and mean discharge rate of 5.4 ftVs ... 

Many important erosion-related phenomena are episodic and infrequent, such as flash floods, landslides, and glaciations, while others such as orogenesis and soil formation involve time scales that exceed those of major climate fluctuations. In either case, the time scale of human existence is too short to make adequate observations. Consequently, it is difficult to directly estimate the rates or characterize the effects of such phenomena on erosion products. The key to understanding weathering and erosion, on a continental scale, is to decipher the relationship between landforms, the processes that produce them, and the chemistry and discharge of river-borne materials. 

Mathematical models are also used for estimating releases, but these are usually relatively simple. For example, if it is known that X kg of a chlorofluorocarbon is manufactured annually, and Y percent enters spray cans, and Z percent of a spray can is usually left unexhausted, then XY(100-Z)/10 kg of that CFC are released to the atmosphere per year. The average discharge rate (kg/sec) nationwide then can be computed easily. (For simplicity in this example, we ignore the contributions from leaking discarded cans and changes in production and use levels.)... 

Rate, kg/h Screw Speed, rpm Specific Rate, kg/(hrpm) Discharge Pressure, MPa Estimated Discharge Temperature, °C... 

The flow rate used for this calculation should be the best estimate flow rate for the safety valve. BS 6759 19] requires that any safety factors used in determining G for relief system sizing, including the 10% de-rating of the safety valye discharge coefficient, should be removed. The actual flow area through the valve should be used., ... 

Heat flask 1 with the flame of a gas burner through an asbestos gauze and estimate the rate of gas evolution according to the number of bubbles in wash bottle 2. When a uniform stream of gas is established, carefully wear eye protection heat the bottom part of vessel 3 with the open flame of a burner. Do not let the products clog the gas-discharge tube. The amount of the aluminium chloride condensing in the upper part of the apparatus should be insignificant. 

The effect of discharge rate is shown in Figs 3.13 and 3.14 where closed circuit voltage characteristics and service life of D-size cells are shown as a function of current drain. The fact that service life increases as current density decreases suggests that for this type of system it is always best to use as large a cell as possible. It has been estimated that over a wide range of current densities, the service life is tripled by halving the current density. 

A 500-gallon water tank has a continuous feed and discharge rate of 10 gpm and 15 lb of NaCl are added to the tank in a batch method. The tank has uniform mixing to maintain a uniform salt concentration at all times. Estimate the amount of salt in the tank after 2 hours. 

With reasonable estimates of rate coefficients, this does not require an unreasonable concentration of vibrationally excited H2 in the gas flowing from the discharge. 

These estimated specific discharges for the buoyancy-driven migration of oil through a carrier rock are about 5 orders of magnitude greater than the estimated expulsion rates for oil from source rocks as given in Chapter 3. 

Consider the lake shown in Fig. 1-2. For this example, assume that the discharge pipe releases to the lake small amounts of various alcohols from an industrial fermentation process, and it is desired to estimate the rate at which alcohols are degraded in the lake. One of them, butanol (C4H9OH), is released to the lake at the rate of 20 kg/day. Butanol is measured in the lake water on several occasions at a concentration of 10-4 kg/m3 no butanol is detected in the inflowing stream. Average streamflow at the outlet of the lake is measured to be 3 X 104 m3/day. What is the magnitude of internal sinks of butanol ... 

A recent analysis of the emissions and their discharge rates allows gaseous pollutant emission factors per tonne of ammonia produced to be estimated for relatively old and newer production facilities (Table 11.6). 

A rough estimate of the volume of oil in the present ballast waters (case 1) was obtained by assuming that the oil discharge rate between points A and B was constant. In such a case, the width of the spill at point B at 192 min will be the same as near point A on the SAR image (Figure la). Since... 

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