3.3. Flash Point

Flash point is widely used to assess hazard associated with a flammable liquid to determine its fire and explosion risk. It is defined as the minimum temperature needed for a material to start emitting sufficient vapor and form a flammable mixture with air (Crowl and Louvar, 2011; Engineers. Center for Chemical Process Safety, 1993; Lees, 2005; Moghaddam et al., 2012) at atmospheric conditions. For a liquid mixture consisting of a single flammable liquid with miscible nonflammable liquids, the flash point of the mixture occurs at a temperature where the partial pressure of the flammable liquid in the mixture is equal to the vapor pressure of the pure liquid at its flash point temperature. It is used to determine a chemical's storage temperature and handling requirements for its safe transportation. Several series of explosions has, in an unfortunate way, demonstrated the importance of flash point values (Santon). On the other extreme, conservative models for flash point can potentially overestimate a flammable hazard and thereby lead to an expensive mitigation approach. Estimation of flash point with reasonable accuracy thus has significant importance in process hazard analysis studies. Computational modeling for flash point can often get tricky owing to exhibition of minimum flash point behavior (MFPB) by some chemicals. It is exhibited when the flash point of a mixture is below the flash point of the individual components. Several mixture rules, as illustrated in Section 3.1, owing to their definitions of estimating flash point of a mixture, limits the result within the range of minimum and maximum flash point of individual component of a mixture. A conservative approach in estimating flash point is typically to use the minimum flash point among the individual constituents as the flash point for the whole mixture. As we will observe and as the definition goes, chemicals exhibiting MFPB behavior, is an exception to this understanding and has the potential to pose a problem if unaddressed.
Experimentally, there are generally two ways to determine flash point of a chemical:
• Open cup
• Closed cup
Fundamentally, closed cup measurements are conservative as all the vapors are available and none escapes. Various standardized test methods have been developed basing these methods and review of these are presented in ASTM E 502 (Harrison). In addition, experimental measurements of flash point is expensive, resource intensive, and, especially for toxic, volatile, and explosive chemicals, it is even more difficult to measure (Bagheri et al., 2012; Annual Book of ASTM Standards, 2002; Katritzky et al., 2001; Mannan and Lees, 2005). Design of test apparatus, as in the case of estimating flammability limits, also plays a role in contributing toward uncertainties in flash point estimation (Rowley et al., 2010). Therefore, development of reliable computational models to estimate flash point can provide significant value including determination of flash point for new chemicals without the need for synthesizing it. In the next section we will look into detail on the current state of the art approaches and methodologies at various scales which helps estimates flash points with different extent of limitations. Several of the theoretical approaches on estimation of flash points have been reviewed (Vidal et al., 2004; Catoire and Naudet, 2004) to a reasonable extent. Mathematical models for estimating flash points can be divided into two broad categories:
1. Empirical and semiempirical correlations
2. Molecular modeling approaches
Empirical and semiempirical approaches generally refer to estimation of vapor pressure through such methods and that in turn is fed into an advanced and more computer-intensive approaches. In the section that follows, we will emphasize various methods with a different level of details incorporated in their models to estimate flash point. The origin of estimation of flash point through mathematical modeling is almost a century old; in 1923, Mack et al. reported calculating flash point of pure organic substances based on its LFL as estimated by Thornton (1917). This is done by using vapor pressure curve of a pure component. Thornton noticed that irrespective of bond types, the heat of combustion difference between successive members of paraffins, olefins, and other CxHyOz type compounds is reasonably constant for the radical CH2.image. In other words, it meant that the heat of combustion of a molecule was directly proportional to the number of oxygen atoms it required for complete its combustion. Mack et al. used these formulations to estimate LFL of a flammable gas and calculated corresponding vapor pressure required for that component to meet its LFL. The flash point was then defined as the temperature in which the organic substance will have the required vapor pressure. However, in addition to being only validated with a limited number of single compounds, this approach also yielded results deviating as much as 14 K for isomeric compounds (Liu, 2010).
In general estimating flash points for a mixture with a single flammable liquid is done as follows:
1. Note mole fraction of the flammable liquid in liquid solution (xi), flash point temperature of the pure flammable liquid (Tf), and total pressure
2. Calculate or find the saturation vapor pressure Pi,sat of the flammable liquid at its flash point Tf.
3. Iteratively find the flash point of the mixture so that the saturation vapor pressure Pi,sat of the flammable liquid at the mixture flash point is equal to the partial pressure (pi) of the flammable vapor as calculated by vapor liquid equilibrium information of the mixture
Other computational approaches for flash point estimation includes correlating flash point with boiling point data (Hshieh, 1997; Patil, 1988; Satyanarayana and RAO, 1992; Prugh, 1973; Butler et al., 1956), specific gravity data (Satyanarayana and Katati, 1991; Metcalfe and Metcalfe, 1992), and a combination of boiling point and enthalpy of vaporization data (Catoire and Naudet, 2004). The basis for correlating flash point with boiling point of a substance lies in the fact that flash point is expected to be correlated to vapor pressure and hence its boiling point (Voutsas et al., 2002). Most of these models developed, dealt with pure organic compounds (Mack et al., 1923; Hshieh, 1997) and built empirical relations between the variables. The polynomial functions used to fit the data varied in form, from second order with respect to the boiling point or Tb (Satyanarayana and Katati, 1991; Patil, 1988) to second order with respect to inverse of Tb (Hshieh, 1997). See Table 3.5 for more details. While these methods can provide a rough estimate of flash point in an efficient manner, the downside of these approaches lies in the fact that these are heavily dependent on reliable experimental data and extrapolation of the data beyond the domain of materials utilized for model development. As a result, implementation must be done with their limitations in mind. As an example (Hshieh, 1997), for the compound phenyltriethoxysilane, with a predicted flash point of 92 °C, using Patil's correlation (Patil, 1988), as provided below, is lower by 28 °C than its actual flash point. Such deviation observed in the particular example will result in overly conservative set of decisions. A worse scenario, predictions resulting in higher flash point values than actual and thereby creating a potential for devastating consequences.

Table 3.5

Various Empirical Relations for Predicting Flash Points

References Flash Point (Tf) Estimation from Boiling Point (Tb), Density (d), and Heat of Vaporization (ΔHvapimage)
Patil (1988) Tf=4.656+0.844Tb−0.000234Tb2 image
Units of Tf and Tb are in K
Butler et al. (1956) Tf=0.683Tb−119 image
Units of Tf and Tb are in °F
Satyanarayana and Katati (1991) Tf=−83.3362+0.5811Tb+(0.0001118Tb)+38.734d image
Units of Tf and Tb are in °C and units of d are in g/cm3
Metcalfe and Metcalfe (1992) Tf=−84.794+0.6208Tb+37.8127d image
Units of Tf and Tb are in °C and units of d are in cm−3
Hshieh (1997) Tf=−54.5377+0.5883Tb+0.00022Tb2 image
Units of Tf and Tb are in °C
Satyanarayana and Rao (1992) Tf=a+b[(c/Tb)e−(c/Tb)]/(1−e−(c/Tb))2 image
Units of Tf and Tb are in K. a, b, and c are constants
Catoire and Naudet (2004) Tf=(1.477Tb0.79686)ΔHvap0.16845n−0.05948 image
Units of Tf and Tb are in K, units of ΔHvapimage is in kJ/mol, and n is the total number of carbon atoms

image

Boiling point of a substance is primarily related to its nonbonded interactions such as van der Waals forces. A flash point of a substance, however, is not only a function of its ease of being vaporized at a certain temperature but also its ability to react with oxygen. Hence, any empirical formulation, which correlates only boiling point to its flash point, has potential to generate misleading information. The same argument holds for any correlation, such as the one using specific gravity or heat of vaporization alone or in combination with boiling point to predict flash point. For mixtures, a reliable way must be known to estimate the mixture boiling point, specific gravity, and heat of vaporization prior to estimation of flash points. Due to all these legitimate concerns of applicability, some developers of these models even recommended (Hshieh, 1997) the use of experimental data (if available) over predictions based on empirical equations. Theoretical models (Liu, 2010) such as those specific for hydrocarbon mixtures in air (Affens and McLaren, 1972; White et al., 1997; Affens, 1966), model using Raoult's law for alkanes in air (Affens, 1966) have also been used to estimate flash point of specific set of chemicals. Because of the possibility of MFPB, simply assigning the minimum flash point value of the individual constituents as the mixture flash point does not guarantee a conservative approach and underestimates the risk assessed (Liaw et al., 2003). On the contrary, it has also been demonstrated that a mixture flash point can be more than the maximum flash point (Liaw et al., 2002; Liaw and Lin, 2007) of its individual components, thereby hinting at possibilities of overly conservative estimation of flash point. To overcome these inconsistencies, more rigorous mathematical models have been developed (Liaw et al., 2002, 2004), such as one that can also predict MFPB. Figure 3.8 (Liaw et al., 2002), illustrates an example, where the developed method in the same article can successfully predict MFPB. One can observe that the method proposed by Liaw et al. is in very good agreement with experimental results as opposed to differences shown by some other methods.
Computational model based on molecular structures, as demonstrated in the next section, if constructed and implemented appropriately, has a great potential of predicting flash points of various mixtures in much more efficient manner. The key, however, is to have a validated robust and reliable model for an approach to predict flash points with reasonable accuracy.

3.3.1. Molecular Modeling Flash Point

QSPR-based estimation methods of flash points of pure compounds, mainly organic compounds include multiple linear regression (MLR), group contribution method, and ANN methods. Description of molecular structure in these studies has often been through use of molecular fragments, topological indices, and quantum mechanical calculation–based descriptors (Liu, 2010). While its necessity has been debated (Puzyn et al., 2008) in favor of semiempirical methods, QSPR-based model can also have its roots based on first principle calculations such as DFT. QSPR approaches find quantitative mathematical mapping between measureable properties of chemical compounds and its intrinsic molecular structure. Molecular descriptors, as required to complete the model, can be calculated by implementation of quantum chemical calculations (Katritzky et al., 2007) and thus have the potential to provide a reliable way of estimating flash point through first principle–based QSPR approaches. We have already discussed briefly how quantum mechanical calculations can be implemented in estimating molecular descriptor values for chemicals in Section 3.1.4. As demonstrated in Section 3.1.4, molecular structure–based methods such as QSPR and QSAR, provides an excellent way to estimate properties and activities of a chemical in relation to its structure. Having the capability of formulating a model with multiple response output and reliable prediction performance, neural network–based QSPR models has made some key breakthroughs in flash point predictions (Liu, 2010). Back propagation (Pan et al., 2007), radial basis function, and group contribution method (Gharagheizi et al., 2008)—based neural network have also been used with QSPR to estimate flash points (Tetteh et al., 1999; Li et al., 2004). Besides estimating flash point for pure components, reliably predicting flash point of mixtures as a function of its composition is also important. To illustrate the importance of incorporating the effect of molecular in flash point estimation of a chemical, let's take an example from the literature (Rogers and Mannan, 2006). Molecular interaction affects vapor pressure of a mixture, which in turn affects flash point of a chemical. A mixture of similar-sized alkanes such as heptane and octane, when mixed in various proportions, will have properties that can be predicted with reasonable accuracy by simple mixing rules. Simple mixing rules do not incorporate effect of nonbonded interactions between individual components. Such an assumption holds reasonably true for these type of system of interest (mixture of alkanes). However, for example, addition of an alcohol in the system changes the interaction dynamics owing to polarity differences. Properties estimated through simple mixing rules in such cases may mislead assessment of hazards present. A repulsive action among the atoms owing to nonbonded forces will consequently result in higher vapor pressure leading to lower flash point of the mixture. Therefore, in a mixture, effect of intermolecular interaction could be significant in determining its flash point. Such interactions, in the absence of experimental data, these are best estimated at the atomistic level.
image
Figure 3.8 Comparison of the flash point–prediction curves with experimentally derived data for octane (1) 1-butanol (2) solution. Reprinted with permission from Liaw et al. (2002).

3.3.1.1. First principle–based approaches

The need for accurate thermodynamic models is especially evident in flash calculations (Chen and Mathias, 2006) as correctly pointed out by Chen et al. In light of that, however, a survey (Hendriks et al., 2010) found minimal awareness of industry on advanced computational techniques such as quantum mechanics and molecular dynamics. Industry rarely updates or reinvents its current modeling approach unless a clear advantage is proven ahead of implementation (Chen and Mathias, 2006).
Figure 3.9 (Hendriks et al., 2010), which is based on a survey on industrial requirements for thermodynamic and transport properties by the Working Party on Thermodynamic and Transport Properties (http://www.wp-ttp.dk/) of the European Federation of Chemical Engineering, EFCE (http://www.efce.info/) demonstrates the current industrial need for accurate thermodynamic data and highlights advanced scientific tools such as molecular dynamics simulation and quantum mechanics calculations as possible solutions.
We have already demonstrated the significance of predicting MFPB in the previous section. MFPB has been predicted (Rogers and Mannan, 2006) very effectively for binary mixtures using first principle calculations. The intermolecular and intramolecular interactions in presence of other components that have an effect on a mixture's flash point are neglected when using mixing rules but are appropriately captured in calculations through first principles.
Quantum mechanics, ab initio– or first principle–based approaches, has the potential to provide specific input information to help estimate flash point of various chemicals. Being of fundamental nature, such an approach is an efficient and reliable alternative to performing numerous set of experiments for estimating flash point. Before we illustrate these implementations, we must also bear in mind, as seen before, that there are two parts toward estimation of flash point of a chemical, namely that of individual components and that of the mixture. In order to do that, we need to estimate following:
1. Flash point of a pure component
2. Flash point of a mixture
image
Figure 3.9 Schematic illustration of the position of thermodynamic tools for the oil and gas, chemical, and process industries (Hendriks et al., 2010). Reprinted with permission from American Chemical Society.
a. Activity coefficient
b. LFL
While estimation of flash point is significant importance, screening chemicals for potential hazardous MFPB is another area where ab initio calculations can help us significantly. COSMO-RS–based estimation of γ∞image can help us to identify mixtures exhibiting MFPB. ADF-COSMO-RS (te Velde and Bickelhaupt, 2001), a variant of COSMO-RS, which have been demonstrated in the latter parts of this chapter, uses results from quantum mechanical calculations and Le Chatelier's rule of mixtures to estimate flash point of mixtures.
In the section below, we discuss how approaches based on quantum mechanics or first principles can help us in estimating flash point, by addressing concerns related to individual components and their mixture. For individual component–related approaches we focus on first principle calculations input–based QSPR approaches, whereas for mixtures we focus on using quantum mechanics to estimate activity coefficient through accurately estimating binary parameters. In addition, we also take a look into usage of COSMO-RS–based approach in screening MFPB chemicals. First principle approaches such as DFT can be useful in reliably estimating data such as binary interaction parameters among variety of chemicals, where prior experimental data are not available (Rogers and Mannan, 2006). Binary interaction parameter is an input to activity coefficient model that is required to effectively calculate flash point of a mixture. In this work, the authors did not use first principle approach solely to estimate the flash point of a binary mixture. Instead, quantum mechanics, which accurately calculates energy of a system based on spatial distribution of electronic particles, was used to estimate binary interaction parameter values as input to activity coefficient models where experimental data were lacking. The work is based on an approach (Amadeu, 1999) where ab initio method was used to calculate phase equilibrium of a system. Activity coefficient methods such as UNIFAC, UNIQUAC, and Wilson models are very much dependent on regressed experimental data for interaction energies. Sum et al. (Amadeu, 1999) calculated interaction energies between molecules using ab initio methods and used the same as an input interaction energy parameters to these models, replacing experimental inputs. While brief overview of various quantum mechanical methods such as HF method or DFT can be found in the introductory section, here we will provide the specific approaches taken by the authors to estimate the parameters:
1. Define a cluster of molecules to represent the system fluid. The cluster size (eight molecules or four each of two different kinds in this case) needs to be iteratively determined, by considering consistent energetics and insensitive to initial random structural configuration, reduced end effects, and computational resource usage.
2. Minimize the cluster energy by a less expensive semiempirical method. The authors in this case have used PM3 semiempirical method (Stewart, 1989). The use of a carefully chosen semiempirical method is to develop a reasonably well starting geometry and lessen the burden on subsequent ab initio steps during further refinement. Since parameters in semiempirical methods are based on experimental data, care must be taken in selecting such a method that is appropriate to the set of molecules in question. As an example, in this particular study, PM3 semiempirical method was chosen as it has the ability to qualitatively describe hydrogen bonding. Other semiempirical methods or approach such as molecular mechanics can also be used at this stage.
3. Refine the cluster geometry by minimizing the structure even further by using a higher-level theory, HF method in this particular case with a 6-31G∗∗ basis set. To achieve minimization in a relatively less expensive and gradual manner, the authors gradually increased the rigorousness of the basis set from 6-31-G to 6-31G∗∗. The authors chose HF method, as the system studied was weakly interacting system.
4. Select directly interacting (in close proximity) molecular pairs (like and unlike) and record separation distance and relative orientation
5. Calculate interaction energy of each molecular pair (like and unlike) with the HF method and detailed basis set. The authors used 6-311++G (3d,2p) at the separation and orientation obtained in the previous step. The pair energy is computed as

EABInt=EAB[AB]−EA[AB]−EB[AB]

image

where E is the energy of molecule(s) A and/or B and [AB] refers to combined basis set for A and B.
6. Average among several interaction energies obtained for the same set of molecular pairs to be used as interaction energy parameters in activity coefficient models.
The study, within a pressure domain between 0.01 bar and 100 bars, showed excellent agreement between experimental observations and ab initio method findings, validating the usefulness and soundness of such approaches for thermodynamic property estimation. Broadly speaking, this method can be divided into two steps. In the first step, minimum energy configuration is determined for a defined cluster of molecules. In the next step, from the minimum energy configuration, interaction energies between like and unlike molecules are calculated and provided as input energy parameters for various activity coefficient models.
Quantum mechanics–based method, conductor-like screening model for realistic solvation or COSMO-RS, has been established as a novel and reliable way to predict thermophysical data for liquid systems (Klamt et al., 2010). It is as pointed out previously (Rogers and Mannan, 2006):

a theory where the interactions in a fluid is described as local contact interaction of molecular surfaces and the interaction energies are quantified by the values of two screening charge densities σandσ2image, which form a molecular contact. The screening charge densities can be described as molecular descriptors and provide information about the polarity of the molecules.

As opposed to deriving binary interaction parameters based on functional groups interaction, as done in UNIFAC, COSMO-RS uses the screening charge densities at the local contact area for the same, which is more representative of nonbonded interaction among atoms. Additionally, COSMOS-RS bears the advantage of its ability on screening a large number of compounds from a database (Putnam et al., 2003). Alkanes, alcohols, alkyl in alkanes, ketones in alkanes, and alkenes in alkyl halides are some of the systems best treated through COSMO-RS (Putnam et al., 2003). Lin et al. (Lin and Sandler, 2006) estimated infinite dilution activity coefficients through a group contribution solvation model using ab initio solvation calculations. They found a 7% deviation for their model based on HF method as opposed to 47% and 52% for UNIFAC and modified UNIFAC model while estimating infinite dilution activity coefficient (γ∞)image for a system with water, n-hexane, acetonitrile, and n-octanol.
Quantum mechanics has also been used in deriving QSPR parameters to estimate flash points of various chemical components and mixtures. We will deal with quantum mechanics–based QSPR studies in a later section. While it could be resource intensive computationally, generally speaking it is significantly efficient and cheaper in comparison to carrying comprehensive closed cup tests to determine flash point for every mixture of interest.

3.3.2. Practical Considerations

As discussed in the prior section, flash point of materials is an input to fire modeling problems. It defines the ease of generation of a flammable cloud based on environmental conditions. Even though flash point values have been determined experimentally for several pure components, mixture flash point data are scarce (Rogers and Mannan, 2006). In reality, most process fluid in a plant is a mixture of several chemicals with varying compositions. To make matter worse, these compositions can vary widely during upset conditions in a plant or owing to other unwanted disturbances. Estimation of flash point within acceptable accuracy, of such nonideal liquid mixtures with varying composition through conducting experiments is a daunting task. As Jim Olsen from Forum 2000 correctly pointed out (Hendriks et al., 2010):

We can never conduct all the necessary experiments - but many data measurements are missing. For instance, multi-functional chemicals such as alkanolamines, glycol ethers, excess properties like excess volumes at various temperatures, amides, liquid phase heat capacities, environmental phase equilibrium, safety data e.g., flash-point and auto ignition temperatures, simultaneous physical and chemical equilibrium.

The solution to this problem where need for safety data is a subset probably lies in the following statement from Prausnitz (1999):

Pioneering molecular thermodynamics is concerned not with improvements where primary understanding has already been achieved, but with shedding light on situations where as yet, we know little.

As a consequence, extrapolating flash point data for mixtures from pure component data is not only misleading in some cases but could also result in implementation of unsafe practices in a process facility. To meet the significant demand for flash point data and in lieu of existing expensive tests for flash points (Liaw et al., 2003), alternative theoretical models are needed (Liu, 2010). While models have been developed to predict flash point for the material of interest, those have limited domain of applicability, largely empirical in nature and needs improvement for complex mixtures.
Typically, determination of flash point for mixtures needs the following:
• Flash points of the individual constituents
• Vapor pressure data of the individual constituents
• Activity coefficients of each component
• A reliable approach to predict the flash point of a mixture from these information
In most cases, experimental data of flash point for individual components of a mixture are available (Smallwood, 1996; Yaws, 2003; Lewis and Lewis, 2008). Vapor pressure data of pure components are similarly available in many places (Perry and Green, 1984; Yaws, 1995; Zwolinski, 1971; Mackay et al., 1982). However, activity coefficients, which capture the binary interactions between components of a mixture, can often be challenging to find and is often estimated through generalized theories (Vidal et al., 2004). Along with a dearth of information on mixture data, the need of additional estimation of flammability limits can be attributed to the technological advances leading to emerging novel materials and new environmental concerns leading to stringent conditions and requirement of more accurate predictions even for the smallest relevant constituent of the mixture. Even with today's computational power, the calculations are nevertheless expensive, but with the advent of increased computational power, computer intensive approaches such as this are becoming more feasible to characterize material and phenomenon more accurately. Quantum mechanical calculations can be used to determine the binary interaction parameter used to determine the activity coefficients in the absence of reliable experimental data (Affens and McLaren, 1972; Amadeu, 1999).


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