Differences between GROSS methods 0, 1, and 2 in AGA8 Part 1

[EricLemmon]

In the 2017 edition of AGA8, two new methods were added to the GROSS characterization model to implement the equation of state. These are called methods 0 and 3 (method 3 will not be discussed at this point). Method 0 was given the number 0 because in reality it comes before the other two in terms of how the model was derived, how it should be used, simplicity, and I'm sure many more. Decades ago when the only available information for a particular natural gas stream was heating value, relative density, and mole fractions of nitrogen and carbon dioxide, methods were introduced to use that information in order to calculate properties. The methods were labeled as 1 and 2, where each method required three of these input values to characterize the mixture.

However, there is a much better way! In today's world, the composition of the gas is almost always known. The GROSS equation of state requires ONLY the composition to characterize the gas. The heating value and relative density are nowhere to be found in the actual equation of state, rather they can simply be calculated from the composition (for a mass or molar based heating value). A volumetric heating value requires the density of the gas, and thus the equation of state has to be used to obtain this value at a particular temperature, pressure, and composition. (As a side note, the use of volumetric heating values really complicates your life, switch to the use of mass or molar values and you will find your headaches will greatly decrease!)

Method 0 can be viewed as the method used to develop the equation of state back in the 80's. The database of densities of natural gas contains many thousands of measurements, and these were used to determine the parameters of the equation. Once the model was finished and published, the user would obtain those parameters (called second and third virial coefficients, which is a topic for a different discussion) from the composition, and those are used to obtain the pressure from temperature and density. An iterative procedure is required to determine the density from pressure and temperature.

In the natural gas industry, because composition was not always available back in the, um, dark ages 30 years ago, but rather heating value or relative density, two additional methods were needed to obtain the parameters necessary to calculate the virial coefficients. It was not possible (and I believe still isn't possible) to get these parameters without knowing the nitrogen and/or carbon dioxide concentrations. But if those two are known, the developers of the GROSS equation of state found a way to obtain a pseudo-hydrocarbon number based on these, which was then used to obtain the parameters for the virial coefficients. This required several ancillary equations that used inputs of heating value, relative density, and nitrogen and carbon dioxide concentrations (again, only three of these are needed to implement either method 1 or 2).

When composition is known, the use of methods 1 and 2 results in a slight degradation of property values because a round trip exercise is needed to obtain the parameters that you already know! It works like this: With composition, you can calculate either heating value or relative density. With these, you can implement either method 1 or 2. The setup of these methods requires an iterative procedure to obtain the necessary parameters since both volumetric heating value and relative density depend on density (I guess that means that two round trips are needed to calculate properties). The degradation comes from the use of the ancillary equations, which calculate an equivalent hydrocarbon number to obtain the necessary parameters in the equation of state.

Finally, I come to the exciting part where I tell you why you should use method 0. You already know the composition and thus you can calculate directly the equivalent hydrocarbon number without the double round trip explained above. It is really that simple! Furthermore, your results will be identical to the values obtained by the correlators of the equation of state. They did not use methods 1 or 2, they had the compositions of the measurements and used them directly to correlate the parameters. It was only later that the ancillary equations for heating value and relative density were developed to give industry additional methods to implement the model.

Method 0 should always be used when composition is known. The differences between the three methods are quite small, but not always negligible in the transfer of gas from one company to another. We specifically put methods 1 and 2 in an Annex in AGA8 to emphasize that they are not a fundamental part of the GROSS characterization model, but rather they are a means to obtain the equation of state parameters when the full composition is not known.

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