An Improved Method for the Determination of the Reservoir-Gas Specific Gravity for Retrograde Gases (includes associated papers 20006 and 20010 )
Authors: Gold D.K. , McCain W.D. , Jennings J.W. 
Published: December 2007

Summary
A method is presented that provides an improved estimate of the reservoir-gas specific gravity for retrograde-gas reservoirs from field production information. This method offers several improvements over previous methods. First, a new term has been introduced into the gas-gravity equation in order to emulate the exact solution of the equation. This term, the additional gas production, Gpa, accounts for the gas production from the low-pressure separator and stock tank. Second, a correlation for the vapor equivalent of the primary-separator liquid, Veq, has been improved. And third, Gpa and Veq correlations were developed for both two-stage and three-stage separation systems. These correlations were developed with the flash liberation results from laboratory fluid analyses. The models were fit to the data by nonlinear regression. The estimate of the reservoir-gas specific gravity is significantly improved by incorporating the new Gpa and improved Veq correlations into the gas-gravity equation. Also, the improved Veq correlation, which accounts for the low-pressure separator gas, stock-tank gas, and stock-tank liquid production, can be used to obtain better estimates of oil fluid withdrawal.

Introduction
The reservoir-gas specific gravity is used by petroleum engineers to gas pseudocritical properties, gas-law deviation factors, and real-gas pseudopressure for bottomhole pressure calculations, deliverability analysis, and reservoir material-balance calculations. The reservoir-gas specific gravity for a retrograde-gas reservoir can be determined by two methods. The first method requires that fluid samples of the primary-separator liquid and gas be obtained from the well, that their respective compositions be determined in the laboratory, and that they then be recombined according to the producing gas/liquid ratio. The second method uses the field production information in the form of a mathematical recombination expression. The laboratory fluid analysis provides the most accurate determination of reservoir-gas specific gravity; however, the field production information can provide a very reliable estimate. The equation for calculating the reservoir-gas specific gravity from production information requires knowledge of separator gas and stock-tank liquid production and the specific gravities of the respective fluids. For a three-stage separation system (consisting of primary and secondary separators and a stock tank), the gas specific gravities and production rates from the primary separator, secondary separator, and stock tank, and the stock-tank liquid gravity, must be known. For a two-stage separation system (consisting of a primary separator and a stock tank), the gas specific gravities and production rates from the primary separator and stock tank, and the stock-tank liquid gravity, must be known. In many cases, only the primary-separator gas production rate and specific gravity, and the stock-tank liquid production rate and gravity, are measured. The gas production from low-pressure separators (the secondary separator and stock tank for a three-stage system, or the stock tank for a two-stage system) is often not measured. Hence, to calculate the reservoir-gas specific gravity with production data, either this production has to be measured or a method to predict these values has to be used. The correlations for additional gas production, Gpa, and the vapor equivalent of the primary-separator liquid, Veq, account for the unknown values needed to calculate the reservoir-gas specific gravity. The Gpa correlation is a new correlation. Previously, the terms represented by Gpa have been assumed negligible. The purpose of the Gpa correlation is to predict the gas production after the primary separator so that this production can be incorporated in the equation for the reservoir-gas specific gravity. The Veq correlation presented here is an improvement of an earlier correlation. Veq accounts for the gas and liquid production after the primary separator. The purpose of the Veq correlation is two-fold; in addition to its use in calculating the reservoir-gas specific gravity, it can be used to calculate the reservoir fluid withdrawal. A correlation for Veq was first proposed by Leshikar. This method is based on Eilerts and Cotton's correlation for condensate gravity and molecular weight and on Beal's correlation for gas solubility. The independent parameters in this method are the primary-separator pressure and API gravity of the stock-tank liquid. Leshikar's correlation underestimates Veq at high primary-separator pressures and stock-tank liquid gravities because Beal's correlation was developed with black-oil data and not retrograde-gas data. Additionally, liquids with high molecular weights in addition to retrograde gases were used in the development of Eilerts' correlation. Leshikar's correlation for Veq results in an average absolute error of 16% when compared with the gas samples used in this study. A different approach was taken in the development of an improved Veq correlation. Veq is the equivalent volume of gas represented by the primary-separator liquid, Veq can be defined in terms of the production after primary separation takes place--that is, the secondary-separator gas/liquid ratio (for a three-stage system), the stock-tank gas/liquid ratio, and the gravity and molecular weight of the stock-tank liquid. Similarly, Gpa can be defined in terms of the secondary-separator (for a three-stage system)and stock-tank gas/liquid ratios and gas specific gravities. These production values were generated with a flash liberation algorithm with different conditions of separator pressures and temperatures for 234 retrograde-gas samples collected worldwide. Both two-stage and three-stage separation systems were simulated. Non-linear regression was used to fit appropriate models to the data. The independent parameters in the models are the primary-separator pressure and temperature, the specific gravity of the primary-separator gas, the gravity of the stock-tank liquid, the secondary-separator temperature (for a three-stage separation system), and the stock-tank temperature. The purpose of this paper is to present the new Gpa and improved Veq correlations for both two-stage and three-stage separation systems and to show how to calculate the reservoir-gas specific gravity and reservoir fluid withdrawal with these correlations.

Theory
The specific gravity of the reservoir gas, gamma g, for a three-stage flash liberation process can be calculated with the recombination expression
(1)
The recombination expression for a two-stage separation system is
(2)
JPT
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