Whitson, Curtis H., SPE, U. of Trondheim Abstract Methods are developed for characterizing the molar distribution (mole fraction/molecular weight relation) and physical properties of petroleum fractions such as heptanes-plus (C7 +). These methods should enhance equation-of-state (EOS) predictions when experimental data are lacking. predictions when experimental data are lacking. The three-parameter gamma probability function is used to characterize the molar distribution, as well as to fit experimental weight and molar distributions and to generate synthetic distributions of heptanes-plus fractions. Equations are provided for calculating physical properties such as critical pressure and temperature properties such as critical pressure and temperature of single-carbon-number (SCN) groups. A simple three-parameter equation is also presented for calculating the Watson characterization factor from molecular weight and specific gravity. Finally, a regrouping scheme is developed to reduce extended analyses to only a few multiple-carbon-number (MCN) groups. Two sets of mixing rules are considered, giving essentially the same results when used with the proposed regrouping procedure. Introduction During the development of the application of EOS's to naturally occurring hydrocarbon mixtures, it has become clear that insufficient description of heavier hydrocarbons (e.g., heptanes and heavier) reduces the accuracy of PVT predictions. Volatile oil and gas-condensate volumetric phase behavior is particularly sensitive to composition and properties of the heaviest components. properties of the heaviest components. Until recently there has not been published in technical journals a comprehensive method for characterizing compositional variation, which we call "molar distribution." Several authors have given lucid descriptions of petroleum fraction characterization, though they deal mainly with physical property estimation. Usually, only physical property estimation. Usually, only a single heptanes-plus (C7 + ) fraction lumps together thousands of compounds with a carbon number higher than six. Molecular weight and specific gravity (or density) of the C7 + fraction may be the only measured data available. Preferably, a complete true-boiling-point (TBP) analysis should be performed on fluids to be matched by an EOS. Distillation experiments yield boiling points, specific gravities, and molecular weights, from which molar distribution is found directly. Special analyses of TBP data can also provide estimates of the paraffin/napthene/ aromatic (PNA) content of SCN groups, which are useful in some property correlations. Unfortunately, such high-quality data are seldom available for fluids being matched or predicted by an EOS. If data other than lumped C7+ properties are available, they might include a partial component analysis (weight distribution) from chromatographic measurements. In this case. only weight fractions of SCN groups are reported; normal boiling points, specific gravities, and molecular weights (needed to convert to a molar basis) simply are not available. Compositional simulation based on an EOS involves two major problems:how to "split" a C7 + fraction into SCN groups with mole fractions. molecular weights, and specific gravities that match measured C7+ properties, andif a partial extended analysis (e.g., C 11 + ) is available, how to extend it to higher carbon numbers. The first step in addressing these problems is to find a versatile, easy-to-use probability function for describing molar distribution. The distribution function should allow consistent matching and reasonable extension of partial analyses. Also, it should not contain too many unknown or difficult-to-determine parameters. This paper presents such a probabilistic model and describes its application to several reservoir fluids under "Molar Distribution."The second step in characterizing plus fractions involves estimating SCN group specific gravities, which, together with estimated molecular weights (from the probabilistic model), could be used to estimate critical properties required by EOS's. We address this problem and suggest a simple method for specific gravity estimation under "Physical Properties Estimation." SPEJ p. 683

Summary This paper gives an accurate method for modeling the deliverability of gas-condensate wells. Well deliverability is calculated with a modified form of the Evinger-Muskat1 pseudo pressure (originally proposed for solution-gas-drive oil wells). The producing gas/oil ratio (GOR) is needed to calculate pseudo pressure, together with pressure/ volume/temperature (PVT) properties (black-oil or compositional), and gas/oil relative permeabilities. The proposed method is successfully tested for radial, vertically fractured, and horizontal wells. Using the proposed deliverability model, we show that fine-grid single-well simulations can be reproduced almost exactly with a simple rate equation that uses pseudo pressure. The key is knowing the producing GOR accurately. The effect of near-wellbore damage, vertical fracture, or flow improvement caused by horizontal well trajectory is readily incorporated into the rate equation as a constant skin term. The effect of gas/oil relative permeability is studied. We show that well deliverability impairment resulting from near-wellbore condensate "blockage" is dependent only on relative permeabilities within the range defined by 1 < krg/kro< 50. Usually this represents gas and oil relative permeabilities ranging from 0.05 to 0.3. Gas relative permeabilities at low oil saturations (krg > 0.3) affect deliverability only for richer gas condensates. A key observation and conclusion from this study is that critical oil saturation has no direct effect on well deliverability. We also show that interfacial tension (IFT) dependence of relative permeability has little or no effect on gas-condensate well performance (e.g., length of plateau production). The most important application of this study is to provide a simple method for calculating bottomhole flowing pressure (BHFP) in coarse-grid models. We show that the proposed pseudo pressure method is readily calculated for each well grid cell on the basis of only grid-cell pressure and saturation (i.e., producing GOR). Local grid refinement near wells is not necessary, and relatively large well grid cells can be used and still provide an accurate description of well deliverability. Introduction Calculation of gas-condensate well deliverability has been a longstanding problem without a simple solution. When BHFP drops below the dewpoint, a region of high condensate saturation builds up near the wellbore, resulting in reduced gas permeability and lower gas deliverability. The effect of a condensate-blockage region depends on PVT, absolute and relative permeabilities, and how the well is being produced. Reduced gas deliverability because of condensate blockage is important only when condensate-blockage pressure drop is significant relative to the total-well (tubing and reservoir) pressure drop and the BHFP reaches a minimum (dictated by surface constraints) and the well is forced to go on decline. Muskat2 addresses the condensate-blockage problem in his discussions of gas cycling, where he introduces a simple method for estimating the radius of condensate blockage as a function of time, gas rate, and reservoir-rock and -fluid properties. Fetkovich3 uses Muskat's results to derive a rate- and time-dependent blockage skin for use in the standard gas rate equation. Kniazeff and Naville4 and Eilerts et al.5,6 were the first to numerically model radial gas-condensate well deliverability. These studies show radial saturation and pressure profiles as functions of time and other operational variables, confirming that condensate blockage reduces well deliverability. Kniazeff and Naville also study the effect of non-Darcy flow (in the gas phase) on well deliverability. Gondouin et al.7 contribute toward the fundamental understanding of gas-condensate well deliverability through radial black-oil simulations. They extend the work by Kniazeff and Naville, showing the importance of condensate blockage and non-Darcy flow effects on backpressure performance. They also give experimental procedures and measurements that quantify the effects of relative permeability and multiphase non-Darcy flow. O'Dell and Miller8 present the first gas rate equation that uses a pseudo pressure function to describe the effect of condensate blockage. The equation is valid when the produced wellstream is the original reservoir gas and when the blockage radius is relatively small (Le., the reservoir pressure is significantly above the dewpoint). From their results, it is clear that well deliverability can be significantly reduced even for small regions of condensate blockage. Fussell9 presents equation-of-state (EOS) compositional simulations of radial gas-condensate wells producing by pressure depletion below the dewpoint. He shows that the O'Dell-Miller equation (with a small correction to account for gas dissolved in the flowing oil phase) dramatically over predicts the deliverability loss from condensate blockage, compared with simulation results. Jones and Raghavan10,11 primarily treat transient pressure behavior (drawdown and buildup) of radial wells. They use EOS compositional simulation with simple three-component (C1/C4/C10) gas-condensate mixtures. The key observation they make concerning long-term (boundary-dominated) well deliverability is that the pseudo pressure function presented by Fussell is accurate at all times during depletion. However, the integral must be evaluated with pressures and saturations known as a function of radius at a given time in depletion (reservoir integral pseudo pressure). However, they point out that this isn't very helpful because they have to do compositional simulation to know the pressures and saturations at a given time in depletion. We show in this paper how to get the pressures and saturations easily from the instantaneous producing GOR (i.e., the producing well stream composition).

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A simple and generalized correlation in terms of viscosity and molar density is proposed to estimate diffusion coefficients for hydrocarbon systems. The correlation can be used for both gases and liquids up to a pressure of about 400 bar (6000 psia). It has been shown that the proposed method may also be used to estimate effective diffusion coefficients in multicomponent systems with a reasonable degree of accuracy. Although the proposed correlation is based on experimental data in hydrocarbon systems, preliminary evaluations have shown that it is also satisfactory for nonhydrocarbon systems as well. The proposed equation predicts diffusion coefficients in gases with an absolute average deviation of 8% and in liquid systems with an absolute average deviation of 15%. The input parameters for the correlation are molecular weight, critical properties, and acentric factor of components in the system; mixture molar density; low-pressure gas viscosity; and actual viscosity. The last three properties may be predicted from appropriate correlations.

This paper was prepared for presentation at the 1999 SPE Annual Technical Conference and Exhibition held in Houston, Texas, 3–6 October 1999.

This important addition to any petroleum engineer’s library covers all aspects of gas/oil phase behavior and includes a brief discussion of multiphase and vapor/solid phase behavior. Phase Behavior provides the reader with the tools needed to solve problems requiring a description of phase behavior and specific pressure/volume/temperature (PVT) properties. Also included are four appendices, including an overview of understanding laboratory oil PVT reports by M.B. Standing.

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