FUNDAMENTALS

SLOPE FACTORS AND SLOPE ANALYSIS REVEAL PETROLEUM HISTORY
  • Slope Analysis provides unique and valuable insight into the nature, history, and phase behavior of a reservoir fluid, information which is as critical as the exploration effort itself. It is a powerful data analysis tool, yielding additional information from gas chromatography, applicable to both reservoir fluids (PVT data) and C7+ stock tank oils.

  • Parameters employed here which utilize data in the C1 to C5 range cannot be applied to stock tank oil or separator/line gas analyses as such compounds in these fluids are fractionated upon collection.

  • In their primary application, Slope Factors (SF) assess level of maturity by precise measurement of the pseudo-component profile from PVT data, revealing degree of cracking. Precision is sufficient to allow the filling history of a field to be mapped on the basis of the thermal evolution of the charge. In the case of stock tank analyses, a similar result can be attained for C6+ components by employing either normal-alkane or psuedo-component data. These slopes differ, but are best related by the equation given below, revised from that proposed earlier:

    SF(P10+) = 0.348 +0.676(SF(nC10+)).


  • Slope, defined as the rate of decrease in component concentration with increasing carbon number, is expressed as a Slope Factor, SF, modified by indication of the carbon number range within which it was measured, e.g., SF(C3-nC5), or SF(P10+). Any ratio of the type [Pn]/[Pn+1] (expressing the concentration ratio of two adjacent components) is, ideally, equal to the SF value of the series, though generally is approximate due to "noise". In the studies reviewed here, concentrations are measured in mole percent. Molar concentrations, whence mole percentages, equal weight concentrations divided by molecular weight.

  • As detailed in Section 1 , Section 2 and Section 3 of "INVESTIGATIONS", rates of decrease are measured as exponential series within the ranges C3-nC5, C2-P5 and P6+, although the range P6+ may become irregular due to secondary alteration, commonly stabilizing beyond P10 or P15. SF(C3-nC5) is steeper than SF(C2-P5). Both are markedly steeper than SF(P6+).

  • Slope Factors, "SF" values, are determined by the computerized fitting of an exponential equation defining the regression of y on x. Values of y comprise the set of component concentrations, the values of x the associated set of carbon numbers. Details are given in the following table:



  • SF = e(exp|a|)
    (read "e to the power of a")
    where |a| (the absolute value, positive sign) is abstracted from the exponential equation
    y = A.e(exp(-an))
    fitted to the compositional data.

    n is a carbon number,
    A is the y axis intercept at n = 0;
    "-a" is a logarithmic expression of slope, first devised by Kissin (1987).
    The antilogarithm of "a" (positive) is a linear variable, defined above as a Slope Factor.

  • Slope Analysis assesses level of maturity, and four economically significant processes of secondary alteration: gas injection (mixing), evaporative fractionation, biodegradation and migration depletion (see ASSESSMENT OF ALTERATION below). All are recognizable at incipient levels employing Slope Analysis, but otherwise may remain unnoticed. Detecting gas-liquid interactions is key to the appraisal of regional GOR, i.e., proneness to oil or to gas.

  • INPUT DATA

    Molar concentration data, as reported in conventional engineering (PVT) analyses of reservoir fluids, are the starting point. PVT analyses provide either an abbreviated table of concentrations, C1 through C6's plus C7+, or extended data. Extended analyses include determinations of methane, ethane, propane, normal- and isobutane, normal- and isopentane, plus 24 pseudo-component concentrations: C6's through C29's, plus C30+. Each pseudo-component sums the concentrations of all compounds of a given carbon number, for example, P6, P7 etc. P30+ sums all of the heavier remainder. The principal light cyclic compounds are conventionally excluded from the "hexanes", "heptanes" "octanes" and "nonanes" and are reported individually. These compounds are cyclopentane, methylcyclopentane, cyclohexane, benzene, methylcyclohexane, toluene, ethylbenzene + m- & p-xylene, o-xylene and 1,2,4 trimethylbenzene. Their assignment is described below.

  • PSEUDO-COMPONENTS

    Pseudo-components are defined to reduce to manageability the number of "compounds" evaluated simultaneously. In the work presented here, definitions differ from petroleum engineering practice. In the latter, the six-carbon pseudo-component, P6, for example, includes all compounds eluting immediately after n-pentane, up to, and including, n-hexane. Other pseudo-components are defined analogously. Here, however, treatment differs because of the assignments of the light cyclic compounds. The polarity of these causes most to elute outside the expectable carbon number window. For example, methylcyclohexane, C7H14, elutes after nC7. In engineering practice it would be assigned to P8, but here the light aromatics and naphthenes are assigned by carbon number to their appropriate pseudo-component, in this instance P7, regardless of elution anomalies. Engineering protocol is satisfactory at and beyond P10. Gas-chromatographic integration to quantify pseudo-components involves peak area determinations measured from the empty column baseline, established separately, not determinations skimmed from a potentially elevated baseline.

    Compositional data are transformed into a curve, the molecular or molar profile, which is evaluated for Slope Factors by fitting an exponential equations within the chosen regions of n. Data are best presented on log-linear axes, plotting molar concentrations on a logarithmic ordinate scale (y) versus carbon number (x). Ideal exponential concentration distributions are thus seen as straight lines, providing visual appraisal of perfection or alteration in a reservoir fluid composition.

  • ORIGINAL COMPOSITIONS

    Slope Analysis involves a theoretical model of petroleum composition and comparison with observed compositions. A summary of ideal, or model, compositions is given in Section 1. Concepts are based on pyrolysis data representing model precursor compounds such as n-hexadecane, also asphaltenes which generate realistic synthetic petroleums. (Thompson, 2002, ( Bibliography )).

    In unaltered oils, slope is constant from C6 to beyond C30. The four major alteration processes principally modify only the configuration or slope of the front end. After modification the front end slope is no longer compatible with that of the heavy ends. Slope Analysis facilitates comparison of the actual light end profile with that theoretically predictable from the heavy end distribution, facilitating a means of recognition and quantification of gas-related alteration. These relationships are discussed in "INVESTIGATIONS", Section 4 .

    Techniques were developed using databases representing over one thousand analyses of reservoir fluids (PVT data) and stock tank oils.

  • ASSESSMENT OF LEVEL OF MATURITY

    Slope Analysis facilitates the assessment of level of maturity, as well as the diagnosis and quantification of secondary alteration. These processes affect GOR, API gravity, saturation pressure, viscosity, formation volume factor, and other economically significant petroleum properties.

    Increasing maturity in oils is expressed through the thermal cracking of precursor entities (long chains of normal-alkane type) and secondary reactions, leading to progressive decrease in mean molecular weight. Heavy ends are progressively cracked to light ends. This results in increasing API gravity and gas/oil ratio (GOR), decreasing viscosity, accompanied by the progressive modification of all petroleum properties. Figure 1 illustrates the slope aspects of a fluid of low maturity and Figure 2 those of one of relatively high maturity.

  • ASSESSMENT OF ALTERATION

    1. GAS INJECTION The most significant modes of alteration of oil involve the injection of dry gas or gas- condensate into an oil reservoir. The gas is postulated to migrate from deeper higher pressure sources. The effects are illustrated in Figure 3 , Figure 4 and Figure 5 . They result in enhanced GOR and API gravity, and frequently in the generation of elevated pressure in the oil reservoir.

    2. EVAPORATIVE FRACTIONATION Evaporative fractionation involves several essential processes. Firstly, advection of gas into an oil reservoir, secondly, mixing, then depressurization of the gas-saturated oil due to fault activation. Degasification follows, with resulting loss of gas/condensate, generally into faults connecting to shallower reservoirs (Thompson, 1987). The products are light end-depleted oils of increasing aromatic content and non-thermal gas-condensates which contain the more volatile components from the oil. Figure 6 illustrates the features of a strongly fractionated oil, residual after generation of gas-condensate. The fractionating gas is methane, the only light component which is not depleted in the process. C2 - P5 are removed in proportion to their fugacities. Liquid components are less affected.

    3. BIODEGRADATION Bacterial activity in shallow reservoirs at temperatures below approximately 80C removes hydrocarbons, particularly normal-alkanes. Removal commences in the nC10 - nC12 region, where a “valley” develops in the profile. As bacterial activity proceeds the valley widens towards both higher and lower carbon numbers, as shown in Figure 7 .

    4. MIGRATION DEPLETION Migration depletion involves loss of dissolved light hydrocarbons from saturated oils, principally methane, ethane and propane, extending to higher carbon numbers in greatly reduced amounts, proportional to their fugacities under the conditions of decreasing temperature and pressure prevailing along migration paths. Migration depletion progressively lowers GOR and saturation pressure (bubble point), maintaining the latter at the local pressure along the path. Effects on a typical oil are illustrated in Figure 8 .

    In contrast to the behavior of liquids, migration depletion in gas-condensates has comparatively little effect on the light end composition but is extremely effective in controlling the composition of the dissolved liquid components. Pressure decrease causes precipitation of heavier dissolved components in amounts inversely proportional to their fugacities, to the extent that path or reservoir pressure is the dominant factor controlling SF(P6+) and therefore the API gravity of the condensate liquid (Thompson, 2004, p21). Again, saturation pressure (dew point) is maintained at the local pressure along the path. As opposed to the case with oils, SF(P6+) and the API gravity of gas- condensate liquids is unrelated to maturity, except in the instance of thermal gases. Ultimately, these also probably have an origin in evaporative fractionation, with pressure control of liquid slope. At elevated pressures, greater than, say, 10,000 psi, SF(P6+) in gas-condensate liquids is as low as that in many oils, with comparable API gravities. The relationship between SF(P6+) in gas-condensates and their saturation pressure (dew point) is shown in Figure 9 .


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