Compositional Grading—Theory and Practice
- Lars Høier (Statoil) | Curtis H. Whitson (NTNU/Pera)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- December 2001
- Document Type
- Journal Paper
- 525 - 535
- 2001. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 5.5.11 Formation Testing (e.g., Wireline, LWD), 5.1.5 Geologic Modeling, 5.6.9 Production Forecasting, 4.1.5 Processing Equipment, 5.4.2 Gas Injection Methods, 4.3.3 Aspaltenes, 2.2.2 Perforating, 1.8 Formation Damage, 5.1 Reservoir Characterisation, 4.6 Natural Gas, 5.2.2 Fluid Modeling, Equations of State, 5.1.1 Exploration, Development, Structural Geology, 5.2 Reservoir Fluid Dynamics, 5.5.8 History Matching, 5.8.8 Gas-condensate reservoirs, 5.6.4 Drillstem/Well Testing, 5.2.1 Phase Behavior and PVT Measurements
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This paper quantifies the potential variation in composition and pressure/volume/temperature (PVT) properties with depth owing to gravity, chemical, and thermal forces. A wide range of reservoir fluid systems has been studied using all of the known published models for thermal diffusion in the nonisothermal mass-transport problem.
Previous studies dealing with the combined effects of gravity and vertical thermal gradients on compositional grading have been either (1) of a theoretical nature, without examples from reservoir fluid systems, or (2) proposing one particular thermal-diffusion model, usually for a specific reservoir, without comparing the results with other thermal-diffusion models.
We give a short review of gravity/nonisothermal models published to date. In particular, we show quantitative differences in the various models for a wide range of reservoir fluid systems. Solution algorithms and numerical stability problems are discussed for the nonisothermal models that require numerical discretization, unlike the exact analytical solution of the isothermal gradient problem.
We discuss the problems related to fluid initialization in reservoir models of complex fluid systems. This involves the synthesis of measured sample data and theoretical models. Specific recommendations are given for interpolation and extrapolation of vertical compositional gradients. The importance of dewpoint on the estimation of a gas/oil contact (GOC) is emphasized, particularly for newly discovered reservoirs in which only gas samples are available and the reservoirs are near-saturated.
Finally, we present two field case histories—one in which the isothermal gravity/chemical equilibrium model describes measured compositional gradients in a reservoir grading continuously from a rich gas condensate to a volatile oil, and another example in which the isothermal model is grossly inconsistent with measured data and convection or thermal diffusion has apparently resulted in a more-or-less constant composition over a vertical column of some 5,000 ft.
Composition variation with depth can result for several reasons:
Gravity segregates the heaviest components toward the bottom and lighter components like methane toward the top. [1-3]
Thermal diffusion (generally) segregates the lightest components toward the bottom (i.e., toward higher temperatures) and heavier components toward the top (toward lower temperatures). [3,4]
Thermally induced convection creating mixed fluid systems with more-or-less constant compositions is often associated with very high permeability or with fractured reservoirs. [5-7]
Migration and equilibrium distribution of hydrocarbons is not yet complete because the times required for diffusion over distances of kilometers may be many tens of millions of years. 
Dynamic flux of an aquifer passing by and contacting only part of a laterally extensive reservoir may create a sink for the continuous depletion of lighter components such as methane.
Asphaltene precipitation (a) during migration may lead to a distribution of varying oil types in the high- and low-permeability layers in a reservoir  and (b) in the lower parts of a reservoir (tar mats) caused by nonideal thermodynamics and gravitational forces. [10,11]
Varying distribution of hydrocarbon types (e.g., paraffin and aromatic) within the heptanes-plus fractions. [2,12]
Biodegradation varying laterally and with depth may cause significant variation in, for example, H2S content and API gravity.
Regional (tens to hundreds of kilometers) methane concentrations that may lead to neighboring fields having varying degrees of gas saturation (e.g., neighboring fault blocks that vary from saturated gas/oil systems to strongly undersaturated oils).
Multiple source rocks migrating differentially into different layers and geological units.
These conditions and others, separately or in combination, can lead to significant and seemingly uncorrelatable variations in fluid composition, both vertically and laterally. For a given reservoir, it is impossible to model numerically most of these complex phenomena because (a) we lack the necessary physical and chemical understanding of the problem, (b) boundary conditions are continuously changing and unknown, and (c) we do not have the physical property data and geological information necessary to build even the simplest physical models.
One purpose of this paper is to evaluate simple 1D models of vertical compositional gradients caused by gravity, chemical, and thermal effects, with the fundamental simplifying assumption of zero component mass flux defining a stationary condition.
We show that the gravitational force usually results in maximum compositional variation, while thermal diffusion tends to mitigate gravitational segregation.
Published field case histories13-17 and a number of fields where we have studied vertical compositional gradients show that (a) the isothermal model describes quantitatively the compositional variation in some fields; (b) some fields show almost no compositional variation, even though the isothermal model predicts large variations; (c) a few fields have compositional variations that are larger than predicted with the isothermal model; and (d) some fields show variations in composition that are not at all similar to those predicted by zero-flux models.
Another purpose of this study was to compare quantitatively the various thermal-diffusion models for a wide range of reservoir fluid systems. Such a comparison was not available, and we were unsure whether the available models showed significant differences.
Finally, we wanted to give guidelines for how to use measured field data for defining initial fluid distribution, and how simple gradient models can be used to assess measured data and to extrapolate compositional trends to depths where samples are not available.
Compositional Grading—Zero-Mass-Flux Model
Calculating the variation of composition with depth is usually based on the assumption that all components have zero mass flux—existing in a stationary state18-21 in the absence of convection.
To satisfy the condition of zero component net flux, a balance of driving forces or flux equations are used. The driving forces considered include:
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