September 2015: Compositional Grading
Calsep recently got access to data for the compositional variation with depth in five North Sea reservoirs. All five reservoirs have a gas-oil contact in the interval fluid samples were taken. Figure 1 shows the variation in saturation pressure with depth in two of the reservoirs. The depths are relative to the depth of the top sample. Reservoir 1 contains a fairly paraffinic fluid while the fluid in Reservoir 5 is rich in asphaltenes. In Reservoir 1 the saturation pressure decreases by approximately 0.2 bar per meter while it decreases by as much as 1.6 bar per meter in the oil zone of Reservoir 5.
For an isothermal reservoir the compositional variation with depth can be modeled using equilibrium thermodynamics taking gravity segregation into account (Schulte, 1980). The action of gravity increases with molecular weight and that makes the concentration of heavy molecular weight components increase with depth. For an oil zone that leads to a decrease in saturation pressure with depth. In the gas zone the saturation pressure is a dewpoint and the dewpoint pressure will increase with depth as the gas becomes richer in heavy molecular weight components. A gas-oil contact is seen in a depth at which the saturation pressure and reservoir pressure coincide. The reservoir will has a gas zone above the gas-oil contact and an oil zone below.
Figure 1 Depth gradient data for two North Sea reservoirs.
Several field observations show that the compositional gradient in most reservoirs cannot be explained by gravity segregation alone. There is an additional contribution from a vertical temperature gradient. That is also the case for the actual North Sea reservoirs, which had a vertical temperature gradient of around 0.025 K/m. Question is how to model the influence of the temperature gradient.
Figure 2 shows a sketch of an experimental setup used by Rutherford and Roof in 1959. They transferred a mixture of C1 and nC4 to two connected chambers. The temperature was higher in one chamber than in the other one and the concentrations of C1 and nC4 in each chamber were measured. The concentration of C1 was higher in the warmer chamber than in the colder one. The outcome of the experiment can be explained using the theory of irreversible thermodynamics.
Figure 2 Experiment of Rutherford and Roof on C1 and nC4
It presents the mechanisms and equations for how a heat source can initiate a compositional gradient. The most fundamental work on that topic was conducted in the late nineteen twenties and early nineteen thirties by the Norwegian Nobel Prize Winner, Lars Onsager (Onsager, 1931). Onsager’s reciprocal relations express a relation between flow and thermodynamic forces and those relations provide a key to simulating the contribution to the compositional grading originating from a temperature gradient.
In 1969 Haase showed that the equations of Onsager can be much simplified by assuming stationarity and that all heat transport is tied to molecular movement. Ignoring gravity effects the Haase model says that a component with an absolute specific enthalpy above average will prefer a warmer zone as compared to components with a lower absolute specific enthalpy. The absolute specific enthalpy is absolute enthalpy per mass unit and unfortunately difficult to quantify. When enthalpy enters into heat exchange calculations, it is not the absolute enthalpy, but the enthalpy relative to some reference state that is evaluated. The reference state could for example be ideal gas at 273.15 K. The concept with relative enthalpy works for a fluid of a constant composition, but is inapplicable to simulate compositional grading.
The absolute enthalpy is the sum of two contributions, the absolute ideal gas enthalpy and the residual enthalpy. The residual enthalpy can be evaluated from an equation of state. The absolute ideal gas enthalpy is more complex to evaluate. It covers the energy held inside a molecule and may vary significantly between molecules of different chemical constitution. The absolute ideal gas enthalpy must be related to the standard heat of formation, which is the energy required to form a molecule from its atoms. The standard heat of formation is much higher for aromatic compounds than for paraffinic and naphthenic compounds of the same molecular weight. That could suggest that the absolute specific ideal gas enthalpy is higher for an aromatic compound than for paraffins and naphthenes. Asphaltenes are high molecular weight aromatics with condensed ring structures. They will have the highest standard heat of formation per mass unit of all reservoir fluid constituents. If that translates into the absolute ideal gas enthalpy, the highest compositional variation with depth must be expected in reservoirs with a high asphaltene content. That is exactly what is seen for the North Sea reservoir fluids. Reservoir 5 has a high asphaltene content and shows a much higher compositional variation with depth than the remaining four reservoirs.
As is illustrated in Figure 3 Calsep was able to model the compositional variation with depth of the North Sea reservoir fluids. The Haase model was used and the C7+ pseudo-components were assigned different ideal gas specific enthalpies depending on the content of aromatics. The highest ideal gas specific enthalpies were assigned to the fluid rich in asphaltenes. The work is documented in an SPE paper (Pedersen and Hjermstad, 2015).
Figure 3 Depth gradient simulation results for two North Sea reservoirs.
Onsager, L., “Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 1931, pp. 405-426 and II. Phys. Rev. 37, 1931, pp. 2265-2279.
Pedersen, K.S. and Hjermstad, H.P., “Modeling of compositional variation with depth for five North Sea reservoirs”, SPE 175085-MS, SPE ATCE Houston, Tx, September 28-30, 2015.
Rutherford, W.M. and Roof, J.G., “Thermal diffusion in methane n-butane mixtures in the critical region”, J. Phys. Chem. 63, 1959, pp. 1506-1511.
Schulte, A.M., “Compositional variation within a hydrocarbon column due to gravity”, SPE 9235, presented at the SPE ATCE, Dallas, September 21-24, 1980.