A new computational model for the non-isothermal gravitational compositional equilibrium is developed and presented.
The mathematical formulation is based on the works of Bedrikovetsky (gravityand temperature using irreversible thermodynamics) and Whitson (algorithm). The computational model is validated on published data and previous simplified models.
An application case is presented for a reservoir in a large deep water fieldin Brazil. The magnitude of the calculated oil composition variations issufficient to explain most observed data. The results suggest that the reservoir is partially connected and that the temperature effect can be asimportant as the gravity effect on the oil composition variation. The changes are significant and the methodology applied is an example of the application of thermodynamic data to the evaluation of reservoir connectivity and fluid properties distribution under the conditions approaching those encountered in natural reservoirs.
Compositional variations along the hydrocarbon column are observed in many reservoirs around the world.
They may affect reservoir/fluid characteristics considerably, such asviscosity, total hydrocarbon volume in place and the development of miscibility, leading to different field development strategies.
These variations are caused by many factors, such as gravity, temperaturegradient, rock heterogeneity, and hydrocarbon genesis and accumulation processes.
In the cases where thermodynamic associated factors are dominant, the existent gravitational compositional equilibrium (GCE) models, which do not properly account for the temperature gradient effect, allow the explanation of most observed variations. However, it is noted that in some cases, the thermaleffect could have the same order of magnitude as the gravity effect.
In this paper, a non-isothermal compositional gravitational model is developed and presented. The model is validated and applied to some fields inBrazil, among them a large deep water field.
The formulation for calculating compositional variation under the force ofgravity for an isothermal system is first given by Gibbs.
P = pressure
Z = fluid composition
= chemical potential
ref = reference
i = component indices
n = number of moles
ln = natural logarithm
g = gravitational acceleration
T = temperature,
M = mass
h = depth
EOS = equation of state
R = real gases constant
f = fugacity
X = component concentration
Muskat, in 1930, provides an exact solution to equation (1), assuming asimplified equation of state and ideal mixing. Because of the oversimplifiedassumptions, the results suggest that gravity has a negligible effect oncompositional variation in reservoir systems.
In 1938, a more realistic EOS (3) is used by Sage & Lacey in order toevaluate equation (2). At this time, the results show significant composition variations with depth and greater ones for systems close to criticalconditions.
Schulte, in 1980, solves equation (1) using a cubic equation of state (3).The results show significant compositional variation.