A New Stability Criterion for the IMPSAT Formulation of Compositional Fluid Flow

A new stability criterion for the IMPSAT formulation of compositional fluid flow has been developed. The new criterion may allow for significantly larger stable timesteps than the conventional IMPSAT stability criterion. <br>The IMPSAT formulation implies that interblock flow terms are evaluated with pressure and saturations from the current time level (implicitly), but with additional variables from the previous<br>time level (explicitly). The new criterion is associated with explicit treatment of variables that may be interpreted as complementary to volumes, referred to as isochoric variables. Analysis shows that the isochoric variables represent the part of the system that may change even though pressure and volumes are kept fixed. The interpretation leads to the identification of two mutually orthogonal subspaces of the computational space, a volume space and an isochoric space. The stability criterion is based on projections onto the isochoric space, and requires that the hyperbolic, isochoric part of the flow must not exceed the corresponding part of the mass present in a gridblock. <br><br><br><br>Whereas the conventional IMPSAT stability criterion puts restrictions on the entire flow of each component, the new criterion only limits the isochoric part of the flow. In many cases, larger timesteps are therefore allowed. The relative improvement may be in the range of 50-150 %, as shown in numerical examples, and the predicted maximum stable timesteps are reasonably close to the observed maximum stable timesteps. However, for cases where there is little or no saturation change between the hydrocarbon phases, e.g., for retrograde gas condensate cases or single hydrocarbon phase cases, the improvement is insignificant.<br>