Material Balance of Saturated Reservoir

 A saturated reservoir is a reservoir where the reservoir pressure has decreased below the bubble point pressure line. Black oil and volatile oil reservoirs show an example of saturated reservoir behavior, therefore their material balance derivations are same. Once we evaluate any material balance situation, we should think the initial state and current state of the reservoir. We should also keep in mind the phase behavior of the fluid. Consider the states of a saturated reservoir as illustrated below:


Figure-1: States of Saturated Reservoir

Figure-2 Phase Diagram of Saturated Reservoir

It can be seen from the Figure-1 above, a saturated reservoir contains oil and no free gas. As reservoir pressure goes down below the bubble point, free gas begins to release in the reservoir. In the Figure-2, number 1 is initial state, number 2 is final state and letter "S" represents the separator condition. While we considering the material balance equation, we eliminate terms that do not apply because we know the reservoir states and general pressure decline path of a saturated reservoir as it is shown in Figure-2. The results are illustrated below:




  • (G_{fg})_i =0: No gas is initially in place
  • G_I = 0: assume no gas injected into the reservoir
  • R_v = 0 : No condensate dropping out of gas because we are to the left side of the critical point
  • W_p = 0 : assume negligible water production
This result should make sense. When the pressure falls below the bubble point pressure, we have a gas phase in the reservoir. This means B_g is defined. Further, we have multiple phases in the reservoir, therefore the two phase oil formation volume factor (B_{to}) is defined. The above result can be simplified further if we assume a volumetric reservoir. Recall, for a volumetric reservoir one neglects water and rock compressibilities and assumes no aquifer support. The equation below shows which terms are eliminated if one assumes a volumetric reservoir:


After eliminating terms with the volumetric assumption, the material balance equation for a volumetric saturated reservoir is the following:




The material balance equation for a saturated reservoir is just as easy as the material balance derivation for an undersaturated reservoir. In conclusion, if we consider the states of the reservoir and the phase diagram, the material balance derivations are intuitive. 


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