Material Balance of Undersaturated Reservoir

 An undersaturated reservoir is a reservoir where the reservoir pressure was above the bubble point at initial state, and then it has decreased below the bubble point pressure line similar to saturated reservoir. Once we evaluate any material balance situation, we should think the initial state and current state of the reservoir and the phase behavior of the fluid. Consider the states of an undersaturated reservoir as illustrated below:



Figure-1: States of Undersaturated Reservoir


Figure-2: Phase Diagram of Undersatureated Reservoir

 It is evident from the previous diagram that the second state is evaluated at a pressure above the bubble point, while the initial state is examined at the initial reservoir pressure. Additionally, a phase diagram containing the states for an undersaturated reservoir is displayed. The letter "S" further indicates the separator conditions. Take a look at the extended material balancing formula. We may start intelligently eliminating terms that don't apply because we are aware of the reservoir states and the overall pressure decline path of an undersaturated reservoir on a phase diagram. The results are displayed below:



  • (G_{fg})_i =0: No gas is initially in place
  • B_{to} = B_o : the reservoir pressure stays above the bubble point pressure
  • R_v = 0 : No condensate dropping out of gas because we are to the left side of the critical point
  • B_g = 0 : undefined because there is never any gas in the reservoir
  • W_p = 0 : assume negligible water production

After reducing the unnecessary terms, the material balance equation for an under saturated reservoir becomes the following:


In some cases we can simplify the equation further by assuming the reservoir is volumetric. A volumetric reservoir is a reservoir where water and rock compressibilities are neglected and we assume there is no aquifer support (W_e = 0). A volumetric reservoir assumes that oil or gas is the only fluid that can expand. The equation below shows which terms are eliminated from the material balance equation when we assume a volumetric reservoir:

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





Ni(Bo−Boi)+Wi(Bw−Bwi)+vfcf(Pi−P)+We=NpBo









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