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Material Balance for Oil Reservoirs

Material Balance for Oil Reservoirs. Why do it? Basic Principle Data available for performing material balance Derivation of the material balance equation. Uses of material balance. Provide insight into the production characteristics of the reservoir

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Material Balance for Oil Reservoirs

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  1. Material Balance for Oil Reservoirs • Why do it? • Basic Principle • Data available for performing material balance • Derivation of the material balance equation

  2. Uses of material balance • Provide insight into the production characteristics • of the reservoir • 2 History matching, reservoir drive mechanisms • 3 Determination of initial oil in place • Linearized form of material balance equation • used to estimate the initial oil in place (the intercept of the • straight line) - Havlena and Odeh procedure applied in: • “Reservoir characterization, geological modeling and • reservoir simulation of the N’Sano field - G.R. King 1998

  3. Initial gas cap Expanded gas cap Oil + dissolved gas Expanded of oil + dissolved gas Reduction in PV due to increased grain packing and connate water expansion Pinit > P Basic Principle Expanding Gas Cap Bubble point Liquid shrinking due to liberation of dissolved gas Undersaturated oil p2 p3 p4 p1 > > >

  4. Gas cap C A B Oil + dissolved gas Pinit > P In this lecture we will derive the material balance as a volumetric balance. Material balance is also a critical step in modern reservoir simulation where a mass balance of components within the different fluid phases is generally performed. Withdrawl = Expansion of oil+originally (rb) dissolved gas (B) (rb) + Expansion of gascap gas(A)(rb) + Reduction in PV due to expansion of connate water and tighter grain packing(C)(rb) NOTE that the volume balance is written in terms of fluid at reservoir conditions or as underground withdrawl and fluid expansion.

  5. Another interpretation: compressibility or In this case since dV is production and VdP is volume expansion, the negative sign is removed: i.e. Production is directly related to the volume expansion of fluids. Parameters related to the PVT behaviour of fluids and the fluid phases present are rolled into a equivalent compressibility ce

  6. Data available to do material balance Production Data Np = Cummulative oil volume produced (stb) Rp = Cummulative gas-oil ratio = PVT properties Bo = Oil FVF (bbl/STB) Bg = Gas FVF (cu.ft/SCF) Bw = Water FVF(bbl/STB) Cw = Compressibility of water (psi-1) Rso = Solution Gas-Oil Ratio Reservoir properties Cf = Rock Compressibility Swi = Connate water saturation

  7. Other parameters N = Initial volume of oil in reservoir (rb) = (stb) m = Initial gas cap = These are listed as other parameters because these may either be known by wireline logs, reservoir modeling etc. Or they may be the objective of the material balance computation.

  8. Derivation of the material balance Expansion of the oil + liberated gas Two components: 1. Expansion of oil: Initial Oil = N (stb) Initial oil at reservoir conditions = N Boi (rb) Volume of oil at reduced pressure p = N Bo (rb) Net oil expansion = N(Bo-Boi) (rb) 2. Expansion of liberated gas: Gas dissolved at initial condition = NRsi (scf) Gas dissolved at reduced pressure p = NRs (scf) Liberated gas = N(Rsi-Rs) (scf) Volume of gas at reservoir conditions = N(Rsi-Rs)Bg (rb)

  9. Volume change due to expansion of oil and liberated gas: = N(Bo-Boi) + N(Rsi-Rs)Bg (rb) Let us consider a material balance accounting for just this volume change term (ignoring gas cap expansion, water influx or pore volume reduction): Withdrawl: Amount of oil produced = Np (stb) Oil produced at reservoir conditions = NpBo (rb) Volume of gas produced = NpRp (scf) Let us look at this quantity of gas at the reduced pressure p Volume of gas dissolved in Np vol. of oil at p = NpRs (scf) Remainder gas is the subsurface gas withdrawl in the form of expanding liberated gas and expanding free gas Subsurface withdrawl of gas = Np(Rp-Rs) (scf) Subsurface withdrawl of gas in reservoir bbls = Np(Rp-Rs)Bg (rb)

  10. Therefore, the total subsurface fluid withdrawl : = NpBo + Np(Rp-Rs)Bg (rb) Now writing the material balance: NpBo + Np(Rp-Rs)Bg = N(Bo-Boi) + N(Rsi-Rs)Bg Recovery : If the initial oil in place is unknown and the reservoir drive mechanism is strictly solution gas: (stb) Alternatively denoting the withdrawl term as F and the expansion term [(Bo-Boi) + (Rsi-Rs)Bg]= Eo, the material balance becomes: F = NEo

  11. Material balance : F = NEo • i.e. a plot of F (withdrawl) vs. expansion Eo should be • a straight line with slope N (the initial oil in reservoir). • If the plot is not a straight line - other reservoir drive • mechanisms are present • Remarks: • The recovery is determined once Np, N and the PVT • properties are known. • The material balance equation shows no explicit • dependence on pressure. The influence of the pressure • drop is implicitly introduced through the PVT parameters. • The material balance as derived above is zero dimensional • i.e. the entire reservoir volume is assumed to be • concentrated at a point. The pressure specification is • therefore at that point.

  12. Remarks (cont’d) • For a undersaturated reservoir, all the produced gas Rp can • be dissolved in the oil at reservoir conditions I.e. Rp=Rs=Rsi • The recovery in such a reservoir is simply: • Recovery :

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