Vietnam National University – Ho Chi Minh City University of Technology Vietnam National University Ho Chi Minh City University of Technology Faculty of Geology & Petroleum Engineering Department of D[.]
Vietnam National University - Ho Chi Minh City University of Technology Faculty of Geology & Petroleum Engineering Department of Drilling - Production Engineering Course Reservoir Engineering Trần Nguyễn Thiện Tâm Email: trantam2512@hcmut.edu.vn 12/11/2017 Reservoir Engineering References 12/11/2017 Reservoir Engineering Chapter Material Balance 12/11/2017 Reservoir Engineering Contents Introduction Material balance model for an oil reservoir Derivation of the General Material Balance Equation (GMBE) 12/11/2017 Reservoir Engineering Introduction The General Material Balance Equation (GMBE) as developed in this book is based on an oil reservoir with a primary gas cap at initial conditions and reservoir pressure designated as pi At a later time, t, reservoir pressure is assumed to have been reduced from pi from p production of oil, water, and gas During the production period, it is assumed that there was water influx into the reservoir from an aquifer It is also assumed that water and/or gas was injected into the reservoir 12/11/2017 Reservoir Engineering Material balance model for an oil reservoir 12/11/2017 Reservoir Engineering Derivation of the General Material Balance Equation (GMBE) 12/11/2017 Reservoir Engineering Derivation of the General Material Balance Equation (GMBE) The ratio of original reservoir gas cap volume and the original reservoir oil zone volume is defined as: Initial reservoir free gas volume m Initial reservoir oil volume 12/11/2017 Reservoir Engineering Derivation of the General Material Balance Equation (GMBE) Initial reservoir free gas volume GBgi m Initial reservoir oil volume NBoi Initial volume of the gas cap = GBgi = mNBoi The total volume of the hydrocarbon system is then given by: Initial oil volume + initial gas cap volume = (PV)(1 − Swi) NBoi + mNBoi = (PV)(1 − Swi) or NBoi (1 m) PV S wi 12/11/2017 Reservoir Engineering Derivation of the General Material Balance Equation (GMBE) Pore volume occupied by the oil initially in place at pi + Pore volume occupied by the gas in the gas cap at pi = Pore volume occupied by the remaining oil at p + Pore volume occupied by the gas in the gas cap at p + Pore volume occupied by the evolved solution gas at p + Pore volume occupied by the net water influx at p + Change in pore volume due to connate-water expansion and pore volume reduction due to rock expansion + Pore volume occupied by the injected gas at p + Pore volume occupied by the injected water at p The above nine terms composing the MBE can be separately determined from the hydrocarbon PVT and rock properties, as follows: 12/11/2017 Reservoir Engineering 10 Pore Volume Occupied by the Gas Cap at Reservoir Pressure p As the reservoir pressure drops to a new level p, the gas in the gas cap expands and occupies a larger volume Assuming no gas is produced from the gas cap during the pressure decline, the new volume of the gas cap can be determined as: mNBoi Bg Bgi 12/11/2017 Reservoir Engineering 14 Pore Volume Occupied by the Evolved Solution Gas Volume of the evolved solution gas = Volume of gas initially in solution - Volume of gas produced - Volume of gas remaining in solution = [NRsi – NpRp – (N – Np)Rs]Bg 12/11/2017 Reservoir Engineering 15 Pore Volume Occupied by the Net Water Influx Net water influx = We − WpBw 12/11/2017 Reservoir Engineering 16 Change in Pore Volume Due to Initial Water and Rock Expansion The component describing the reduction in the hydrocarbon pore volume due to the expansion of initial (connate) water and the reservoir rock cannot be neglected for an undersaturated-oil reservoir The water compressibility cw and rock compressibility cf are generally of the same order of magnitude as the compressibility of the oil The effect of these two components, however, can be generally neglected for the gas-cap-drive reservoir or when the reservoir pressure drops below the bubble-point pressure 12/11/2017 Reservoir Engineering 17 Change in Pore Volume Due to Initial Water and Rock Expansion V c => V Vcp V p T Where ΔV represents the net changes or expansion of the material as a result of changes in the pressure Therefore, the reduction in the pore volume due to the expansion of the connate-water in the oil zone and the gas cap is given by: Connate-water expansion = Vwcw Δp = [PV Swi] cwΔp NBoi (1 m) Expansion of connate water S wi cw p S wi 12/11/2017 Reservoir Engineering 18 Change in Pore Volume Due to Initial Water and Rock Expansion Similarly, the reduction in the pore volume due to the expansion of the reservoir rock is given by: NBoi (1 m) Expansion of reservoir rock PVc f p c f p S wi Total changes in the pore volume = Expansion of the connatewater + Expansion of the formation NBoi (1 m) Total changes in pore volume ( S wi cw c f )p S wi 12/11/2017 Reservoir Engineering 19 Pore Volume Occupied by the Injection Gas and Water Assuming that Ginj volumes of gas and Winj volumes of water have been injected for pressure maintenance, the total pore volume occupied by the two injected fluids is given by: Total volume = Ginj Bginj + Winj Bw where Ginj = cumulative gas injected, scf Bginj = injected gas formation volume factor, bbl/scf Winj = cumulative water injected, STB Bw = water formation volume factor, bbl/STB 12/11/2017 Reservoir Engineering 20