Energy Engineering - Fundamentals of Oil and Gas Engineering

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1. Material balance for a gas field (50 marks total) (i) You have the following production data for a gas field that might be produced by a natural water drive. Gp Pressure Bg (10 6 scf) (MPa) (rb/scf) 0 40 0.012 26 38 0.0132 52 36 0.0148 75 34 0.0166 93 32 0.0185 The initial water saturation is 0. 20 and the residual gas saturation, from laboratory measurements, is 0.2 5. The material balance equation is: Assuming the pot aquifer model, plot a graph and use this to make an approximate estimate of the original gas in place and the value of the aquifer size times the aquifer compressibility. You may neglect the compressibility of the connate water and rock in the gas field itself. (18 marks ) (ii) What is the recovery factor now? What is the average gas saturation in the field? What is the relative contribution of gas expansion and aquifer drive to production? How would you produce this field? Explain your working carefully. (20 marks) (iii ) What is the pressure at which the aquifer sweeps the entire reservoir leaving just the residual gas saturation behind ? Comment on this value. (12 marks) g e g gi p B W B B G G +      − = 1 2. You measure the following from appraisal wells in a small oilfield: (50 marks total) Depth (m) Pressure (MPa) Fluid and density (kg.m -3) 2,971 32.14 Gas, 420 2,995 32.23 Oil, 780 3,015 32.41 Water, 1,040 The acceleration due to gravity = 9.81 ms -2. Depths are measured from the surface. (i) Is the reservoir normally pressured, over pressured or under pressured? (2 marks) (ii) Find the depths of the free oil and free water levels. Hence find the height of the oil column. (18 marks ) (iii) Explain why the oil pressure should be close to the bubble point. How would you define the gas pressure in terms of a phase diagram ? (10 marks) (iv) The top of the field is located at 2,960 m. What is the capillary pressure between gas and water at the top of the field? Also find the oil/water capillary pressure at the free oil level (base of the gas column). (8 marks) (v) The average horizontal cross -sectional area of the field is 1 0 km 2 throughout the field, while the average porosity and water saturation in the hydrocarbon -bearing zones are 0.21 and 0.2 4 respectively. The oil formation volume factor is 1. 2. Rsi = 1 50 sm 3/sm 3. Bg = 0.004 rm 3/sm 3. The net -to-gross is 0. 8. Estimate the original oil in place and the original gas in place. Comment on your answers. Is oil production likely to be economic? (12 marks) 3. Buckley -Leverett analysis and relative permeability . (50 marks total ) (i) In waterflooding, water is usually injected from the bottom of the field an d moves upwards. Explain why this leads to improved recovery, compared to injection through a vertical well across the whole oil column. Does injecting from the bottom improve the local displacement efficiency? Explain you answers carefully . (20 marks) (ii) Plot the fractional flow using the relative permeabilities below . (6 marks) ������������� = (�������− 0.2)2 �������� = 2.5(��− 0.2)2 o = 0.00 2 Pa.s w = 0.001 Pa.s (iii) Calculate the saturation as a function of dimensionless velocity , and the pore volumes produced as a function of pore volumes injected. Plot your answers on a graph. (12 marks) (iv ) From production data the pore volumes recovered after 1 pore volume of water injected is 0. 24. Comment on this result compar ed to the prediction in part (iii ). Why is there a discrepancy? What is the sweep efficiency? (12 marks) 4. Material balance for a n oilfield . You are given the following data for a n oilfield that is being produced under primary production . There is no water influx. (50 marks total ) Np (MMstb) Rp (scf /stb ) P (MPa) Rs (scf/stb) Bo (rb/stb) Bg (rb/scf) 0 0 48 400 1.314 0.00614 10 400 47 380 1.311 0.00656 14 500 46 360 1.295 0.00712 18 600 45 340 1.254 0.00812 19 700 44 320 1.201 0.00903 (i) From the material balance equation below, find the size o f the oilfield and the size of the gas cap . You may ignore the compressibility of the formation and connate water . (18 marks) �������(�������+ (��− ��)������������)= ������ (�������− ������������� + ������������(�������� − ��)) +������������������� [������ (������������ ������������������ − 1)+ (1+ ������ )(������������+������������������ ������������ 1−������������������ )Δ������]+ ������������ Δ������ (ii) For the last set of data quantify the contribution to production of the different production mechanisms and the current recovery factor. (12 marks) (iii) The field is used to store carbon dioxide. There is no further production of any fluids from the last set of data and only carbon dioxide is injected until the pressure reaches the original reservoir pressure. Find the mass of carbon dioxide that can be stored in kg if the reservoir -condition density of carbon dioxide is 600 kg/m 3 and 1 barrel = 0.16 m 3. Explain your reasoning carefully . (20 marks)