PROBLEMS
3.1 3.1 A petroleum reservoir has an areal extent of 20,000 ft2 and a pay zone thickness of 100 ft. The reservoir rock has a uniform porosity of 35%. What is the pore volume of this reservoir? reservoir ? (2 marks) Pore Volume=Areal Extent*Thickness*porosity Extent*Thickness*porosity=20000*100*.3 =20000*100*.35=700000ft 5=700000ft2
3.2 Assuming 3.2 Assuming unit formation thickness, determine the average porosity for porosity for the following system when = 0.2, =0.11, = 0.29, L = 0.35 L, and h = h = 0.5 a
h
b
c
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(6 marks)
c
Areal-weighted Average =∑(L* *h )+ (h (L-L1)*0.5)+ c
c
c
1
b
a
b
3.3 A 37.5485 g cleaned and dried core plug was flooded with a 0.75 g/cm 3 crude oil for several days to ensure complete saturation. On termination of the flood, the plug weighed 44.4178 g. What is the oil storage capacity of this plug ? (3 marks). 3.4 Assuming a sandstone grain density of 2.65 g/cm 3, calculate the porosity of a 3 in. long sandstone core sample of 1.5 in. width and breadth, respectively, if the grains weigh 250.0 g? (3 marks).
3.5 Calculate the weight of 1 m3 sandstone of 14% porosity, assuming a sand grain density of 2.65 g/cm 3? (3 marks).
3.6 Calculate the arithmetic average and thickness-weighted average porosity for the following core data:
Sample Number
Depth (ft)
Porosity (%)
1
3705.5
40.1
2
3707
35.1
3
3708
39.3
4
3710
36.5
5
3713
29.1
2
PROBLEMS 4.1 In an experiment similar to that of Darcy's, the flow rate of water was observed to be 5.0 cm3/min. If the experiment were repeated with oil, what would be the flow rate for oil? The difference between the upstream and downstream hydraulic gradients h are the same for both the experiments (measured with water for water experiment and with oil for oil experiment). (4 marks). Additional data: oil viscosity = 2.5 cP, water viscosity = 0.8 cP, oil density = 0.85 g/cm3 and water density = 1.0 g/cm3?
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4.2 Brine flood in a 1.9-in-long and l·.5-in-diameter core plug from the North Sea resulted in a stabilized pressure drop of 46.05 psi. The flood was carried out at 0.05 mL/min with brine viscosity of 0.443 cP. Determine the absolute permeability of this plug in millidarcies. (3 marks). 4
4.3 Three beds of equal cross section have permeabilities of 100, 200, and 300 mD and lengths of 50, 15, and 85 ft, respectively. What is the average permeability of the beds placed in series? (3 marks).
4.4 Three beds of 50, 110, and 795 mD, and 5, 7, 15 ft thick, respectively, are conducting fluid in parallel flow. If all are of equal length and width, what is the average permeability? (3 marks). 4.5 Develop equations for radial flow- in parallel and serial flow systems. (4 marks).
PROBLEMS 5.1. A 10-mm-diameter and 50-mm-long sandstone core plug is pulled with 1500N force. The final reading of the extensometer (an instrument used to measure deformations) is 50.07 mm. Calculate the stress and strain under this load. 5.2. An unconfined triaxial test was carried out on a 1.0-in.-diameter and 2.5-in.long core sample from an Australian field. The sample was axially loaded at a rate of 210 lb/sec up to 80 sec, the time at which it failed. The triaxial test resulted in a deformation in both the axial and lateral directions. The change in the diameter is 0.0005 in.; the change in the length is 0.004 in. Calculate the latitudinal and longitudinal strains, Poisson's ratio, Young's modulus, and the ultimate strength of the sample.
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5.3. Estimate the total reservoir compressibility for a sandstone formation that is characterized by a porosity of 25%. The reservoir is undersaturated (i.e., no initial gas cap is present) and the oil and water saturations are 70 and 30%, respectively. The compressibility of oil and water are 7.5 x 10 -5 psi-1 and 2.5 x 10-5 psi-1, respectively. 6
Figure 2.68. Pore volume compressibility versus porosity (Hall, 1953).
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5.4. Six cylindrical core plugs of 2.54 cm diameter and 3.81 cm length were taken from an Alaskan North Slope reservoir. After cleaning, porosities of all the plugs were measured by a helium porosimeter. Subsequently, all samples were fully saturated with a 0.07 m brine such that, S w= 1. Each sample was placed in a resistivity apparatus and V values were measured for current flow of 0.01 A. Determine the formation factor F , for each core plug and estimate parameters a and m for Archie's formation factor equation.
5.5. Sample 4 from the previous data set was flooded with crude oil, in several steps, in order to displace the brine. The remaining water saturation and V values were measured at each of these displacement steps. Based on the measured data given below and other data from the problem 3, calculate the true formation resistivity Rt , as a function of water saturation S w and subsequently determine the saturation exponent n of the Archie's saturation equation.
5.6. Based on the results from problems 3 and 4, estimate the hydrocarbon saturation in the reservoir if the log analysis indicates that the porosity is 20% and the true formation resistivity is 5.25 m. 5.7. The following table gives the values of the resistivity, R oa of clay-laden rocks when 100% saturated with water of resistivity, R w. Based on the given data,
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calculate the values of Rc, and F . Subsequently, calculate and plot the apparent formation factor vs . the water resistivity in the range of 0.01 to 20 m.
PROBLEMS 6.1. A petroleum reservoir has an areal extent of 55,000 ft 2 and a oil pay zone thickness of 100 ft. The reservoir rock has a uniform porosity of 25% and the connate water saturation is 30%, Calculate the initial oil in place .
6.2. A chalk core plug having a pore volume of 17.0307 cm3 is fully saturated with reservoir brine; A synthetic oil (Isopar-L) flood is conducted on this plug. It is found that 12.25 cm3 of reservoir brine was displaced from this plug by the Isopar-L. After reaching this value, no further reservoir brine could be displaced from the core plug. What is the connate water or irreducible water saturation of this core plug? 6.3. For the following core plugs, gas floods were carried out using nitrogen. The oil produced from plugs 1 and 2 for the gas floods was 9.0 and 6.9 cm 3, respectively. 9
What is the residual oil saturation ( S org ) in these two plugs? Plug Initial Saturations
6.4. A Dean-Stark extraction is performed on a North Sea chalk core plug sample, which extracted 5.77 cm3 of water. The core plug has a porosity of 36.1% and bulk volume of 24.5 cm3. The wet and dry weights of the sample are 50.64 and 42.33 g, respectively. The gas, oil and water densities are 0.001, 0.85 and 1.035 g/cm3, respectively. Calculate the gas, oil and water saturations in the core plug sample. 6.5. The following data is available for the end trim of a c halk core plug sample: S g = 5%, So = 48% and S w = 47%, grain = 2.713 g/cm3
= 38.31% Additional data include gas, oil, and water of densities 0.001, 0.8532 and 1.0351 g/cm3, respectively. The bulk volume of the core plug sample (in a preserved state), from which the end trim was taken, is 65.91 cm 3 and its measured weight (trimless) is 133.0 g. No additional data are available for the core plug sample. Perform an assessment check to evaluate if the end trim data is also valid for the core plug, so that the core plug sample can either be used or discarded for SCAL tests. .
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