ENPE429 Reservoir Engineering Mingzhe Dong

1 Fall 2013

Assignment #1 Questions (Due date: September 30, 2013)

1. The oil-water capillary data was measured in the laboratory using a model oil and water

on a reservoir core sample from a field. However, the contact angle and interfacial tension for the reservoir oil and formation water in the reservoir were not the same as those measured for the model oil and water. Using the following data, convert the capillary pressures from laboratory conditions to reservoir conditions. Interfacial tensions and contact angles σ (mN/m) θ (Degrees) Laboratory conditions 35 10 Reservoir conditions 25 35

Pc data from laboratory conditions Sw PC (kPa) 0.30 2300 0.35 825 0.50 610 0.65 500 0.70 60

2. The following table shows the capillary pressure curve of a core sample as a function of mercury saturation in the core. The total volume of mercury intruded into the core is 15 cm3 and the bulk volume of the core sample is 75 cm3. Mercury surface tension is 480 dyne/cm and contact angle on the pore surface is 180o. Calculate:

i. The porosity of the core sample. ii. Plot the capillary curve.

iii. The pore size distribution α(De). Show results in a table, one calculation example, and plot of α(De) vs. De.

SHg Pc (kPa) SHg Pc (kPa)

0  100 0.55 254 0.05  136 0.6 270 0.1  170 0.65 280 

0.15  190 0.7 296 0.2  200 0.75 328 

0.25  210 0.8 400 0.3  222 0.85 520 

0.35  228 0.9 750 0.4  233 0.95 1200 

0.45  240 1 1800 0.5  248 0.55 254 

ENPE429 Reservoir Engineering Mingzhe Dong

2 Fall 2013

3. Given the following oil-water and gas-oil relative permeability data: Sw krw kro So krg kro 0.2 0 0.96 0.2 0.1 0 0.25 0.0011 0.85 0.25 0.085 0.0032 0.3 0.0029 0.72 0.3 0.072 0.008 0.35 0.0047 0.6 0.35 0.06 0.013 0.4 0.0091 0.47 0.4 0.047 0.0254 0.45 0.0157 0.35 0.45 0.035 0.044 0.5 0.025 0.24 0.5 0.024 0.0698 0.55 0.0375 0.165 0.55 0.0165 0.104 0.6 0.053 0.10 0.6 0.093 0.148 0.65 0.073 0.06 0.65 0.075 0.204 0.7 0.097 0.03 0.7 0.0045 0.271 0.75 0.126 0.015 0.75 0.0027 0.352 0.8 0.16 0.005 0.8 0.002 0.447 0.85 0.2 0 0.85 0.001 0.559 0.9 0.0005 0.687 0.95 0 0.834

1) Construct the ternary diagram of water isoperms (krw =0.0029, 0.0091, 0.025, 0.073) 2) Construct the ternary diagram of gas isoperms (krg = 0.0005, 0.002, 0.0045, 0.093) 3) Fill in the following table with the oil relative permeability data using Stone’s Model

II. Show one calculation example.

So = 0.4 So = 0.6 So = 0.8 Sw = 0.2 Sw = 0.4 Sw = 0.6 Sw = 0.8

ENPE429 Reservoir Engineering Mingzhe Dong

3 Fall 2013

4. A core sample is 15 cm in length and 2.5 cm in diameter. The porosity of the core is 25%.

The permeability of the core is 0.35 D. The viscosities of water (brine) and the oil are 1.05 and 2.0 cP, respectively. The core was first saturated with brine and then flooded with oil at a rate of 0.02 cm3/s to displace the brine in the core. When the brine production ceased, 15.62 cm3 water (brine) was produced and the pressure drop for oil flow was 0.45 atm. After that water and oil were injected simultaneously to reduce oil saturation in steps. The oil and injection rates (qo and qw), oil and water volumes injected and produced (VoI, VwI, VoP, VwP), and pressure drop at each step are listed in the following table. In the last step, only water was injected to reach the residual oil saturation.

Step 

qo (cm3/s) 

qw (cm3/s) 

VoI (cm3) 

VwI (cm3) 

Vop (cm3) 

Vwp(cm3) 

∆p  (atm)

ko (D) 

kw (D)  Sw  kro  krw 

1  0.019808  0          0.45    2  0.016293  0.00056  58.653 2.018 59.572 1.099 0.5    3  0.01029  0.001681  37.044 6.053 38.882 4.215 0.5    4  0.005031  0.002242  18.110 8.071 19.948 6.233 0.4    5  0.002601  0.003531  9.364 12.711 11.201 10.874 0.35    6  0.001029  0.006053  3.704 21.791 5.542 19.953 0.3    7  0.000343  0.010761  1.235 38.739 3.072 36.901 0.3    9  0  0.020008  0.000 22.000 1.838 20.163 0.35    

1) Calculate the oil-water relative permeability curves as a function of water saturation.

Show example of calculation at step 4. 2) Plot relative permeability curves as a function of water saturation. 3) What are the irreducible water saturation, residual oil saturation, the relative

permeability of oil at irreducible water saturation, and the relative permeability of water at residual oil saturation?