CMG Project Report

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LEMMY OSHENYE

PE 3123 PROJECT

TUNING EQUATION OF STATE AND ASSESSING THE IMPACT OF FLUID TRANSPORT WITHIN A RESERVOIR

INTRODUCTION

The Peng-Robinson equation-of-state (PR EOS) was tuned to match the saturation pressure and volumetrics in two lab reports namely CHT-LA-950201 and Good Oil Company using the CMG 2011 software package. The reservoir fluid is classified before the tuning process begins and after tuning the EOS, the tuned data was then used in a reservoir simulation package to assess the impact of fluid transport within the reservoir. The reservoir is an idealized reservoir, circular in shape with uniform thickness, permeability and porosity with a producing well in the center. Important information and results from both labs are detailed below. The Peng-Robinson EOS is given below:

𝑃 + 𝑎!

𝑉! 𝑉! + 𝑏 + 𝑏 𝑉! − 𝑏𝑉! − 𝑏 = 𝑅𝑇

CHEVRON COMPANY (CHT-LA-950201)

Fluid Classification This reservoir fluid is classified as a Gas condensate based on relevant data from the lab report because initial C7+ mole % = 7.36 < 12.5

Tuning Procedure The first step in tuning the EOS is to match the saturation pressure, PSAT of the fluid lab report. The composition of each of the components, including the molecular weight (MW) and specific gravity of the heaviest fraction are first input into the software prior to tuning. To achieve the match for the saturation pressure, the MW of the heaviest fraction, which in this case was C7+, was chosen for the software to modify by running regression. Normally, this should in turn modify the critical temperature, Tc and critical pressure, Pc but for this software, the Tc and Pc had to be selected for the software to modify. Regression is then run to match the saturation pressure.

The next step in tuning the Peng-Robinson EOS is matching the volumetrics by calculating the volume shift, Vs of each component using data from the Constant Composition Expansion (CCE), Differential Liberation (DL), or Separator Test equivalent depending on what is included in the lab report. This fluid study only reported the CCE test and the relative volumes of each component had to be normalized to make the relative volume at the dew point 1 cc. After inputting the necessary volumetrics and gas deviation factor (z-factor), and selecting the volume shift of each component as the parameter to calculate, regression is then run on the data. Results and analysis of important and relevant findings are detailed below.

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RESULTS AND ANALYSIS

Results and Analysis from Tuning EOS The table below summarizes the change in the modified parameters for matching the PSAT.

Component Before Regression After Regression Critical

Temperature, Tc (K)

Critical Pressure, Pc (atm)

Molecular Weight

Critical Temperature, Tc (K)


Molecular Weight

C7+ 748.45 15.07 226.7 749.85 15.07 226.7

From the table, every parameter remained the same except for the critical temperature that had a minute change. The saturation pressure from the lab report was 7975 psia and the reservoir temperature was 309℉. The saturation pressure was properly matched after tuning the EOS. The fact that the MW of the heaviest fraction didn't change to match the PSAT of the lab is reasonable and shows that the lab data is acceptable.

The figure below shows the summary plot of the relative volume vs. pressure from the CCE test after tuning to match the volumetric.

Fig. 1-1. Plot of Relative Volume vs. Pressure before and after regression.

From the graph above, it can be seen that the tuned EOS properly matched the relative volumes of the components reported in the fluid study. However, the liquid volume % (cell volume) was not properly matched at pressures below the saturation pressure due to inaccurate data from the lab report. This is shown in the graph below.

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Fig. 1-2. Plot of Liquid Volume % vs. Pressure before and after regression.

The deviation factor (z) was properly matched as shown in the graph below.

Fig. 1-3. Plot of Gas z-factor vs. Pressure before and after regression

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GOOD OIL COMPANY

Fluid Classification This reservoir fluid is classified as a Black Oil based on relevant data from the lab report because of the following reasons:

Initial C7+ mole % = 33.29 > 20±2.5

FVF (Bo) at bubble-point = 1.474 < 2.0

GOR = 768 < 2000

Tuning Procedure

The tuning procedure is the same for the previous lab report except that for this lab, the Differential Liberation along with the CCE tests are included as reported in the lab report.

Results and analysis of important and relevant findings are given below.

RESULTS AND ANALYSIS

Results from Tuning EOS

The table below summarizes the change in the modified parameters for matching the PSAT.

Component Before Regression After Regression Critical

Temperature, Tc (K)


Molecular Weight

Critical Temperature, Tc (K)


Molecular Weight

C7+ 751.16 16.15 218 751.16 15.94 218

From the table, every parameter remained the same except for the critical pressure that had a 1.3% change, which is reasonable. The PSAT from the lab was 2620 psia and the reservoir temperature was 220℉. Before regression, the PSAT given by the EOS of state was 2654 psia and after regression, it matched the PSAT of 2620 psia of the lab report.

The figure below shows the summary plot of the relative volume vs. pressure from the CCE test after tuning to match the volumetrics. This plot shows that it matches the lab data.

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Fig. 2-1. Plot of Relative Volume vs. Pressure before and after regression.

The graphs below show the summary plots from the Differential Liberation data.

Fig. 2-2. Plot of GOR and Relative Oil Volume vs. Pressure after regression.

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Fig. 2-3. Plot of Gas z-factor and Gas FVF vs. Pressure before and after regression.

It can be seen from Figure 2 - 2 that the tuned EOS was not able to match the Relative Oil Volume of the lab report.

COMPARISON AND CONTRAST

Results and Analysis from Reservoir Modeling After using the data from the tuned EOS in the reservoir simulation, details of findings and conclusions are reported as follows.

The reservoir pressure simulations showed pressure drop towards the wellbore with time for both the gas condensate and the black oil. For a typical gas condensate, as pressure drops below the dew point, liquid begins to form. As the pressure keeps decreasing, more liquid is being dropped out in the reservoir. The liquid usually comprises of the heavier components leaving the lighter components in the gas phase. Since gas is preferentially produced (condensate is usually immobile), we see a progressive increase in the percent of the lighter components and a corresponding decrease in the heavier ones. Figure 1 - 4 (left) shows this trend as the oil mole fraction of the heaviest component is decreasing towards the wellbore because it is being dropped out.

However, for a typical black oil, as pressure drops below the bubble point, gas is evolved in the pore spaces of the reservoir. More pressure decline would result in additional gas being evolved thereby leaving the liquid remaining in the reservoir with less gas. Figure 1 - 4 (right) shows the trend for black

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oil and it can be seen that the oil mole fraction for the heaviest fraction increases after 3 years because the lighter components have evolved out of the solution leaving the heavier components behind.

Fig. 1-4. Change in Oil Mole Fraction (C7+) for gas condensate and black oil after 3 years.

Figure 1-5 (a) and (b) below shows the GOR and cumulative gas trend with time (date) change for the gas condensate and the GOR and cumulative oil trend for the black oil. For a typical gas condensate, the GOR and cumulative gas is supposed to increase since gas is preferentially produced. The GOR decreases at first and then starts to increase, which does not match a typical gas condensate but reservoirs have slightly different properties or it can be due to inaccuracy with the original lab report. The GOR and cumulative gas does continually increase afterwards for the whole life of the reservoir.

On the other hand, the GOR of a typical black oil is constant at pressures above the bubble point because the black oil is undersaturated but then decreases below the bubble point as gas have evolved in the reservoir, leaving less gas dissolved in the liquid. The GOR from the simulation plot follows the typical trend for some time then starts fluctuating. This could be due to inaccuracy in the data from the original lab report.

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Fig. 1-5 (a). Plot of GOR and Cumulative Gas with Time (Date) change.

Fig. 1-5 (b). Plot of GOR and Cumulative Oil with Time (Date) change.

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The condensate dropout from the gas condensate leads to the blockage of some pores and increased resistance to the flow of gas; hence, we usually see a dramatic reduction in well productivity. Plot (a) below shows the gas and oil rate trend with time (date) change for the gas condensate while plot (b) shows that of black oil.

Fig. 1-6 (a). Plot of Gas and Oil rates vs. time (Date).

Fig. 1-6 (b). Plot of Oil and Gas rates vs. time (Date).

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For the gas condensate, Figure 1-7 (a) shows that the oil saturation is increasing with time due to increasing amount of liquid dropout. This is the opposite for the gas saturation since the liquid dropouts are filling up more pore spaces.

Fig. 1-7 (a). Change in Gas and Oil saturation after 3 years for the gas condensate.

Figure 1-7 (b) for the black oil show that the oil saturation is decreasing with time and decline in pressure because it was all liquid at pressures above the bubble point until the pressure drops below the bubble point then gas starts evolving out of the solution. The gas saturation shows an opposite trend, which complements the reason behind the decrease in the oil saturation.

Fig. 1-7 (b). Change in Oil and Gas saturation after 3 years for the black oil.

For the gas condensate, the effects of condensate dropout can also be seen in the relative permeability of the gas and oil since it depends on saturation. Low gas saturation causes low relative permeability to gas. These effects are shown in Figure 1-8 (a) below. For the black oil, the relative permeability of gas starts increasing while that of oil decreases as pressure drops below the bubble point due to gas evolving out of the solution. This can be seen in Figure 1-8 (b).

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Oil Saturation 2014-01-01 K layer: 1

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Fig. 1-8 (a). Change in Gas and Oil Relative Permeability after 3 years for gas condensate.

Fig. 1-8 (b). Change in Oil and Gas Relative Permeability after 3 years for black oil.

Near-Wellbore 2-Phase Flow vs. Single-Phase Flow

Single phase flow occurs above the saturation pressure which is far away from the wellbore and it is either in a liquid phase for black oils or gas phase for gas condensate.

Near-wellbore 2-phase flow occurs below the saturation pressure which is close to the wellbore. For black oils, gas starts coming out of the solution in the 2-phase so you have both gas and liquid flow while for gas condensate, liquid start to form and dropout of the gas in the 2-phase but the liquid dropout is immobile and blocks the pores and cannot be produced.

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Molar Composition Predictions

GAS CONDENSATE PSAT = 7975 psia

Near-Wellbore (2192 psia) 7347 psia 88617 psia

Components yj xj yj xj yj xj

CO2 0.0288 0.0243 0.0267 0.0306 0.0282 0.0000 N2 0.0016 0.0004 0.0015 0.0012 0.0014 0.0000

CH4 0.8883 0.3422 0.8677 0.7177 0.8106 0.0000 C2H6 0.0409 0.0322 0.0397 0.0397 0.0397 0.0000 C3H8 0.0199 0.0269 0.0197 0.0228 0.0209 0.0000 IC4 0.0073 0.0146 0.0075 0.0096 0.0083 0.0000 NC4 0.0050 0.0117 0.0053 0.0071 0.0060 0.0000 IC5 0.0026 0.0090 0.0029 0.0044 0.0035 0.0000 NC5 0.0019 0.0074 0.0022 0.0034 0.0027 0.0000 FC6 0.0030 0.0180 0.0040 0.0070 0.0051 0.0000 C7+ 0.0007 0.5131 0.0226 0.1566 0.0736 0.0000

TOTALS 0.9999 0.9999 0.9999 1.0001 1.0000 0.0000 BLACK OIL PSAT = 2620 psia

Near-Wellbore (1375 psia) 2404 psia 4520 psia

Components yj xj yj xj yj xj

CO2 0.0125 0.0078 0.0103 0.0090 0.0000 0.0091 N2 0.0037 0.0007 0.0043 0.0014 0.0000 0.0016

CH4 0.7375 0.2108 0.7624 0.3415 0.0000 0.3647 C2H6 0.1316 0.0829 0.1172 0.0955 0.0000 0.0967 C3H8 0.0630 0.0725 0.0551 0.0703 0.0000 0.0695 IC4 0.0093 0.0165 0.0084 0.0148 0.0000 0.0144 NC4 0.0222 0.0464 0.0202 0.0404 0.0000 0.0393 IC5 0.0055 0.0181 0.0053 0.0149 0.0000 0.0144 NC5 0.0048 0.0179 0.0048 0.0146 0.0000 0.0141 FC6 0.0095 0.0571 0.0102 0.0452 0.0000 0.0433 C7+ 0.0004 0.4692 0.0016 0.3522 0.0000 0.3329

TOTALS 1.0000 0.9999 0.9999 0.9999 0.0000 1.0000

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CONCLUSION From the molar predictions at the selected pressures above and below the saturation pressure, and comparing them with the molar composition near-wellbore, it is clear that these results support the results, analysis and findings explained priori.

For the gas condensate, it can be inferred that it was a single-phase flow at pressures above the saturation pressure because it is all gas. At a pressure below the dew point and near-wellbore, the mole fraction of the lighter components start increasing in the gas phase and decreasing in the liquid phase while the C7+ mole fraction starts increasing in the liquid phase and decreasing in the gas phase showing that there is liquid dropout in the reservoir and also indicating 2-phase flow. The C7+ mole fraction increases more near-wellbore because of more decline in pressure.

For the black oil, it can be concluded that it was a single-phase flow at the selected pressure above the saturation pressure because it is all liquid. At the selected pressure below the saturation pressure and near-wellbore, the mole fraction of the heaviest component (C7+) starts increasing in the liquid phase and decreasing in the gas phase because gas is evolving out of the solution, leaving less gas in the solution. In addition, the mole fraction of the lighter components starts decreasing in the liquid phase and increasing in the gas phase since gas has started coming out of the solution. This indicates a 2-phase flow.

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