text:
## I have never been here or I have never been there, which is more natural?

8

1

A friend of mine invited me to visit her.
She was afraid that I would get lost, so she said she would be waiting for me at the bus station.

When we finally met at the bus station, I said,

"Sorry I am late. I have never been here."

Is it natural to say I have never been here in this conversation?
Or instead, should I say I have never been there?

29

Native speakers would typically say "I have never been here before" in this context.

You are talking about the place where you are currently, so here is correct. But the sentence "I have never been here" sounds self-contradictory: how can you have never been in the place where you are right now? Adding before restricts the "have never been" to the past and removes the contradiction.

11Perhaps just my opinion, but as a native speaker I might easily omit "before" and I wouldn't take any notice of whether someone added it or not. If they're here now, then it's implicitly speaking about the past. – Darren Ringer – 2018-04-19T13:26:21.900

You definitely do not always need before. "I've been..." said the soldier, trailing off as he peered around at the miraculous equipment in the secret laboratory. He suddenly remembered he had been speaking. "I've been to this building so many times, but I've never been *here*. What *is* this place?" – Ben I. – 2018-04-19T18:14:14.030

7Reminds me of an exchange from a show, after shaking hands with Gray Davis: "This is quite an honor. I've never shaken hands with a governor" "Actually, I was just voted out of office" "Like I said,I've never shaken hands with a governor". – Acccumulation – 2018-04-19T18:39:32.120

3@BenI. It's a matter of emphasis. In your example, you're emphasizing a specific part of the building, and you stress "here". But in the OP, the reason for getting lost is that this is a new experience, and "before" emphasizes that. – Barmar – 2018-04-20T03:49:07.667

@Acccumulation IRL the ex-governor would smile and probably think: "what a smart@.. this guy is..." – CPHPython – 2018-04-20T08:58:48.700

@DarrenRinger I agree, the meaning is implicit when omitting before or previously. Another meaning that it might relate to is that you are currently exploring the place and every new step you take makes that sentence nearly accurate. – CPHPython – 2018-04-20T09:06:21.610

10

What you said is correct and natural. You use "here" when the place is near your current position, while "there" is used when the place is far from you. So, in the situation that you were already there, and you wanted to talk about the place you were in then "here" is the correct word of choice.

2I agree that "here" is correct - but as @zwol says, it would be much more natural to say "never been here before" :) – psmears – 2018-04-19T14:46:50.117

2Also, it's natural for native speakers (USA) to use the contraction "I've" instead of "I have." "I've never been to Greece" and "I've never been here before." – user8356 – 2018-04-19T15:43:58.280

2@user8356 It's natural for all native English speakers to use contractions. I have has a slight emphasis on have, whereas I've has no emphasis and is neutral. Second language speakers of English often don't realise this distinction. – CJ Dennis – 2018-04-20T04:49:09.787

2

I would have said

Sorry I am late. I had never been here.

Because I would, at that moment, be there. Of course, I am not there now, so I do not use the word "here" now. But I would have used "here" in the moment. Now that I am no longer there, I say there. I am always here in the present, but in the past I may have been there. Although I was here in the morning as well.

The "before" at the end would magnify that sense of prior to that moment, but I think that the "had" is sufficient. There is an English grammar "rule" not to end sentences with a preposition, so some would prefer not to end the sentence with "before" to comply. However, non-compliance is common, particularly in spoken English. Adding the "before" to the sentence with "have" makes it descriptively correct if not perfect grammar.

You could also say

Sorry I am late. I had never been here previously.

"Previously" is never a preposition, so it won't make people think that you are ending a sentence with a preposition. But "previously" doesn't come through as naturally as "before" does. It sounds more stilted and formal.

Sorry I'm late. This is my first time here.

This also works.

To restate, here is where I am now. There is someplace that I am not currently. So in your original sentence, it should be "here" rather than "there" because you are currently at the time of speaking at that place.

Now, you might say

Sorry I was late. I had never been there.

Because you are presumably no longer in that place. So it is now there rather than here (wherever you may be now). Unless of course you are reading this on your mobile in the same location. Then you would properly still use here.

I disagree. You use "had never" when the time you're comparing to is in the past, you use "have never" when you're comparing to the present. Google "had never versus have never". – Barmar – 2018-04-20T03:53:38.437

I like that you mentioned how we'd use there instead of here if we are having our conversation later on, and we are no longer near the meeting place. – J.R. – 2018-05-04T13:57:38.000

2

The answer to the question you asked is very clear: we say "here" when you are describing a place you are in (physically or metaphorically), and "there" when you're describing something you are far from or separate from.

However, as often happens on this site, the answerers seemed more interested in a different question: whether or not to say "before" at the end of your sentence. Nobody's cited any evidence, which is probably why we are seeing disagreement. (It seems like the disagreement is mostly due to personal preference.)

Looking at Google NGram, both are well-attested. The line on the chart for "never been here" should include every entry for "never been here before". It looks like about 60% of instances from this corpus are "never been here before", so this phrasing may be slightly privileged, but either one should be unremarkable. There was a brief period in the 1810s when "before" seems to have been required, but that looks like an unusual outlier from 200 years ago.

Now that I've complained about personal anecdotes, here's my own personal anecdote. For me, if I added "before", I would probably barely pronounce it: if I said it at all it would be as "I've never been here 'fore". I expect this means I would consider the word superfluous.


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# Modeling of CO2-LPG WAG with asphaltene deposition to predict coupled enhanced oil recovery and storage performance

## Abstract

Combined carbon capture and storage and CO2-enhanced oil recovery (CCS-EOR) can reconcile the demands of business with the need to mitigate the effects of climate change. To improve the performance of CCS-EOR, liquefied petroleum gas (LPG) can be co-injected with CO2, leading to a reduction in the minimum miscibility pressure. However, gas injection can cause asphaltene problems, which undermines EOR and CCS performances simultaneously. Here, we systematically examine the mechanisms of asphaltene deposition using compositional simulations during CO2-LPG–comprehensive water–alternating-gas (WAG) injection. The LPG accelerates asphaltene deposition, reducing gas mobility, and increases the performance of residual trapping by 9.2% compared with CO2 WAG. In contrast, solubility trapping performance declines by only 3.7% because of the greater reservoir pressure caused by the increased formation damage. Adding LPG enhances oil recovery by 11% and improves total CCS performance by 9.1% compared with CO2 WAG. Based on reservoir simulations performed with different LPG concentrations and WAG ratios, we confirmed that the performance improvement of CCS-EOR associated with increasing LPG and water injection reaches a plateau. An economic evaluation based on the price of LPG should be carried out to ensure practical success.

## Introduction

Concerns about climate change are driving global efforts to reduce atmospheric CO2 concentrations. Many options to reduce CO2 emissions have been studied. Climate change mitigation will depend at least in part on combining CO2 capture and utilization with microalgal carbon capture and biomass production1. Improving energy efficiency and using renewable energy in residential and industrial contexts can also reduce CO2 emissions. Carbon capture and storage (CCS) is regarded as an effective way to reduce atmospheric CO2 concentrations due to its negative CO2 emissions2,3. Forty-three large-scale commercial CCS facilities were in operation globally in 20184, with that number increasing to 51 in 20195. These operations have the combined capacity to capture and store an estimated 40 million tons of CO2 every year. The disadvantage of CCS in aquifers is the lack of a profitability model. Coupling CO2-enhanced oil recovery with CCS (CCS-EOR) could improve the economics through oil production6,7.

Miscible gas flooding as an EOR technology changes the composition of oils and results in the precipitation and deposition of asphaltene in oil reservoirs8 as changes in the composition of the oil affect the solubility of asphaltene9,10. Precipitated asphaltenes can be deposited throughout a reservoir, damaging geological formations. Such damage can affect both EOR performance and CO2 storage mechanisms during CCS-EOR11. Oil and asphaltene do not have to be taken into account in conventional CCS involving aquifers. But in CCS-EOR, both the oil and asphaltene phases must be considered to enable precise performance predictions due to interactions among phases.

The effectiveness of CO2 injection in CCS-EOR is limited due to difficulties reaching miscible conditions, which requires that the reservoir pressure exceed the minimum miscible pressure (MMP). Increasing only the injection pressure is challenging because of the cost and the risk of formation damage. Co-injection of liquefied petroleum gas (LPG) and CO2 can address this problem by lowering the MMP instead of increasing reservoir pressure12,13. CO2-LPG co-injection improves both the displacement and vertical-sweep efficiencies of EOR, but its effectiveness depends on other factors, such as heterogeneity and reservoir fluid properties14,15. Experimental studies of CO2-LPG flooding have verified the advantages of LPG12,13. Because adding LPG accelerates oil swelling by improving miscibility and reducing oil density, it also intensifies asphaltene precipitation16. Previous studies assumed asphaltene only affected EOR, and not CO2 storage17,18. To overcome these application limits, an integrative model that considers asphaltene deposition in a CO2-LPG system was developed for this study. The model is an improved version of a CCS-EOR model developed by Cho et al.11 that used only CO2 injection. The new model can take into account the effects of both CO2-LPG co-injection and formation damage on CO2-trapping mechanisms during CCS-EOR.

### Numerical model for major mechanisms

#### Porosity and permeability reduction

A solid model proposed by Gupta19 was used for this study. Precipitating and non-precipitating components were used to calculate the fugacity of the solid phase20. While the solid model calculates the fugacity of the precipitating asphaltene, S1, using Eq. (1), the Peng-Robinson equation of state (EOS)21,22 computes the fugacity of the components in oil and gas phases:

$$\ln f_{{S_{1} }} = \ln f_{{S_{1} }}^{*} + \frac{{V_{{S_{1} }} \left( {p - p^{*} } \right)}}{RT}$$
(1)

where $$f_{{S_{1} }}^{*}$$ is the fugacity of S1 at onset pressure p* and $$V_{{S_{1} }}$$ is the asphaltene molar volume. The equilibrium condition can be achieved when the fugacities of each component in solid (the solid model), water (Henry’s law), oil, and gas (Peng-Robinson EOS) are equal. The amount of asphaltene precipitation can be estimated using the equilibrium condition.

After estimating asphaltene precipitation through the equilibrium condition of the fugacity of each component, the Wang and Civan23 equation can be applied to estimate the amount of asphaltene deposition as follows:

$$\frac{{V_{{S_{2}^{d} }}^{n + 1} - V_{{S_{2}^{d} }}^{n} }}{\Delta t} = \alpha C_{{S_{2}^{f} }}^{n + 1} \phi^{n + 1} - \beta V_{{S_{2}^{d} }}^{n + 1} \left( {v_{o}^{n} - v_{cr,o} } \right) + \gamma u_{o}^{n} C_{{S_{2}^{f} }}^{n + 1}$$
(2)

where $$V_{{S_{2}^{d} }}$$ and $$C_{{S_{2}^{f} }}$$ are the volume of deposited and flowing solid S2 and vo and vcr,o are the interstitial and critical velocity of the oil phase, respectively. The coefficient of the surface deposition is represented by α. The re-entrainment term β has a non-zero value when vo is greater than vcr,o for the re-entrainment phenomenon, and can reduce the amount of asphaltene deposition. If vo is lower than vcr,o, β is set to zero and re-entrainment does not occur. The γ value is the pore throat-plugging coefficient.

Deposited asphaltene plug pores, which can reduce porosity and absolute permeability, are described by equations for the power law and the oil resistance factor24:

$$\phi = \phi_{0} - V_{{S_{2}^{d} }}$$
(3)
$$\frac{{k_{0} }}{k} = \left( {\frac{{\phi_{0} }}{\phi }} \right)^{n} = F_{r,o}$$
(4)

where the superscript 0 refers to the initial condition and Fr,o is the oil resistance factor.

### Residual and solubility trapping

Asphaltene deposition not only changes absolute permeability but also relative permeability with wettability alterations25. To reflect this effect, the Brooks–Corey model is applied with the contact angle change26:

$$k_{r,w} = k_{r,w}^{*} \left( {\frac{{S_{w} - S_{r,w} }}{{1 - S_{r,w} - S_{r,nw} }}} \right)^{{e_{w} }}$$
(5)
$$k_{r,w}^{*} = 1 + \left[ {k_{r,w}^{0*} + \frac{{\cos \theta - \cos \theta^{0} }}{{\cos \left( {\pi - \theta^{0} } \right) - \cos \theta^{0} }}\left( {k_{r,nw}^{0*} - k_{r,w}^{0*} } \right) - 1} \right]\left( {\frac{{1 + T_{w}^{0} N_{T,w}^{0} }}{{1 + T_{w} N_{T,w} }}} \right)$$
(6)
$$e_{w} = 1 + \left[ {e_{w}^{0} + \frac{{\cos \theta - \cos \theta^{0} }}{{\cos \left( {\pi - \theta^{0} } \right) - \cos \theta^{0} }}\left( {e_{nw}^{0} - e_{w}^{0} } \right) - 1} \right]\left( {\frac{{1 + T_{w}^{0} N_{T,w}^{0} }}{{1 + T_{w} N_{T,w} }}} \right)$$
(7)

where subscript O indicates the initial condition, and w and nw indicate the wetting and non-wetting phases, respectively, $$k_{r}^{ * }$$ is the endpoint of the relative permeability, Sr is the residual saturation, ew is the exponential parameter, and Tw and NT are the trapping parameter and number, respectively.

Relative permeability and contact angle changes are assumed to be affected only by asphaltene deposition. The initial condition of reservoir is considered as strongly water-wet, changing to slightly water-wet at maximum asphaltene deposition, as determined by the interpolation method. To ensure reliability, the same reference is used for relative permeability and fluid data, which are widely used in asphaltene simulation studies, and a previous base study11,27. The reservoir gradually changes to slightly water-wet conditions using the interpolation method, depending on the amount of asphaltene deposition (Fig. 1).

The Larsen and Skauge28 three-phase hysteresis model can be applied to reflect the residual trapping performance with the estimated relative permeability curves. Aziz and Settari29 derived oil’s relative permeability in a three-phase system from two-phase relative permeability data through a modified version of Stone’s first model. Henry’s law30 estimates solubility-trapping performance. While an EOS calculates the fugacity of CO2 in gas and oil phases, Henry’s law calculates fugacity in the aqueous phase.

## Results

### Asphaltene and fluid modeling

In this study, fluid modeling for asphaltene precipitation and compositional simulations used WinProp and GEM, which were developed by the Computer Modelling Group Ltd. (CMG) in Canada31,32.

Many simulation studies have used data from Burke Oil 133, which were also applied here11,17. Table 1 provides the oil composition and properties, and the experimental and calculated oil properties produced by a regression method are compared in Table 2, which shows the acceptable results. The MMP of Burke Oil 1, as estimated by the multiple-mixing-cell method, was 33,584 kPa with pure CO234. The MacLeod–Sugden correlation35 was used to calculate the interfacial tension (IFT) between CO2-LPG gas and crude oil. The MMP is considered when the IFT is less than 0.001 mN/m, and we used the same criterion in our study. Results of the MMP computation are shown in Table 3. The higher the LPG (63% propane and 37% butane) concentration, the lower the MMP, a trend that has been verified by previous studies36,37.

Figure 2 depicts the amount of precipitated asphaltene versus CO2 and LPG concentrations at a reservoir pressure of 15,857 kPa. The amount of precipitated asphaltene initially increased with the CO2 mole fraction, but it began to decline after the injected gas mole fraction reached 0.7, likely because the saturation pressure also increased with CO2 injection, making it a two-phase region10. The LPG accelerated more asphaltene precipitation relative to 100% CO2 injection16.

### EOR performance

Because water–alternating-gas (WAG) injection increases the performance of both EOR and CCS, the process was applied in this study38,39. For the first three years, waterflooding was conducted as a secondary recovery, and WAG injection with a 1:1 ratio was performed for 10 years. All input parameters for the simulation are shown in Table 4.

Liquid propane gas can increase oil production by improving the displacement efficiency. The added LPG consists of 63% propane and 37% butane30. The enhanced displacement efficiency was confirmed by measurements of oil viscosity and density, and IFT changes. Figure 3 depicts the two-dimensional oil viscosity. In the blue region of the swept area where displacing fluids contact reservoir oil the most, the minimum oil viscosity obtained with 100% CO2 injection is 1.02 mPa·s (Fig. 3a). When LPG was added as 10% of the molar fraction in the injected gas stream, the molecular weight and viscosity at the reservoir condition were 44.54 and 0.0673 mPa·s, respectively. The CO2-LPG associated with the blue region spread more widely, and the oil viscosity decreased to 0.63 mPa·s, which was 38% lower than it in the CO2 case (Fig. 3b). As the LPG concentration reached 20%, the oil viscosity decreased to 0.46 mPa·s (Fig. 3c). The white zone, which indicates a viscosity of greater than 5 mPa·s, spreads out near the injector because intermediate components were expelled from the initial oil, and heavier components accounted for a greater percentage of the residual oil. The zone becomes wider with increased LPG concentration due to the improved displacement efficiency. LPG also reduces oil mass density by accelerating oil swelling. Figure 4 illustrates the changes in oil density during WAG injection at the center of the reservoir. The minimum values were 841, 811, and 774 kg/m3 for the 100% CO2, 90% CO2 + 10% LPG, and 80% CO2 + 20% LPG cases, respectively, indicating that oil swelling was accelerated by the addition of LPG. In the area swept by the injected gas, oil density began to increase due to heavy components in the residual oil. Residual oil in the 80% CO2 + 20% LPG WAG injection had the highest densities, which were 2% and 1% higher than in the 90% CO2 + 10% LPG and 100% CO2 cases, following the same trend as the residual oil viscosity.

The effect of LPG on the IFT change was investigated using IFT values plotted in the same area (Fig. 5). Because CO2 and LPG co-injection increased the density of the displacing fluid (due to the higher molecular weight of LPG), the CO2 and LPG mixture became similar to oil, resulting in IFT reduction. As a result, the IFT between the stream with 20% added LPG and the reservoir oil had the lowest value, 0.2 mN/m. The IFT values between the 100% CO2 and 90% CO2 + 10% LPG streams and the reservoir oil were 1.4 and 0.5 mN/m, which were 600% and 150% higher than that of the stream with 20% added LPG.

Although adding LPG can improve miscibility, it can also increase asphaltene-related deposition in the reservoir (Fig. 6). The first stage of asphaltene deposition resulted from pressure depletion during pre-waterflooding for three years (2007–2010), and the compositional change of oil caused deposition again after 2010 due to WAG injection. Figure 7 shows the effects of the oil resistance factor, with that of CO2-LPG WAG injection 4% higher than it was in CO2 WAG injection. Figure 8 supplies the water relative permeability curves after the wettability alteration by asphaltene deposition. Water permeability was enhanced to the water saturation (shown by the black line) after asphaltene deposition during CO2 WAG injection. For CO2-LPG WAG injection, the improvement was more significant, as indicated by the red line. Overall, LPG improved displacement efficiency, with oil 11% higher than in the case of CO2 WAG injection (Fig. 9).

### CCS-EOR performance

To exclude the effects of differences in the injection rates, the same rate was set for injected gas with molar fractions of 100% CO2 and 90% CO2 + 10% LPG. Figure 10 depicts the gas scanning curves for the asphaltene, hysteresis effects, and residual water saturation. Figure 10a shows the gas relative permeability change during CO2 and CO2-LPG WAG processes. Because LPG gives the rock surface a higher affinity for oil and gas due to surface deposition of asphaltene, the gas mobility decreased and the relative permeability shifted toward the bottom right. This caused 9% more CO2 residual trapping by hysteresis, even though less injected CO2 was involved in CO2 WAG injection (Fig. 11). In contrast, because LPG accelerated the improvement of water mobility and gas hysteresis, trapped CO2 displaced more water, reducing water saturation (Fig. 10b). Consequently, the CO2 dissolved in the water in the CO2-LPG WAG process was 3.9% lower than in the CO2 WAG injection (Fig. 12). However, this does not indicate a reduced performance of CO2 solubility trapping. Because the injected moles of CO2 were different in this study, the ratio between the remaining and injected CO2 in the reservoir should be compared when attempting to make an accurate comparison of trapping performance by mechanism (Fig. 13). The movable CO2 was not yet trapped but can be trapped potentially. As shown in Fig. 13, residual trapped and movable CO2 were 9.2% and 50% higher than in the CO2 WAG case, respectively, while solubility-trapped CO2 was 3.7% lower. The addition of LPG caused more wettability alteration, reduced gas mobility, and increased water mobility. Residual trapping performance was improved due to reduced gas mobility. In contrast, solubility trapping decreased because the increased water mobility reduced the residual water saturation. As a result, the total CCS performance was enhanced by 9.1% after the addition of LPG.

### LPG concentration and WAG ratio effects

By analyzing the effectiveness of adding LPG to the CO2 process, we investigated the effects of LPG concentrations and WAG ratios on CCS-EOR performance during CO2-LPG WAG injection. As can be seen in Fig. 14, adding 10% LPG to the injection gas led to a 4% increase in oil recovery compared with 100% CO2 injection. The recovery of 80% CO2 + 20% LPG was 2% higher than that of the 90% CO2 + 10% LPG case, and the increase was the same in the 30% LPG + 20% LPG conditions. This indicates that the incremental increase in EOR performance plateaus as the amount of added LPG increases.

The ratio between the remaining CO2 in the reservoir and the injected CO2 was compared for different LPG concentration models (Fig. 15). The performance of residual trapping was enhanced until the added LPG concentration reached 20% because the increased wettability reduced the gas mobility. When the added LPG concentration was increased to 30%, the efficiency of residual trapping did not change, as the wettability had already reached its maximum and the gas mobility was not further reduced. Because greater asphaltene deposition increased the reservoir pressure, solubility trapping was enhanced. In contrast, the average reservoir pressure increased due to more-severe plugging effects, and the solubility trapping performance could be enhanced. In summary, the ratios of residual to injected CO2 were 50.7%, 55.3%, 61.3%, and 61.8% for cases with 100% CO2 and 10%, 20%, and 30% LPG additions, respectively. The efficiency of CCS tended to be enhanced as the concentration of LPG increased. Economic analysis should be performed for both EOR and CCS, because the improved CCS efficiency with LPG addition shows diminishing returns.

To detect the effect of the WAG ratio, simulations were also conducted for models with WAG ratios of 1:1 (the previous model) and 2:1 (the amount of water injection was double compared to the previous model) during CO2-LPG WAG. Because the same amount of gas was injected, the quantity of the deposited asphaltene was almost equal. However, the reservoir pressure increased due to greater water injection at a 2:1 WAG ratio (Fig. 16). The performance of CO2 residual trapping in the 2:1 WAG model was less than that of the 1:1 model because the duration of each inhibition period was longer. This caused CO2 to be expelled from trapped positions, despite the comparable amount of asphaltene deposition and wettability alteration. However, the higher reservoir pressure and greater water injection in the 2:1 WAG injection enhanced the performance of solubility trapping (Fig. 17). As a result, CCS performance did not change significantly, even though more water was injected in the 2:1 WAG injection. Increased water injection can therefore improve EOR performance with oil recovery by 1.1% (Fig. 18).

## Discussion

This study examined the effects of adding LPG to an CO2 stream in CCS-EOR with respect to asphaltene deposition using a compositional two-dimensional reservoir simulation. The effects of gravity and heterogeneity were ignored to focus on miscibility and damage to geological formations. We expect that the developed model can be expanded to a three-dimensional heterogeneous model that can be applied real field cases.

The significance and the speed of wettability alteration by asphaltene deposition remain controversial. Many studies, including this one, have assumed that wettability alteration depends on the amount of asphaltene deposition and the contact angle as determined by a computational method without experimental data6,12,20,22. This does not pose a logical problem, but it is necessary to select simulation parameters through experimentation to accurately evaluate the impact of asphaltene deposition on wettability alteration.

For field applications, an optimum CO2-LPG WAG design that considers economic feasibility, such as tax credits; CAPEX; OPEX; and the price of CO2, LPG, and oil, is necessary. Because these factors depend on reservoir characteristics, a site-specific design that incorporates economic feasibility is essential.

## Conclusions

An integrated model that incorporates a fluid model with a reservoir simulation under dynamic conditions was developed to investigate the effects of LPG on a coupled CCS-EOR process with asphaltene deposition. For the reservoir simulation of WAG-based CCS-EOR, a three-phase hysteresis model was applied to determine trapping phenomena under dynamic conditions. Formation damage from asphaltene deposition was incorporated into models of the CO2 and CO2-LPG WAG processes. The following conclusions can be drawn:

1. 1.

Because of the improved displacement efficiency caused by the increased oil viscosity, increased density, and IFT reduction, LPG enhances EOR performance during WAG injection. Reduction in oil density by LPG addition lowers the asphaltene solubility of oil, and CO2-LPG co-injection accelerates asphaltene precipitation and resulting formation damages. EOR performance of CO2-LPG WAG injection without asphaltene 18% higher than that with asphaltene, according to the model. The performance of CO2-LPG WAG injection can be overestimated if the formation damage is not considered.

2. 2.

An integrated model for CO2-LPG WAG injection with three-phase hysteresis was applied to the coupled CCS-EOR process. LPG lowers oil density by more than does CO2 WAG injection, and this accelerates asphaltene deposition. The residual trapping performance of CO2-LPG WAG injection can be improved compared with CO2 WAG injection. In contrast, more formation damages due to LPG addition lowers the solubility trapping performance compared with CO2 WAG injection, although LPG increases the reservoir pressure. Adding LPG improves total CCS performance by 9.1% and enhances oil recovery by 11% compared with CO2 WAG injection, and CO2-LPG co-injection enhances not only EOR but also CCS performance during CCS-EOR.

3. 3.

To apply the integrative model in various conditions, reservoir simulations were conducted with different LPG concentrations and WAG ratios. Although both EOR and CCS performances can be enhanced at higher LPG concentrations, the increment becomes smaller with more LPG. Therefore, economic evaluations should consider the price of LPG to determine the optimum LPG concentration. WAG ratios of 1:1 and 2:1 can also be compared to investigate the effect of the injection scheme with the same amount of gas. Although the amount of injected water with a 2:1 WAG ratio is much greater, long-term CCS and EOR performances do not change meaningfully. However, short-term oil recovery can be enhanced by up to 9.4% due to higher pressures and sweep efficiency. For optimum application of CCS-EOR in terms of LPG concentration and WAG ratios, an economic analysis that considers the price of LPG and water should be undertaken.

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Cho, J., Kim, T. H. & Lee, K. S. Compositional modeling of hybrid CO2 EOR with intermediate hydrocarbon solvents to analyze the effect of toluene on asphaltene deposition. J. Petrol. Sci. Eng. 146, 940–948 (2016).

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Darabi, H., Sepehrnoori, K. & Kalaei, M.H. Modeling of wettability alteration due to asphaltene deposition in oil reservoirs. Paper presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 8–10 October 2012.

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Teletzke, G.F., Patel, P.D. & Chen, A. Methodology for miscible gas injection EOR screening. Paper presented at the SPE International Improved Oil Recovery Conference in Asia Pacific, Kuala Lumpur, Malaysia, 5–6 December, 2005.

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Sifuentes, W., Blunt, M.J. & Giddins, M.A. Modeling CO2 storage in aquifers: assessing the key contributors to uncertainty. Paper presented at the SPE Offshore Europe Oil & Gas Conference & exhibition, Aberdeen, UK, 8–11 September, 2009.

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Jun, W., Feng, W., Deping, Z., Guojun, Y., Ruosheng, P. & Shuai, X. CO2 flooding WAG safety control technology. Paper presented at the SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, Indonesia, 22–24 October, 2013.

## Acknowledgements

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (No. 2018R1A6A1A08025520 and No. 2020R1F1A1070406). Dr. Jinhyung Cho was supported by a NRF Grant (No. 2020R1I1A1A01067015).

## Author information

Authors

### Contributions

J.C. designed the overall study and analyzed the results of this numerical work. J.C., B.M., M.S.J. and Y.W.L. reviewed and revised the manuscript. K.S.L. supervised the work.

### Corresponding author

Correspondence to Kun Sang Lee.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

### Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Reprints and Permissions

Cho, J., Min, B., Jeong, M.S. et al. Modeling of CO2-LPG WAG with asphaltene deposition to predict coupled enhanced oil recovery and storage performance. Sci Rep 11, 2082 (2021). https://doi.org/10.1038/s41598-021-81316-2

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## Use the calculator to see how much you can save. Let’s say you start with $2,000, save$100 a month for 10 years, and the account has a 2.5

Question

Use the calculator to see how much you can save. Let’s say you start with $2,000, save$100 a month for 10 years, and the account has a 2.5% interest rate. Based off of that calculation, how much interest would you earn?

in progress 0
7 months 2021-08-10T23:56:57+00:00 1 Answers 7 views 0


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# An underwater canyon begins at 40 feet below sea level and is 105 feet deep. What is the elevation of the bottom of the canyon?

###### Question:

An underwater canyon begins at 40 feet
below sea level and is 105 feet deep.
What is the elevation of the bottom of
the canyon?

### Why does pressure vary in the atmosphere

Why does pressure vary in the atmosphere...

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Recommendations Skill plans A Math Language arts E IN Standa Seventh grade GG. 1 Identify adjectives JFL Select the two adjectives. Don't select any articles (a, an, or the). Lucia, curious, followed the melodic sound down the stairs and found Nicholas at the piano. Submit...

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What is the change in temperature from -45°F to - 71°F? A. -116°F B. 116°F C. -26°F D. 26°F So, I did this both adding and subtracting, in subtraction I got -34, which is obviously wrong, and addiction is what's needed to be used, right? In addition, I got -116. Help? Also, it would be nice if...

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text:
# The order of an automorphism

Let $A\in \mathrm{GL}(n, q)$. What is the maximum order $A$ can have?


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# Derivation of Holographic Negativity in AdS_{3}/CFT_{2}.

@article{Kusuki2019DerivationOH,
title={Derivation of Holographic Negativity in AdS\_\{3\}/CFT\_\{2\}.},
author={Yuya Kusuki and Jonah Kudler-Flam and Shinsei Ryu},
journal={Physical review letters},
year={2019},
volume={123 13},
pages={
131603
}
}
• Published 17 July 2019
• Physics
• Physical review letters
We present a derivation of the holographic dual of logarithmic negativity in AdS_{3}/CFT_{2} that was recently conjectured in Phys. Rev. D 99, 106014 (2019PRVDAQ2470-001010.1103/PhysRevD.99.106014). This is given by the area of an extremal cosmic brane that terminates on the boundary of the entanglement wedge. The derivation consists of relating the recently introduced Rényi reflected entropy to the logarithmic negativity in holographic conformal field theories. Furthermore, we clarify…

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## References

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Holographic Derivation of Entanglement Entropy from AdS/CFT
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• 2006
A holographic derivation of the entanglement entropy in quantum (conformal) field theories is proposed from AdS/CFT correspondence. We argue that the entanglement entropy in d+1 dimensional conformal
Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence.
• Physics
Physical review letters
• 2006
It is argued that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy.
Aspects of Holographic Entanglement Entropy
• Physics
• 2006
This is an extended version of our short report [1], where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a
Entanglement negativity and minimal entanglement wedge cross sections in holographic theories
• Physics
Physical Review D
• 2019
We calculate logarithmic negativity, a quantum entanglement measure for mixed quantum states, in quantum error-correcting codes and find it to equal the minimal cross sectional area of the
Entanglement negativity in extended systems: A field theoretical approach
• Mathematics, Physics
• 2012
We report on a systematic approach for the calculation of the negativity in the ground state of a one-dimensional quantum field theory. The partial transpose rho_A^{T_2} of the reduced density matrix
Entanglement of purification through holographic duality
• Physics
• 2018
The gauge/gravity correspondence discovered two decades ago has had a profound influence on how the basic laws in physics should be formulated. In spite of the predictive power of holographic
Finite temperature entanglement negativity in conformal field theory
• Physics, Mathematics
• 2014
We consider the logarithmic negativity of a finite interval embedded in an infinite one dimensional system at finite temperature. We focus on conformal invariant systems and we show that the naive
Entanglement negativity in quantum field theory.
• Physics
Physical review letters
• 2012
A systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory is developed, using a path integral formalism to construct the partial transpose ρ(A)(T(2) of the reduced density matrix of a subsystem and applied to conformal field theories.
The gravity dual of Rényi entropy
• Xi Dong
• Physics, Computer Science
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• 2016
It is shown that all Rényi entropies satisfy a similar area law in holographic theories and are given by the areas of dual cosmic branes, a one-parameter generalization of the minimal surface prescription for entanglement entropy.
A covariant holographic entanglement entropy proposal
• Physics
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With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal


text:
Answer
Comment
Share
Q)

# One end of string of length l is connected to a particle of mass 'm' and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in circle with speed 'v' the net force on the particle (directed towards center) will be (T represents the tension in the string)

( A ) $T$
( B ) Zero
( C ) $T - \frac{mv^2}{l}$
( D ) $T + \frac{mv^2}{l}$


text:
# 2.4 Metre

(Redirected from 2.4 Metre (keelboat))
Development Class symbol International 2.4mR Development class 1 1 m (3 ft 3.370 in) (Mark III) 260 kg (570 lb) 4.16 m (13 ft 8 in) (Mark III) 0.805 m (2 ft 7.7 in) 4.65 m (15.3 ft) 7.5 m2 (81 sq ft) (Mark III) 1250[1]

The International 2.4mR is a one-person keelboat. The class is a development class governed by the 2.4mR rule. The rule is controlled by World Sailing (ISAF) since it is one of few classes designated as an International class. The class rule is closely related to the 12mR rule that was used in the America's Cup and the shape often resembles the larger sister.

While there is a small but active group of amateur designer/builders around the world, around 90% of boats are the commercially produced Norlin Mark III designed by yacht designer Peter Norlin of Sweden. Recently, new designs have come into production, such as the Stradivari III and the Proton.

The boat is primarily used for racing and the class holds highly competitive national events in many countries. World and European championships (only when the World Championship is not in Europe) are attracting around 100 boats every year. In some countries it features mainly as a class for sailors with a disability.

The 2.4mR is ideal for adapted sailing since the sailor does not move in the boat, and everything is adjustable from right in front of the sailor. Both hand-steering and foot-steering are possible. The boat's ability in integrated sailing has been proven on the result lists of several World Championships. In 2002 and 2005 there were handicapped World Champions. The boat is sailed without a spinnaker, but with a whisker-pole for the jib.

## History

After the 1980 America's Cup, people in the Newport, RI area started sailing boats called Mini-12s named for the 12-Metre yachts used in the America's Cup. As the class developed, word of it spread to Sweden, home of yacht designer Peter Norlin. Norlin tweaked the design, and along with other naval architects he created the 2.4 meter yacht class. Although the 2.4mR is a construction class, Peter Norlin is in practice the totally dominating designer, and the class is therefore often mistaken as a one design class. In addition to all the sailing aspects of the boat, Norlin has worked the design to incorporate features for the physically disabled to use the boat.

## One-design

In recent years an attempts have been made to develop a one design class based on the Norlin III. This is primarily because of the need for competition within the paralympics for racing to be about the sailor and not a technical development race. This led to the introduction of (Appendix K to the Class rules) and now a group is working on a set of stand alone One-design rules. This is still at the early stages but it is likely a new one design class is formed alongside the development class.

## Rating formula

As an open class rather than a one-design, all boat designs must meet the following formula.[2]

${\displaystyle R={\dfrac {L+2d-F+{\sqrt {S}}}{2.37}}}$

Where (all measurements in mm)

• L = the "corrected" length of the hull (see rule D.6.3)
• d = the midship girth difference (see rule D.6.4)
• F = the average freeboard height (see rule D.6.5)
• S = the total rated area of the mainsail and jib combined.

## Events

### World Championships

Year
Gold Silver Bronze
1993 Kokkola  Patrik Forsgren (SWE)  Peter Norlin (SWE)  Ralf Casen (FIN)
1994 Rutland Water  Bo Hedensjö (SWE)  Carl-Gustaf Fresk (SWE)
1995 Aahus  Carl-Gustaf Fresk (SWE)  Marko Dahlberg (FIN)
1996 Cannes  Peter Norlin (SWE)  Bo Hedensjö (SWE)  Imma Björndahl (FIN)
1997  Marko Dahlberg (FIN)  Peter Norlin (SWE)  Patrik Forsgren (SWE)
1998 Tampere  Rikard Bjurström (FIN)
1999  Tom Björndahl (FIN)  Marko Dahlberg (FIN)  Peter Norlin (SWE)
2000 Melbourne  Stellan Berlin (SWE)  Rikard Bjurström (FIN)  Peter Norlin (SWE)
2001 Tønsberg  Heiko Kroeger (GER)  Stellan Berlin (SWE)  Peter Norlin (SWE)
2002 Miami  Stellan Berlin (SWE)  Hans Meyers (USA)  Tom Brown (USA)
2003  Marko Dahlberg (FIN)  Damien Seguin (FRA)  Stellan Berlin (SWE)
2004  Stellan Berlin (SWE)  Ulf Arvidsson (SWE)
2005  Nick Scandone (USA)  Stellan Berlin (SWE)  Helena Lucas (GBR)
2006 Helsinki  Stellan Berlin (SWE)  Thierry Schmitter (NED)  Harri Malm (FIN)
2007 Kolding  Lennart Heselius (SWE)  Stellan Berlin (SWE)  Ulf Arvidsson (SWE)
2008 Gran Canaria  Stellan Berlin (SWE)  Damien Seguin (FRA)  Hans Asklund (SWE)
2009 Fort Myers  John Ruf (USA)  Carl Horrocks (USA)  Paul Tingley (CAN)
2010 Hoorn  Paul Tingley (CAN)  Stellan Berlin (SWE)  Hans Asklund (SWE)
2011 Ålesund  Stellan Berlin (SWE)  Marko Dahlberg (FIN)  Rikard Bjurström (FIN)
Peter Andersson (SWE)  Stellan Berlin (SWE)  Megan Pascoe (GBR)
2013 Poole  Stellan Berlin (SWE)  Helena Lucas (GBR)  Megan Pascoe (GBR)
2014 Toronto  Stellan Berlin (SWE)  Bjørnar Erikstad (NOR)  Helena Lucas (GBR)
2015 Rauma  Stellan Berlin (SWE)  Bjørnar Erikstad (NOR)  Heiko Kröger (GER)
2016 Hobart  Megan Pascoe (GBR)  Matt Bugg (AUS)  Paul Francis (NZL)

### Para World Sailing Championships

The 2.4 metre has been used a number of times as equipment for the One-Person Technical Disabled displine which holds an annual World Championships.

Year
Gold Silver Bronze
2017 Kiel[3]  Heiko Kröger (GER)  Matthew Bugg (AUS)  Damien Seguin (FRA)

### Paralympics

Since 2000 the 2.4 Metre has been the official single-crew class boat for sailing at the Summer Paralympics although it has been used in a more one design form utilising the Norlin Mk3 design.

## References

1. ^ "Portsmouth Number List 2012". Royal Yachting Association. Retrieved 31 July 2012.
2. ^ Marie. "International 2.4 mR Class Rules (2006)" (PDF). Inter24metre.org. Archived from the original (PDF) on 2009-08-22. Retrieved 2009-08-16.
3. ^ "Kieler Woche 2017 manage2sail". www.manage2sail.com.


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## CryptoDB

### Jiwu Huang

#### Publications

Year
Venue
Title
2008
EPRINT
In this paper, we suggest that all pairings be in a group from an abstract angle. It is possible that our observation can be applied into other aspects of pairing-based cryptosystems.
2007
EPRINT
The Ate pairing has been suggested since it can be computed efficiently on ordinary elliptic curves with small values of the traces of Frobenius $t$. However, not all pairing-friendly elliptic curves have this property. In this paper, we generalize the Ate pairing and find a series of variations of the Ate pairing. We show that the shortest Miller loop of the variations of the Ate pairing can possibly be as small as $r^{1/\varphi(k)}$ on more pairing-friendly curves generated by the method of complex multiplications, and hence speed up the pairing computation significantly.
2006
EPRINT
Pairing-based cryptosystems have been developing very fast in the last few years. The efficiencies of the cryptosystems are determined by the computation of the Tate pairing. In this paper a new efficient algorithm based on double-base chain for computing the Tate pairing is proposed for odd characteristic $p>3$. The inherent sparseness of double-base number system reduces the computational cost for computing the Tate pairing evidently. It is $9\%$ faster than the previous fastest method for MOV degree k=6.
2006
EPRINT
In this paper we present an algorithm for computing the bilinear pairings on a family of non-supersingular elliptic curves with non-trivial automorphisms. We obtain a short iteration loop in Miller's algorithm using non-trivial ecient automorphisms. The proposed algorithm is as ecient as Scott's algorithm in [12].

#### Coauthors

Fangguo Zhang (4)
Chang'an Zhao (1)
Chang-An Zhao (3)


text:
# Dihedral group of order 8

Writing Dihedral group $D_{8}$ (order 8)as a semidirect product $% V\left\langle \alpha \right\rangle$, where $V$ is a four-group and $\alpha$ an involution, and so we have $D_{8}=\left\langle \alpha ,\beta \right\rangle$ and $V=\left\langle \beta ,\beta ^{\alpha }\right\rangle .$

I want to show that: Let $D$ be isomorphic with $D_{8}=\left\langle \alpha ,\beta \right\rangle$ and suppose that $D$ acts on a group $G$ in such a manner that $C_{G}(V)$ is finte, where $V=\left\langle \beta ,\beta ^{\alpha }\right\rangle$ and $\alpha$ sends every element of $G$ to the inverse, then $C_{G}\left( \beta \right)$ is finite.

My solution:

Let $\phi \in AutG,$ then $g^{\phi \alpha }=\left( g^{-1}\right) ^{\phi }$ and $g^{\alpha \phi }=\left( g^{-1}\right) ^{\phi }$. Therefore $\alpha \in Z\left( AutG\right)$ and so $C_{G}(\left\langle \beta ,\beta ^{\alpha }\right\rangle )=C_{G}\left( \beta \right)$ is finite. ($V=\left\langle \beta \right\rangle$???)

I think there's a problem in my solution for the Klein group is not cyclic.

Help!

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Your solution looks basically OK to me. Since the action of $\alpha$ is central in ${\rm Aut} G$, the actions of $\beta$ and $\beta^\alpha$ on $G$ are the same, so $C_G(\beta) = C_G(\beta^\alpha) = C_G(V)$. Why should this imply that $V = \langle \beta \rangle$? –  Derek Holt Dec 17 '12 at 16:57
Because $V=\left\langle \beta ,\beta ^{\alpha }\right\rangle$ and $\beta ^{\alpha }=\beta .$ Would not it be so? –  User2040 Dec 17 '12 at 17:26
It is not true that $\beta^\alpha = \beta$. They induce the same automorphism of $G$, but that does not make them equal. It implies that $\beta^{-1}\beta^\alpha$ induces the identity automorphism of $G$, which means that the action of $D_8$ on $G$ is not faithful. –  Derek Holt Dec 17 '12 at 22:18
Lima:I understood. Thank you! –  User2040 Jan 2 '13 at 12:39