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# How to Create a Compressibility Factor Calculator in Python

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### @kunalaichKunal Aich

A Software Engineer by profession, works with Python, Django, PostgreSQL and Microsoft Azure.

﻿In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, is a correction factor which describes the deviation of a real gas from ideal gas behavior behavior.

The calculations below can be used to find the inlet or the outlet compressibility factor by using the values for temperature and pressure. T and P are the temperature and pressure in units of °R and psia, respectively. The value calculated for Z should not be greater than zero. The compressibility factor has no units of measure.

Below are the steps and the equations to calculate the compressibility factor for a given gas based on the Redlich-Kwong equation of state:

Step 1: Calculate the Reduced temperature as:

where T and Tc have the units of °R.

``````# Reduced temperature
# T and Tc have the units of °R.
def reduced_temperature(temperature, tc): tr = temperature / tc return tr``````

The reduced temperature of a fluid is its actual temperature, divided by its critical temperature. A critical point (or critical state) is the end point of a phase equilibrium curve. At the critical point, defined by a critical temperature Tc and a critical pressure Pc, phase boundaries vanish.

Step 2: Calculate the Reduced pressure as:

where P and Pc have the units of psia.

``````# Reduced pressure
# P and Pc have the units of psia
def reduced_pressure(pressure, pc): pr = pressure / pc return pr``````

The reduced pressure is defined as its actual pressure divided by its critical pressure.

Step 3: Calculate the Redlich-Kwong constants as:

``````# Redlich-Kwong constant A
def redlich_kwong_constant_a(pr, tr): a = 0.42748 * (pr / tr ** 2.5) return a # Redlich-Kwong constant B
def redlich_kwong_constant_b(pr, tr): b = 0.08664 * (pr / tr) return b``````

In thermodynamics, the Redlich–Kwong equation of state is an empirical, algebraic equation that relates temperature, pressure, and volume of gases. The Redlich–Kwong equation is adequate for calculation of gas phase properties when the ratio of the pressure to the critical pressure (reduced pressure) is less than about one-half of the ratio of the temperature to the critical temperature (reduced temperature).

Step 4: Calculate the Cubic constants as:

``````# Cubic constant α
def cubic_constant_alpha(a, b): alpha = (1 / 3) * (3 * (a - b - b ** 2) - 1) return alpha # Cubic constant β
def cubic_constant_beta(a, b): beta = (1 / 27) * (-2 + (9 * (a - b - b ** 2)) - (27 * a * b)) return beta``````

Step 5: Calculate the Discriminant as:

``````# Discriminant
def discriminant(alpha, beta): d = (beta ** 2 / 4) + (alpha ** 3 / 27) return d``````

Step 6: Calculate the Solution constants as:

``````# Solution Constant A*
def solution_constant_a_star(beta, d): a_star = np.cbrt((-beta / 2) + np.sqrt(d)) return a_star # Solution Constant B*
def solution_constant_b_star(beta, d): b_star = np.cbrt((-beta / 2) - np.sqrt(d)) return b_star # Solution Constant Theta
def solution_constant_theta(beta, alpha): theta = math.acos(-sign(beta) * (math.sqrt((beta ** 2 / 4) / (-alpha ** 3 / 27)))) return theta``````

SIGN(β) is calculated as below:

``````# SIGN(β)
# If β > 0, SIGN(β) = 1
# If β = 0, SIGN(β) = 0
# If β < 0, SIGN(β) = -1
def sign(beta): if beta > 0: sign_beta = 1 elif beta < 0: sign_beta = -1 else: sign_beta = 0 return sign_beta``````

Step 7: Calculate the Trial Roots as:

where the cosine term is in radians, not degrees.

``````# Trial Root Z1
def trial_root_z1(a_star, b_star): z1 = a_star + b_star + 1 / 3 return z1 # Trial Root Zi
# for i = 2, 3
def trial_root_zi(a_star, b_star, i): zi = (-(1 / 2) * (a_star + b_star)) + ((1 / 3) * i) return zi # Trial Root Zi+1
# for i = 1, 2, 3
def trial_root_zi1(alpha, theta, i): zi1 = (2 * math.sqrt(- alpha / 3) * math.cos((theta / 3) + (i * ((math.pi * 2) / 3)))) + (1 / 3) return zi1``````

Critical Constants for Selected Gases are given below:

``def table_gas_critical_constants(gas_name): """ Retrieves gas critical constants table data :param gas_name: Gas name :type gas_name: str :return: Gas critical constants data :rtype: list """ gas_critical_constants = { "Air": [238.56, 549.11, 28.965], "Carbon Dioxide": [547.60, 1070.600, 44.011], "Hydrogen": [59.82, 190.82, 2.02], "Methane": [343.90, 673.100, 16.04], "Nitrogen": [227.25, 492.420, 28.13], "Propane": [666.00, 618.700, 44.09], "Typical Natural Gas": [360.00, 777.373, 17.185] } return gas_critical_constants.get(gas_name)``

If Discriminant (D) is lesser than zero, Solution constant (θ) and Trial roots (Zi+1 for i = 1, 2, 3) will be calculated. The max of the Trial roots will be calculated as compressibility factor (Z).

If Discriminant (D) is greater than or equal to zero, Solution constants (A* and B*) will be calculated. On that if D is equal to zero, then Trial roots (Z1 and Zi for i = 2, 3) will be calculated. The max of the Trial roots will be calculated as compressibility factor (Z). But if D is greater than zero, then Trial root (Z1) will be calculated and it will give the compressibility factor (Z).

Below is the program using all the above equations and steps for the compressibility factor calculation for a given gas based on the Redlich-Kwong equation of state:

``def compressibility_factor_calc(gas, temperature, pressure): """ Calculates compressibility factor :param gas: Gas name :type gas: str :param temperature: Temperature :type temperature: float :param pressure: Pressure :type pressure: float :return: Compressibility factor(z) :rtype: float """ values = table_gas_critical_constants(gas) tc = values[0] pc = values[1] tr = reduced_temperature(temperature, tc) pr = reduced_pressure(pressure, pc) a = redlich_kwong_constant_a(pr, tr) b = redlich_kwong_constant_b(pr, tr) alpha = cubic_constant_alpha(a, b) beta = cubic_constant_beta(a, b) d = discriminant(alpha, beta) if d < 0: theta = solution_constant_theta(beta, alpha) z1 = trial_root_zi1(alpha, theta, 1) z2 = trial_root_zi1(alpha, theta, 2) z3 = trial_root_zi1(alpha, theta, 3) else: a_star = solution_constant_a_star(beta, d) b_star = solution_constant_b_star(beta, d) if d == 0: z1 = trial_root_z1(a_star, b_star) z2 = trial_root_zi(a_star, b_star, 2) z3 = trial_root_zi(a_star, b_star, 3) else: z = trial_root_z1(a_star, b_star) return z z = max(z1, z2, z3) return z``

Cover image from Compressibility Factor, ScienceDirect

Hope this helps. Happy Coding!

A Software Engineer by profession, works with Python, Django, PostgreSQL and Microsoft Azure.

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# What is an Action Refund Review?

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You have been defrauded by a fraudulent broker. What are you going to do ? In this Action Refund review, we’ll explain everything to you.

A study by “Scamwatch”, with the help of the ACCC (Australian Competition & Consumer Commission), suggests that so far, in 2020, around 195,848 reports of all types of scams have been submitted, with a loss of approximately \$ 150,838,567. This is insane!

A real company called “Action Refund” had the ambition to help victims internationally to recover their stolen capital from various crooks in the foreign exchange market. Their team is made up of knowledgeable service agents who have helped dozens of users and victims of scams across the world. In addition, Action Refund offers a free consultation over the phone with a professional case analyst. We suggest that you contact Action Refund as soon as possible.

When you are in the middle of the process of filing a refund claim with a complicated case, it is very important to have professional assistance on your side. If you’re curious about what the company’s collection service is all about, below is an interview with a fraud victim to understand what Action Refund did with their case:

## Can you tell us how it all started? (Action Refund Review)

At the end of 2019, I came across an advertisement in my inbox approving that Bill Gates made a fortune from forex trading, so I thought “I’ll give it a shot” and left some of my details on the site of this company.

They assigned me an account manager named “Gary Silverson”. He was polite and appeared to be an expert, promising the world and more with future profits. He assured me that with his advice, my trading account could be multiplied by 10 in no time. I thought that was probably an overestimate, however, if the forex market is open to everyone it is very possible to increase my income and triple my investments, at least that’s what I got. has sold. I wanted to deposit around \$ 750 to open an account so I followed his instructions.

Gary explained to me very briefly about the application they are using, omitting crucial details and saying “trust me, you don’t need this info, we need more repositories”. You could say that I was very naive.

## That seems good to me…

Back then, I was making decent profits instantly. We had a few trading sessions together for two months. Over time, he started to take control of my account transactions and I followed his lead, not asking anything because I knew he wouldn’t respond correctly. A few days later, the agent reached out to me via WhatsApp regarding a new opportunity emerging due to the announcement of the US election. Gary offered me a zero risk plan so that we could increase my earnings. I confirmed it, and we did make a little more profit.

At the time, my account was showing a profit of \$ 5,129 from my initial deposit. I wanted to request a withdrawal of \$ 1000 and it was returned to me without a problem. I remember I was quite surprised. I thought to myself, “How could I not find this forex trading company before?”. A month passed, and I reconsidered depositing an additional \$ 15,000. Then I got promoted for what the company calls “platinum membership”.

## So you claim that you had no problem withdrawing funds from the trading account?

Not at all. As I mentioned, everything went well at first. Honestly, it looked like Gary was doing a good job.

# Vestle Review 2021 – CySEC Broker Or CySEC Scam?

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Description: Can you be scammed by Vestle broker? Read our comprehensive Vestle review covering the most important information about the broker.

Whether you have or plan to have an account with this broker, this Vestle review is something you must read

 Regulated by: CySEC Headquarters Country: Cyprus Foundation year: 2015 Platforms: Web trader Instruments: FX, commodities, shares, indicies, crypto, ETFs

## Is Vestle a legit broker?

Over the years, many clients had a terrible experience with CySEC regulated brokers. Therefore, we decided to check few things in our Vestle review.

For a start, is Vestle regulation a real regulation or yet another attempt of a regulated company to have an off-sight brand. How the broker operates, and the odds that it will steal your money. Let’s start.

## Vestle Regulation and Security

Vestle is a brand owned by iCFD Limited, regulated by CySEC. The company was formerly known as iForex Ltd. Whenever the broker changes its name, there is a reason for that. And usually, the reason is hundreds of unsatisfied traders and bad reviews.

When it comes to funds, allegedly, every payment method the company uses is supervised by another EU country. It seems that the broker just listed all the countries where payment providers are based.

## What can you trade with a Vestle broker?

Vestle is a broker that provides a high range of trading assets. Clients can trade with currency pairs, commodities, indices, shares, cryptocurrencies, and ETFs. There are over 900 assets available.

All the trades are executed on the web trader of a broker called FXnet. This type of trading platform is always riskier than trading with MT4 or MT5. Every experienced trader prefers MetaTrader in the first place because of security reasons, but also because it has more features. Unfortunately, the broker does not have a Demo account, so we couldn’t test the web trader and decide if it’s good or bad. Besides the web trader, the broker also offers Vestle mobile, its own app for Android and iOS devices.

When it comes to leverage, it’s limited by CySEC rules. The highest leverage is 1:30 for currency pairs.

## Deposit and Withdrawal Methods

When we talk about funding the account, there are several methods available. The client can deposit using debit/credit card, wire transfer, and few E-wallets. For card deposits, funds are visible instantly, while for wire transfers and E-wallets takes up to 5 business days. The same methods are available for withdrawals; only it takes up to 10 business days for the money to appear on the client’s account.

As per our Vestle review, it seems that the broker has issues with double charging. Many clients of this company complained that they see the double transaction in their bank statement.

When it comes to the deposit amount, Vestle keeps it hidden. Nowhere on the website, you cannot find the list of account types and deposits necessary. It seems that after you get a call from their support, they will evaluate your financial situation and require a certain amount of money from you.

The same thing can be said about commissions and fees the broker is charging. We were unable to find this list anywhere. This looks bad for the Vestle broker. As a CySEC regulated broker, it should be very transparent when it comes to money.

Based on everything in our Vestle review, we can say next. The broker shows a low level of transparency about fees and costs. The trades are executed on the web trader, easy to manipulate and change market prices. Even though the company is in the CySEC register since 2015, on the website of Vestle, there is a claim that they are operating for over 15 years. Now, it opens two questions: were they working unregulated or misleading clients to believe they are joining a long-lasting company. Whatever the answer is, a broker should not be proud to publish it.

After saying all this, we will leave it to you to decide if Vestle is a good broker or yet another CySEC scam.

Source : Plato

# New method of investment: Copy trading, or copy trading as it was originally called

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These are busy days for those who have a certain level of savings in the economy. Because already sharp movements occur in the Turkish lira because of their very high rates of investment to translate the uncertainties in Turkey in recent times with a certain amount of savings. This enables people to turn to different investment methods.

If you are looking for a dynamic investment method and still do not know where to start, we will have a profitable suggestion for you. A type of investment, originally called “Forex copy trading”, and another name that can be translated as copy investment in Turkish is social investment. It can be a good entry-level choice for those who do not know exactly how and how to invest in investment vehicles.

The basic logic of copy trading is to imitate the investments of successful investors in the exchange you want to enter. It’s that simple. Anyway, the name of this investment concept is therefore determined as copy investment.

According to one of the studies conducted in recent years, this type of investment is increasingly taking up a place in the market. The copy investment market will reach an amount of € 70 billion by the end of 2025, according to researches.

To start copy trading, the first thing to do is to choose a reliable and profitable investment platform. At this point, the next step in choosing a reliable investment platform is  Forex Copy Trading

that is, to be able to follow reliable investors for copy investment. Therefore, the choice of platform is very important at this point.

A Close Look at Copy Investment

In short, it is important that copy investment or social investment platforms allow experienced investors to copy their investments directly. Here, when you find such an investment exchange, the investment made in this way is also called “auto investment” because you invest your own account directly into the account of the experienced investor.

You can invest in the form of copy investment in the BIST 100, crypto money exchanges and even foreign exchanges. It is a method that can be followed even for foreign currency deposits. However, it will require serious research at the stage of determining the investors you will follow in the first place.

How Exactly to Invest in Copy?

In fact, there are two popular ways to do this.

Following the Investors’ Strategies One to One

Whichever exchange you are investing in, you can learn the investments made by the really experienced names of that stock exchange with a good research and make these investments one by one.

Benefits:

Simple System: The investment you will make in this way will be a very simple and easy-to-use investment type. This is the reason why it is called auto investment as a type of investment that you can directly imitate the investments of expert investors in the field.

Flexibility: You can follow this type of investment from any digital device. It is a very flexible method as you will do the same no matter where you are, as soon as you hear about the direct investment of the person you follow, as there is no subject to think about.

Choosing a strategy is very easy: All you have to do is find the best in the field with the right research. Once you find it, it will be very easy to determine your strategy.

Transaction Fees: Most successful traders will charge you a certain fee to return their investments. These fee claims create an additional cost. However, you can manage your funds with the confidence that there will be no additional fees or expenses for the investment.

Here you will be the one followed. Of course, this has certain advantages and disadvantages.

Your strategies will directly affect the market: Since you will be the person who will determine the strategy, whatever strategy you follow, the strategy you will follow will be a strategy that will affect the market completely.

You will also get the reward for your labor outside of profits: In this way, you will have to spend all your work on this work. However, you will get more than your followers for your efforts.

You will set the rules of the game: However, doing these operations will require both very serious experience and serious work.

Of course, it would be useful for you to carefully investigate whether there is a method to follow completely. However, it is possible to say that you can carry out such transactions with peace of mind with detailed analysis on the leading quality investment and stock exchange platforms such as AMarkets.

# Ethereum Price Smashed \$2000, \$3000 Incoming At Lightning Speed!

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## Ethereum Price (ETH) May Hit \$10,000 This Cycle!

The Ethereum price that is known to maintain a stable price movement, finally broke the previous ATH to form a new one. It took more than a months time to regain its lost position above \$2000, yet sustained successfully.

The price took more time than expected to break the \$2000 barrier, yet \$3000 may be approaching at rocket speed. As predicted by founder of Gokhstein Media, David Gokhstein, the next stop for the ETH price is around \$3,900.

With the continued bullish trend and intensified rally, the price is expected to surge to the highest levels. According to an analyst and Crypto Youtuber, Young and Investing, the Ethereum price may hit \$10,000 within the current bull run.

With the accelerated bull run, many analysts believe Ethereum could lead the market instead of Bitcoin too. Therefore providing a huge opportunity for the altcoins to boom within the ETH bull rally.

### Is Altcoin-Season On the Cards?

Many altcoins normally pop-up with the surge in the price of the second dominant crypto Ethereum. Currently, ETH price is trading around its new all time high around \$2152 and expected to fly high. Therefore, many small cap altcoins are expected to rise from ashes and pump more than 50x or even 100x also.

Many analysts believe the Altcoin Season of 2021 is on the way and is expected to be the greatest season ever. According to a popular analyst, XRPcryptowolf, the season will reach its peak during the summer.

Moreover, the coins which are believed to be dead or not performing are also expected to rise. One of the analysts, MC also has given a brief idea on which all coins might pump in the current AltSeason.

Collectively, the breakout of Ethereum price has led to initialization of the most awaited AltSeason of 2021. The ETH price rally is expected to intensify in the coming days, that might smash \$10,000 soon.