Simulation using Petrel

You need to get those from your reservoir or production engineer.
Pressure will normally fall off as flow from the well increases.

As described by my AI assistant,

Production well testing is a critical process in the oil and gas industry that involves measuring and evaluating the productivity and characteristics of a well. One of the key tools used in this process is the production test curve, which helps in understanding the well's performance and the reservoir's properties.

### Production Test Curve

The production test curve, often referred to as the "PQ curve," is a graphical representation of the relationship between the wellhead pressure (WHP) and the flow rate (Q) of the well. This curve is typically derived from multi-rate well test data, where the well is tested at different flow rates to determine how the pressure responds.

#### Key Components of the PQ Curve

1. **Flow Rate (Q)**: This is the rate at which oil, gas, and water are produced from the well. It is measured in units such as barrels per day (bpd) for oil and standard cubic feet per day (scfd) for gas.

2. **Wellhead Pressure (WHP)**: This is the pressure at the wellhead, which is the point where the well meets the surface. It is measured in units such as pounds per square inch (psi).

#### Purpose of the PQ Curve

- **Inflow Performance Relationship (IPR)**: The PQ curve helps in establishing the IPR, which describes how the well's flow rate changes with the pressure drawdown. This relationship is crucial for optimizing production and understanding the well's potential.

- **Skin Factor**: The skin factor is a dimensionless parameter that indicates the degree of damage or enhancement around the wellbore. The PQ curve can be used to determine the skin factor, which is essential for reservoir management and well stimulation decisions.

- **Reservoir Transmissibility**: The curve also helps in estimating the reservoir transmissibility, which is a measure of how easily fluids can flow through the reservoir rock.

- **Boundary Effects**: By analyzing the PQ curve, engineers can identify the presence of boundaries within the reservoir, such as faults or barriers, which can affect the well's performance.

#### Methods for Creating the PQ Curve

- **Test Separator**: A test separator is a compact cylindrical vessel that physically separates the well fluid into gas, oil, and water streams. Each phase is then measured separately using single-phase meters. This method is considered the reference measurement device for well testing but has limitations in terms of flow stability and maintenance.

- **Multiphase Flowmeters (MPFM)**: MPFM technologies use complex algorithms to measure the well fluid rates at line conditions. These meters are more compact and easier to maintain, making them suitable for offshore platforms and remote wells. However, they are sometimes considered less accurate compared to test separators.

#### Applications

- **Reservoir Management**: The data from production tests and the PQ curve are used for reservoir management, including the evaluation of exploration programs, deciding on well development, and planning field development.

- **Production Optimization**: By understanding the well's performance through the PQ curve, engineers can optimize production by adjusting parameters such as the drawdown and artificial lift methods.

- **Regulatory Compliance**: The results of production tests are often forwarded to regulatory agencies, which use the data to track production and set limits on the maximum amount of gas an operation is allowed to produce.

### Conclusion

The production test curve is a valuable tool in the oil and gas industry, providing essential information for well and reservoir management. By analyzing the relationship between wellhead pressure and flow rate, engineers can make informed decisions to optimize production and ensure the efficient and safe operation of oil and gas wells.

The production test curve, often referred to as the Pressure-Flow (P-Q) curve, can be described using various mathematical models. One of the most common and generalized functions used to describe this relationship is the Inflow Performance Relationship (IPR) model, specifically the Vogel's equation for oil wells and the Fetkovich's equation for gas wells. However, a more general form can be described using a hyperbolic relationship.

### Generalized Function for P-Q Curve

The generalized function for the P-Q curve can be expressed as:

\[ Q = \frac{A \cdot (P_{wf} - P_{ws})^n}{B + (P_{wf} - P_{ws})^m} \]

Where:
- \( Q \) is the flow rate (e.g., barrels per day for oil, standard cubic feet per day for gas).
- \( P_{wf} \) is the wellhead pressure (e.g., psi).
- \( P_{ws} \) is the static reservoir pressure (e.g., psi).
- \( A \), \( B \), \( n \), and \( m \) are empirical constants that depend on the specific well and reservoir characteristics.

### Specific Cases

1. **Vogel's Equation (Oil Wells)**:
Vogel's equation is a simplified form of the IPR and is commonly used for oil wells. It is given by:

\[ Q = Q_{max} \cdot \left(1 - \frac{P_{wf}}{P_{ws}} - \left(\frac{P_{wf}}{P_{ws}}\right)^2\right) \]

Where:
- \( Q_{max} \) is the maximum flow rate (when \( P_{wf} = 0 \)).
- \( P_{ws} \) is the static reservoir pressure.

2. **Fetkovich's Equation (Gas Wells)**:
For gas wells, Fetkovich's equation is often used to describe the IPR. It is given by:

\[ Q = \frac{A \cdot (P_{ws}^2 - P_{wf}^2)}{B + \left(P_{ws}^2 - P_{wf}^2\right)^{0.5}} \]

Where:
- \( A \) and \( B \) are empirical constants.
- \( P_{ws} \) is the static reservoir pressure.
- \( P_{wf} \) is the wellhead pressure.

### Example of a Generalized Hyperbolic Function

For a more generalized hyperbolic function, you can use:

\[ Q = \frac{A \cdot (P_{ws} - P_{wf})^n}{1 + B \cdot (P_{ws} - P_{wf})^m} \]

Where:
- \( A \), \( B \), \( n \), and \( m \) are empirical constants that can be determined from well test data.

### Determining Empirical Constants

The constants \( A \), \( B \), \( n \), and \( m \) can be determined by fitting the generalized function to the actual production test data. This is typically done using regression analysis or other curve-fitting techniques.

### Conclusion

The generalized function for the P-Q curve provides a flexible and versatile way to describe the relationship between wellhead pressure and flow rate. By using empirical constants, this function can be tailored to fit the specific characteristics of different wells and reservoirs, making it a powerful tool for production testing and well management.

Write that using VBA

Certainly! Below is the generalized function for the P-Q curve written in Microsoft VBA notation. This function can be used in Excel VBA to calculate the flow rate based on the wellhead pressure and other parameters.

### VBA Function for Generalized P-Q Curve

```vba
Function CalculateFlowRate(P_wf As Double, P_ws As Double, A As Double, B As Double, n As Double, m As Double) As Double
' Calculate the flow rate (Q) using the generalized P-Q curve function
Dim numerator As Double
Dim denominator As Double
Dim Q As Double

' Calculate the numerator: A * (P_ws - P_wf)^n
numerator = A * (P_ws - P_wf) ^ n

' Calculate the denominator: 1 + B * (P_ws - P_wf)^m
denominator = 1 + B * (P_ws - P_wf) ^ m

' Calculate the flow rate Q
Q = numerator / denominator

' Return the flow rate
CalculateFlowRate = Q
End Function
```

### Example Usage in VBA

You can call this function from another VBA subroutine or directly from an Excel cell. Here is an example of how to use it in a subroutine:

```vba
Sub TestCalculateFlowRate()
Dim P_wf As Double
Dim P_ws As Double
Dim A As Double
Dim B As Double
Dim n As Double
Dim m As Double
Dim Q As Double

' Example values
P_wf = 1500 ' Wellhead pressure in psi
P_ws = 3000 ' Static reservoir pressure in psi
A = 5000 ' Empirical constant
B = 0.01 ' Empirical constant
n = 1.5 ' Empirical constant
m = 0.5 ' Empirical constant

' Calculate the flow rate
Q = CalculateFlowRate(P_wf, P_ws, A, B, n, m)

' Output the result
Debug.Print "Flow Rate: " & Q & " bbl/day"
End Sub
```
You can probably fit that to your design flow and pressure while you complete some preliminary simulation work, then ask your production Engineer to confirm the curve before releasing your report. I have not checked the results myself.

Static pressure is a constant pressure at a point far enough from the well, such that it does not change with local flow effects in the immediate.vicinity of the well.
It is often just assumed during initial investigations as the weight of all the soil and rock layers above the HC strata. Its the pressure driving the Darcy flow through the reservoir rock towards the well.

When doing a well test it is ...
Static reservoir pressure is the pressure measured in a well after it has been closed in for a period of time, often after 24 or 72 hours. This pressure is crucial in understanding the state of the reservoir and its potential for production. When a reservoir is first discovered, the static pressure equals the initial pressure. After production begins, the static pressure approaches the average reservoir pressure.

Otherwise it's the reservoir pressure at depth that typically declines with the age and previous production history. For some shale wells it may be as much as 35%/year.

Assuming you do not include the well tubing itself in your model,
You can add the effects of flow through the production tubing from the well depth to the surface to translate the PQ curve to the well head.