Modern Type Well Construction Methods

The following section provides some background on basic methodologies used for constructing type wells. These approaches are designed to generate representative type curves by leveraging historical production data, statistical techniques, and decline analysis. Each method has its own strengths, limitations, and assumptions, which should be carefully considered when selecting the most appropriate approach for a given development scenario.

Time Slice (TS) Method

The Time Slice method is a common way to build probability-based type curves, and it's the one used in most commercial software.

Here's how it works:

1. For each production month, take the production rates from all wells that have data for that month.

2. Sort the rates from highest to lowest.

3. Pick the value at the desired percentile — for example, the P50 (median), P10, or P90 — and use that as the production rate for that month.

4. Repeat this process for every month where enough wells still have data.

Once the number of wells with data drops below a certain threshold (usually 75% of the original well count), the data is considered too sparse. At that point, you stop using historical data and complete the rest of the curve using decline analysis (like exponential or hyperbolic decline models).

Limitation for TS Method

According to the literature, the limitations include:

• Fewer Wells Over Time: As production time increases, fewer wells have available data, especially after a certain point (like when only 75% of the wells still have data). This can cause inaccuracies in the results.

• Affected by Outliers: The TS method ranks and picks rates month by month. This means that outliers (extremely high or low values) can distort the results, especially when there are not many wells left in later months.

• Doesn't Reflect Real Decline Patterns: Since the TS method picks different wells each month, it doesn’t show the actual decline curve of a single well. Instead, it combines rates from different wells, which doesn’t reflect how a real well would behave.

• Problems When Curves Cross: If the production profiles of wells cross over one another (where a higher-rate well later becomes a lower-rate well), this method doesn’t handle it well, leading to inaccurate results. This is a major issue in the TS method (Russell and Freeborn, 2013).

• Doesn't Match EUR: The TS method doesn’t focus on the EUR of each well. The final type curve doesn’t represent a real well’s EUR, which makes it harder to link to specific real-world wells.

• May Lose Consistency in Data: If the number of wells gets too small or uneven (especially after using 75% of available data), the method may not be consistent anymore, leading to even more inaccurate results.

• Doesn't Capture Individual Well Behaviour: The method doesn’t track how each individual well behaves. It just takes an average from a variety of wells, so the final curve doesn't represent the specific behaviour of any one well.

Monte Carlo-Based Aggregation Method

Aggregation is the process of combining production data from multiple wells to construct a type well or type curve that represents the performance of a group of similar wells (Freeborn and Russell 2016).

Key Aggregation Principles

• Use Forecasted EURs: Estimate the EUR of each well using a consistent method (e.g., 3 years of production data fitted with a modified hyperbolic decline model and a 5% terminal decline rate).

• Be Cautious of Bias: Be aware that using a fixed terminal decline rate (e.g., 5%) can introduce bias, particularly if it's not accurate for all wells.

• Minimise Errors Through Aggregation: When aggregating EURs from multiple wells, random errors tend to cancel out, improving the reliability of the overall EUR distribution.

• Avoid Time-Slice Weaknesses: Methods like the TS approach can lead to inaccurate type wells when production profiles cross or behave differently over time.

• Use Representative Data Only: The aggregated data should represent the wells planned for future drilling, both in geology (reservoir quality) and operational practices (completion methods).

Guidelines for Selecting Representative Wells

• Match Reservoir and Completion: Select wells that have similar reservoir properties (e.g., rock type, pressure) and completion techniques (e.g., fracture stimulation, lateral length) as those intended for future drilling.

• Do Not Mix Operator Performance Levels: Avoid mixing wells from operators with different performance levels. For instance, don't use data from a top-performing (1st decile) operator if your wells are expected to perform at a lower (3rd quartile) level.

• Adjust Profiles If Needed: If you don’t have enough data, you may include additional wells, but you must scale or adjust their rate/time profiles to make them representative of the planned wells.

• Use Consistent Decline Analysis: Apply the same decline method (e.g., modified hyperbolic with 5% terminal decline) across all selected wells to ensure consistency.

• Avoid Crossed Production Profiles: Be cautious of wells whose production curves cross one another, as this can confuse the aggregation process and lead to unreliable type curves.

A Step-by-Step Process to Create Aggregated Type Wells

Step 1: Build the EUR Probability Distribution

1. Estimate EURs for All Wells
   Begin with a set of N wells for which production data is available. For each well, estimate its Estimated Ultimate Recovery (EUR) using a consistent decline curve model — typically a modified hyperbolic model with a 5% nominal terminal decline rate.

2. Generate the EUR Distribution
   After estimating EURs for all wells, compile them into a probability distribution. In most cases, this distribution tends to follow a log-normal shape due to the nature of production variability.

3. Smooth the EUR Distribution (Optional but Recommended)
   To reduce noise and remove local anomalies, apply a sliding-window smoothing technique:

   • Use a 7-point moving window across the sorted EUR values.

   • For each window, fit a log-normal curve.

   • Replace the middle point (4th value) with the fitted curve’s predicted value.

   • Slide the window forward by one position and repeat the process.

   • For the edges of the dataset, use 5-point or 3-point windows to avoid data loss.

This process creates a cleaner, more reliable EUR probability distribution for simulation.

Step 2: Monte Carlo Simulation for Aggregated EUR

1. Define Simulation Parameters
   Choose the number of wells to simulate per trial (e.g., 45 wells), and the total number of trials (e.g., 25,000). The more trials you run, the more robust your aggregated results will be.

2. Run Simulations
   For each trial:

   • Randomly select 45 percentile values between 0.1% and 99.9%.

   • Use your smoothed EUR distribution to convert each percentile into an EUR value.

   • Calculate the mean EUR of the selected values for that trial.

   • Store this mean EUR.

3. Build the Aggregated EUR Distribution
   After thousands of trials, the resulting set of average EURs forms the aggregated EUR probability distribution — representing the expected performance of future drilling programs based on your well dataset.

Step 3: Determine Well Weighting Factors By Running Additional Monte Carlo Trials

To generate a final aggregated type well, we calculate weighting factors for each individual well which were using in the step 1 to create smoothed EUR probability distribution. These factors represent the relative importance or likelihood of each well being part of a forecast, based on successful simulation outcomes.

Here’s the step-by-step process:

1. Identify Successful Trials
   Define a target EUR value (e.g., P90 = 1,010 MMcf), and select a narrow range around it (e.g., 1,009.9 to 1,010.1 MMcf).
   A trial is "successful" if the mean EUR for that trial falls within this range.

2. Track Well Appearances in Successful Trials
   For each successful trial, record how often each well’s EUR (or a bracketing combination) was selected.

3. Bracket EURs (When Needed)

   • If the simulated EUR falls between two known well EURs, distribute the count proportionally between them.

   • If the simulated EUR is outside the known range, assign a scaled value to the nearest extreme well using a ratio (e.g., simulated EUR ÷ closest well EUR).

   Example:
   If a simulated EUR is 800 MMcf and falls between:

   • Well A: 791 MMcf

   • Well B: 836 MMcf
     Then:

   • Well A gets 80% of the tally

   • Well B gets 20%

4. Calculate Weighting Factors
   After processing all successful trials:

   • Sum the tallies for each well.

   • Divide each well’s tally by the total tally across all wells:

These factors indicate how representative each well is in successful outcomes.

Step 4: Construct the Final Aggregated Type Well

Multiply each well’s production rate/time profile (historical and forecast) by its weighting factor, then sum the results across all wells:

The result is a smoothed, probabilistically valid type curve that reflects the expected production performance of a new well drilled under similar conditions.

Parametric Type Well Profiles

The paper "Construction of Parametric Type Well Profiles Using Linear Models" by David S. Fulford (URTeC: 4044927) presents a parametric approach for constructing Type Well Profiles (TWPs) that avoids the biases inherent in traditional averaging methods. Unlike the method you provided, which relies on Monte Carlo simulations and EUR probability distributions, Fulford’s method uses a linear regression model with transformed decline curve parameters to predict EUR and construct a TWP. Below is a step-by-step process for generating TWPs based on the method introduced in the paper, tailored to the document’s content and avoiding any copyrighted material.

A Step-by-Step Process to Create Parametric Type Well Profiles

Step 1: Select Analog Well Set

Identify a set of wells analogous to the prospective well location for which the TWP is being developed.

• Process:

  • Choose wells based on relevant criteria such as geological formation, reservoir characteristics, completion design, and geographic proximity.

  • Example from the paper: The method uses 113 horizontal wells in the Wolfcamp A formation in Howard County, Texas, drilled between 2013 and 2017.

• Considerations:

  • Ensure the dataset is robust and representative of the expected performance of future wells.

  • Source production data from reliable databases

Step 2: Forecast Production for Each Well

Generate a production forecast for each well to characterize its full production history.

• Process:

  • Apply a consistent decline curve model to each well, starting from the initial production date. The paper recommends the Transient Hyperbolic Model (THM) due to its ability to capture linear transient flow to boundary-dominated flow (Fulford and Blasingame 2013).

  • Use an automated probabilistic forecasting method to generate a P50 forecast for each well, which represents the median expected performance.

  • Calculate the 30-year EUR (EUR30) for each well using the decline curve parameters without applying a late-time terminal decline (this can be added later if needed).

• Parameters for THM:

  • q_i​: Initial production rate

  • D_i​: Initial nominal decline rate

  • b_i​: Initial b-parameter (typically 2 for THM)

  • b_f​: Final b-parameter

  • t_elf​: Time to end of linear flow

• Considerations:

  • Avoid manual forecasting to minimize bias.

  • Ensure forecasts cover the entire well life to standardize comparisons.

Step 3: Transform Decline Curve Parameters

Normalize the distribution of decline curve parameters to make them suitable for linear regression.

• Process:

  • Apply transformations to each THM parameter to achieve a more normal distribution, as non-normal distributions violate the assumptions of linear regression.

  • Transformations (based on Box-Cox transform, provided below):

    • q_i​: Natural logarithm (log⁡(q_i​))

    • D_i​: Natural logarithm (log⁡(D_i​)) for nominal decline

    • b_i​: No transformation (equivalent to power transform with λ=1)

    • b_f​​: No transformation

    • t_elf​: Natural logarithm (log⁡(t_elf​​))

  • Similarly, transform the EUR30 using a natural logarithm (log⁡(EUR30_​​)).

• Considerations:

  • The choice of log transforms for q_i​, D_i​, and t_elf​​ is based on their expected lognormal distributions within a population of analog wells.

  • The paper notes that b-parameters often approximate a normal distribution without transformation.

Step 4: Build a Linear Regression Model Using Transformed and Untransformed Parameters

Create a multiple linear regression model to predict log⁡(EUR30_​​) using transformed decline curve parameters, to show how this transformation improve the accuracy of prediction.

Process:

1. Define Predictors and Response:

   • Predictors: Transformed THM parameters (log⁡(q_i​), log⁡(D_i​), b_i, b_f, log⁡(t_elf​​)).

   • Response: log⁡(EUR30_​​) from Step 2 forecasts.

2. Fit the Model:

   • Use linear regression:

   • Train on the dataset (e.g., 113 wells in Wolfcamp A) using statistical software (e.g., Python, R).

3. Validate the Model:

   • Plot predicted vs. actual log⁡(EUR30_​​).

   • Calculate R².

   • Check residuals for randomness and homoscedasticity.

Considerations:

• Transformations normalize distributions, ensuring model validity.

• High R² indicates robustness, but TWP time-rate behavior (Step 6) is the ultimate test.

• Use consistent forecasting (Step 2) to avoid errors.

Step 5: Compute the TWP Parameters

Derive the TWP by calculating the arithmetic mean of the transformed parameters and reversing the transformations.

• Process:

  • Compute the arithmetic mean of each transformed parameter across all wells:

    • Mean of log⁡(q_i​)​

    • Mean of log⁡(D_i​)

    • Mean of b_i​​

    • Mean of b_f​​​

    • Mean of log⁡(t_elf​​)

  • Reverse the transformations to obtain the TWP parameters (Using the following formula):

    • q_i​: exp (mean of log⁡(q_i​)​)

    • D_i​ : exp (mean of log⁡(D_i​)​)

    • b_i​: No transformation (use mean of b_i)

    • b_f​: No transformation (use mean of b_f)

    • t_elf​​ ​: exp (mean of log⁡(t_elf​​)​)

  • Use these parameters in the THM rate function (below equation) to generate the TWP time-rate profile (Fulford and Blasingame 2013).

• Considerations:

  • The resulting TWP EUR is typically close to the P50 of the well set’s EUR distribution (Figure 4).

  • If the TWP EUR deviates significantly from the P50, apply a scalar correction to the initial rate (q_i) to calibrate it.

Step 6: Validate the TWP

Ensure the TWP accurately represents the typical well performance.

• Process:

  • Compare the TWP time-rate profile to the P50, arithmetic mean, and geometric mean of the well set’s production profiles (See figure below).

    

    
    

  • Verify that the TWP EUR lies between the geometric mean and arithmetic mean of the well set’s EURs, ideally near the P50 (Figure 4).

  • Check for robustness against outliers by observing that the TWP is unaffected by extreme production rates (e.g., a single well’s rate spike at 2,750 days in Figure 5).

• Considerations:

  • The TWP should avoid the overprediction bias seen in arithmetic mean-based methods, which are skewed by high-performing wells.

  • The paper demonstrates that the TWP closely matches the P50, indicating a statistically robust representation.

Step 7: Extend to Associated Phases (Optional)

Construct TWPs for associated phases (e.g., gas or water) if needed.

• Process:

  • Use a power-law model (e.g., Fulford et al., 2022) to forecast ratios like gas-oil ratio (GOR), condensate-gas ratio (CGR), water-oil ratio (WOR), or water-gas ratio (WGR).

  • Apply transformations to the power-law model parameters:

    • Intercept or starting rate: Natural logarithm

    • Slope (equivalent to b-parameter): No transformation

  • Compute the arithmetic mean of the transformed parameters and reverse the transformations to obtain the TWP parameters for the associated phase.

• Considerations:

  • Averaging associated phase rates directly (e.g., gas rates) introduces errors due to weighting by the primary phase (e.g., oil rate). The power-law model avoids this by modeling ratios.

  • GOR behavior is often more predictable than production rates, improving TWP accuracy for associated phases.

Key Features of the Parametric Method

• Statistical Rigor: Uses linear regression with transformed parameters to eliminate biases from arithmetic averaging.

• Robustness: The TWP is close to the P50, immune to outlier bias, and validated with a high R² .

• Flexibility: Applicable to primary and associated phases, with potential use for other decline models (e.g., hyperbolic) with calibration.

• Automation: Eliminates subjective interpretation, enabling rapid, consistent TWP generation.

Constraints of the Parametric Method

• Requires forecasting every well, which may be time-intensive initially but can be mitigated by pre-forecasting.

• Industry software may not support full-life forecasting starting from initial production, requiring custom workflows.

• The method assumes the THM is appropriate; other models may need additional calibration.

References:

• Fulford, David S. "Construction of parametric type well profiles using linear models." In Unconventional Resources Technology Conference, 17–19 June 2024, pp. 797-810. Unconventional Resources Technology Conference (URTeC), 2024.

• Russell, Boyd, and Randy Freeborn. "A Practical Guide to Unconventional Petroleum Evaluation Part 2." In SPE Canada Unconventional Resources Conference, pp. SPE-167215. SPE, 2013.

• Freeborn, Randy, and Boyd Russell. "Creating more-representative type wells." SPE Economics & Management 8, no. 02 (2016): 50-58.

• Fulford, D. S., and T. A. Blasingame. "Evaluation of time-rate performance of shale wells using the transient hyperbolic relation." In SPE Canada Unconventional Resources Conference, pp. SPE-167242. SPE, 2013.

• Fulford, David S., Hamid Behmanesh, Christopher R. Clarkson, and Thomas A. Blasingame. "On the relationship between gas-oil ratio and well performance for unconventional reservoirs." In Unconventional Resources Technology Conference, 20–22 June 2022, pp. 2825-2854. Unconventional Resources Technology Conference (URTeC), 2022.