1. Introduction and Background
In the early stages of the shale boom, exploration and production companies commonly drilled a single well for every 640-acre section of their newly acquired leases Cozby and Sharma [
1]. According to the terms of these leases, operators were generally obligated to drill and initiate production within a specific timeframe, usually two to three years, to maintain the lease and prevent its expiration. Successfully producing a well on a leased section renders it “Held by Production” (HBP), which allows operators to extend their drilling activities to other areas before returning to drill additional wells [
2]. While this practice helped operators to hold onto valuable acreage, it has introduced significant challenges in well-to-well interactions, commonly referred to as “parent–child interactions” or “well–towel interference” which have become a focal point in unconventional field development strategies.
In unconventional plays, a parent well is typically the first well drilled and completed in a specific reservoir section or lease, often during the early phases of field development. Over time, additional wells, known as child wells or infill wells, are drilled nearby to optimize the recovery of hydrocarbons from the same reservoir. These child wells are placed within the drainage area of the parent well, typically after a significant period of production occurred.
Ajani and Kelkar [
3] were among the first to analyze how older offset producers were affected by newer infill wells in the Woodford shale. Their findings indicated that the interactions between parent and child wells are primarily driven by pressure depletion around the parent well, which creates regions of reduced pressure in the surrounding reservoir. When a child well is drilled and completed nearby, the hydraulic fractures from the child well tend to propagate into these low-pressure areas. This results in an inefficient fracturing process, where energy is lost into already developed areas rather than creating new fractures in untapped portions of the reservoir. As a consequence, child wells often exhibit lower initial production rates and reduced ultimate recovery compared to parent wells.
Another significant issue is fracture hits, which occur when hydraulic fractures from a child well intersect with the existing fractures of a parent well. Esquivel and Blasingame [
4] outline that factors influencing well-to-well fracture interference, or frac hits, include the extent of pressure depletion, changes in the orientation of the in-site principal horizontal stress, completion design, and the spacing between wells. These fracture hits can lead to immediate and long-term impacts on both wells. The parent well may well experience a rapid drop in production as pressure is transferred from the child well into the depleted areas of the parent well’s fracture network [
5]. Simultaneously, the child’s well completion may be compromised, leading to lower fracture effectiveness and reduced reservoir contact. This interaction not only reduces the productivity of both wells but also adds operational risks, such as potential mechanical damage to wellbore integrity and increased water production [
6].
Various modeling techniques have been employed to simulate fluid flow in unconventional reservoirs, primarily to analyze reservoir performance and enhance forecasting accuracy, as discussed in works by Xu et al. [
7], Gupta et al. [
8], Kumar et al. [
9], Atadeger et al. [
10], Yildirim [
11], Yildirim and Ozkan [
12], and Yildirim et al. [
13]. Specifically, the interference between parent and child wells has been a focal point, analyzed through analytical methods, numerical approaches, and data science or data analytics [
14,
15]. The primary objective of these studies is to address and mitigate parent–child well interactions, which can be caused by depletion, well communication, altered stress, and completion techniques, to maximize hydrocarbon recovery. The main focus of these models has been mostly on optimizing well spacing. Numerous studies, such as those by Cao et al. [
16] and Chu et al. [
17], have highlighted the role of frac hits as a key indicator of well spacing effectiveness. If frac hits are absent, leaving untapped reservoir potential, while in cases where frac hits do occur, child wells often underperform due to poroelastic stress changes caused by reservoir depletion between the parent and child wells [
18,
19]. These stress changes can create asymmetric fracture growth, particularly affecting child well performance when placed too close to a depleted parent well. Researchers so demonstrated that this performance degradation worsens with longer intervals between the start dates of parent and child wells, further stressing the importance of completion timing and its relationship with depletion.
Apart from well spacing, reservoir deliverability and completion design are critical factors influencing these interactions. Rafiee and Grover [
20] combined fracture modeling, reservoir simulation, and data analytics to conclude the wells spaced farther apart with more relaxed cluster spacing produced 30% higher estimated ultimate recoveries (EURs) compared to tighter configurations in the Eagle Ford. Similarly, Shahkarami et al. [
21] noted that a well spacing strategy must consider not only geological and reservoir simulations but also economic factors such as commodity pricing and operational expenditures. Completion design and reservoir energy levels also influence parent–child interactions. Kurtoglu et al. [
22] used decline curve analysis to show that in high-energy reservoirs, indicated by a high GOR and initial pore pressure, frac hits can have a positive impact. However, in low-energy reservoirs, the opposite is true, with frac hits exacerbating production losses, particularly when paired with tight well spacing and large child well completions. Some researchers used a similar approach, combining DCA with data analytics to model the economic impacts of frac hits on well performance, providing operators with insights into optimizing well placement and design.
Recent advances in physics-based and data-driven modeling techniques are enhancing operators’ ability to predict and manage parent–child interactions. These improvements, coupled with advancements in modeling, offer the potential to mitigate production challenges associated with parent–child interactions [
23]. The next logical step is to apply these methods in real-world scenarios. Therefore, this study aims to develop a workflow that integrates decline curve analysis (DCA) with machine learning tools, specifically random forest regression (RFR), to analyze parent–child interactions in the DJ Basin. By focusing on the impact of well spacing and completion timing on production rates and using public data from the Enverus database, this study will assess the short- and long-term effects on both parent and child wells. Although various data analytics approaches have been applied in different basins, a detailed study specific to the DJ Basin is still lacking. This study aims to address that gap. The study area includes the liquid-rich Denver-Julesburg (DJ) Basin, covering over 70,000 square miles across eastern Colorado, southeastern Wyoming, and southwestern Nebraska [
24].
2. Analyzing Parent–Child Wells and the Workflow
In this study, traditional decline curve analysis (DCA) is combined with the machine learning tool Random Forest Regressor to predict the future performance of parent and child wells. The workflow begins with an explanation of DCA, followed by an outline of the processes used for the machine learning tool. Subsequently, parameters influencing parent–child wells are discussed, along with methods for their quantification. This data analytics approach utilizes publicly available data from Enverus for the Denver-Julesburg (DJ) Basin, aiming to offer insights into well interactions and enhance predictive accuracy in this region.
Several useful existing methods, such as machine learning algorithms, statistical regression models, and network analysis, utilize data mining to analyze parent–child well interactions and quantify the impacts, especially on short-term production (over the next 12 months) and reserve estimations (EUR calculations). This paper focuses on the factors affecting the performance of parent and child wells and quantifies their impact on both short-term and long-term production by employing DCA and ML.
The initial step involves the collection of production and operational data for each well in the dataset. This dataset typically comprises historical production rates for each phase (oil, gas, and water), initial production rates, completion details, and geological information. Wellhead pressure data, however, was excluded from this study due to its unavailability in the Enverus database.
The next step is to identify parent and child wells based on their production history. Our proxy is designed to categorize the wells (parent, child, or co-completed) according to their vintage production. To ensure accuracy, we have set a minimum threshold of three months for infill timing; starting from this point, we analyze the parent and child wells. Ref. [
1] showed the importance of using the indicator of “parent produced BOE at child completion” rather than considering only the time difference between the existing well and infill well; therefore, we have considered both at the identification of parent and child wells to update the metrics. After categorizing the parent and child wells, we have employed the decline curve analysis.
Decline curve analysis is a fundamental semi-empirical technique for estimating oil and gas wells’ production decline and future performance. Arps introduced this widely used and well-known method based on the performance of over one hundred oil wells operating at maximum capacity in the US. The decline curve analysis typically involves three types of decline curves: exponential, hyperbolic, and harmonic declines. Hyperbolic decline is frequently observed in the production of unconventional wells. The mathematical expression for hyperbolic decline is shown in Equation (1).
where
is the initial production rate, bbl/d;
is the dimensionless constant;
is the initial decline rate, 1/yr; and
is the time, years. Dimensionless constant, in other words, the
factor, is in between 0 and 1 for conventional plays. However, in unconventional wells, the constant is usually greater than in conventional wells. The cumulative production rate is calculated by using Equation (2).
where
is the cumulative production rate. Following a brief explanation of the decline curve analysis (DCA) methodology, this approach is applied to forecast both short-term and long-term production outcomes in parent and child wells within this study. As previously noted, all data utilized is sourced from the Enverus DJ Basin database. An example of the decline curve analysis applied to a parent well is illustrated in
Figure 1, demonstrating the model’s capability to project production performance over time.
In
Figure 1, the green curve represents the oil production over time for the well nearest to the infill well pad. An unintended drop in the parent well’s production following the completion of a child well—a common indicator of frac hits—is evidenced by the rapid decline in production response. To accurately represent this, two distinct decline curves are applied to characterize the production trends before and after the frac hit. The analysis is conducted beginning from the peak production response, and this process is repeated across other production phases to ensure consistency. The red curve depicts the decline curve analysis (DCA) representing the period before the frac hit, while the blue curve illustrates the decline trend afterward.
Figure 1 provides a short-term production forecast over the next 12 months, indicating a 27% reduction in production response following the initiation of the child wells’ production.
The estimated ultimate recovery (EUR) is calculated and subsequently compared with pre-hit data to forecast long-term production. While a reduction is observed in short-term production, the presence of a child well ultimately enhances the long-term performance of the parent well by approximately 5%. In this analysis, decline curve parameters—including the b-factor, decline rate, and initial rate—are used to inform the proxy, facilitating a basin-wide analysis of parent–child well interactions. Following the display of the parent well’s decline curves,
Figure 2 presents the production performance of the child wells over time.
In
Figure 2, it is consistent with expectations that the production of the child well pad underperformed compared to the existing parent wells in the nearby drainage area. The red curve illustrates the production of the nearest child well, which shows the poorest performance relative to the other wells. The purple curve represents the second child well, while the yellow and green curves represent the co-completed wells, respectively. The classification code for the parent and child wells was written in Python (3.11), taking into account the time gap and expected distance. This classification was then compared with the Enverus database to enhance accuracy.
Figure 3 illustrates the cumulative production profiles of the identified parent and child wells, providing a basis for confirming their respective classifications. This analysis aligns with prior observations: the child well, located nearest to Parent Well 1, which is itself the closest parent well to this child well, demonstrates a notably lower cumulative production rate. This decline in production is likely attributable to interference between the two wells, suggesting that proximity impacts overall yield. Moreover, a significant alteration in the cumulative production trend of Parent Well 1 is observed as the closest child well begins production. This shift occurs precisely 11 months after Parent Well 1 commenced production, highlighting a temporal relationship between well activation and performance interference. These observations underscore the inter-well dynamics within closely spaced well systems and illustrate how the initiation of one well’s production may detrimentally affect another.
DCA was applied to assess both the short- and long-term production of child wells, following the same procedural approach as that employed for parent wells. Percentage differences were subsequently calculated based on both pad and grand levels. Normalized rates and normalized Estimated Ultimate Recoveries (EURs), along with their p50 values, were then compared using the model to verify that these percentage differences were consistent with prior calculations. Here, the p50 value represents the median estimated recovery, meaning there is a 50% probability that the actual recovery will meet or exceed this value, providing a balanced measure of production expectations.
Figure 4 presents the results generated by the Python code for the child and parent pads, illustrating the alignment between calculated values and observed data. The green colored represents the highest value of EURs compared to others while red shows the lowest value.
In the next step, parent and child wells were classified, and decline curve analysis (DCA) was applied to evaluate their production behavior. A random forest regressor was then selected for model training using the collected dataset, which comprised decline curve parameters, spatial distances between wells, time differences, operational characteristics, and intervals within the basin. Following the training process, model performance was assessed using the mean absolute error (MAE) metric, a measure that calculates the average magnitude of prediction errors, providing insight into the model’s accuracy. Additionally, the impact of various features—such as distances, operational similarities, and basin intervals—on interference between parent and child wells was quantified, allowing for a clearer understanding of the factors influencing well performance interactions.
For spatial analysis, Enverus gun barrel views were utilized to analyze the optimum horizontal spacing between parent and child wells, as maintaining adequate horizontal distance is crucial for minimizing interference within the same producing interval. Vertical and 3D distances were also considered to capture any depth differences, especially when wells target distinct formations like the Niobrara and Codell. To incorporate time-related factors, both completion and first production dates were included, along with parameters such as gas–oil ratio (GOR) and completion data. Production metrics—including 12-month barrels of oil equivalent (BOE), peak production, and cumulative production—were analyzed to gain a comprehensive understanding of well performance.
Figure 5 presents the gun barrel view of an example parent and child well pair, illustrating their spatial arrangement and production dynamics. Yellow dots represent the parent wells’ tops while dark purple shows the child wells’ well tops.
3. Results and Discussions
Extensive discussion in the literature has been dedicated to parent–child well relationships, particularly examining how interactions between parent and child wells impact production performance, the various factors influencing these relationships, and approaches to quantifying these effects to guide future performance expectations and operational strategies. In this study, factors influencing well performance in the DJ Basin are identified, with a comprehensive dataset utilized to establish strong correlations and enhance predictive reliability.
Firstly, the study underscores the significance of parent–child well relationships in unconventional resource development, examining how well spacing, timing, and co-completion influence production performance.
Figure 6 and
Figure 7 illustrate trends in parent–child well distribution over the past 14 years, revealing that increased spacing between wells enhances production by reducing interference and minimizing negative impacts. Secondly,
Figure 8,
Figure 9,
Figure 10,
Figure 11,
Figure 12,
Figure 13 and
Figure 14 present formation-specific analyses, showing distinct effects across Niobrara and Codell Formations, indicating that parent–child interactions vary significantly by geological characteristics.
Figure 15 then introduces the b-factor analysis, offering insight into decline trends for parent and child wells, which plays a critical role in shaping long-term productivity. Finally,
Figure 16 and
Figure 17 summarize the short- and long-term impacts on both parent and child wells, highlighting that optimal spacing and co-completion timing strategies are essential for mitigating negative effects and preserving well productivity. Collectively, this analysis emphasizes spacing, timing, and geological considerations as vital for maximizing well performance in unconventional reservoirs.
Figure 6 presents the distribution of parent and child wells over the past 14 years, illustrating a notable trend towards simultaneous drilling within units, as evidenced by an increase in co-completed wells in recent years. Nevertheless, parent wells remain critical for securing leases and continue to contribute to regional depletion, which can often result in diminished performance in associated child wells.
In developing unconventional resources, strategic well spacing plays a crucial role in managing the interactions between parent and child wells, which are vital for optimizing the recovery and economic viability of unconventional oil and gas reservoirs. If child wells are spaced too close to a parent well, they can accelerate the depletion of resources around the parent well. This can lead to decreased pressure and diminished returns from the parent well because the child wells are effectively drawing from the same reservoir segment. Another impact is that close spacing can lead to direct interference between the wells. This is often characterized by issues such as pressure interference or hydraulic communication, where the stimulation of a child well impacts the parent well, potentially reducing the parent well’s productivity or even damaging it. This is often seen when the fracturing of a child well redirects fluids away from a parent well or alters the reservoir pressure that maintains productive flow. Optimum spacing can mitigate the frac hit risks that occur when the hydraulic fracturing of a child well impacts an existing parent well and can result in sudden changes in pressure, spikes in water production, and potential damage to the well structure or casing. For this reason, initially, we evaluated the effect of spacing on the interference between parent and child wells.
To assess the correlation between optimal spacing and parent/child well performances, proxy was initially used in conjunction with the Enverus dataset.
Figure 7 displays a heatmap of the normalized 12-month BOE for parent/child or co-completed wells, color-coded by the mean distance to the nearest parent well. The heatmap reveals that as the minimum distance between wells increases, there is a corresponding rise in normalized BOE, indicating improved well performance with greater spacing.
Figure 8 displays the short-term negative impact (in percent) on the productivity of child wells as a function of the spacing between them and their corresponding parent wells. There is a marked correlation between the well spacing and the short-term (over the next 12 months) production effect. It is evident that the greater the distance at which new wells are drilled from existing ones, the smaller the detrimental effect on production performance. Specifically, for short-term output, when the distance between existing wells and new infill wells exceeds 800 feet, the adverse impact on child wells is typically negligible. Conversely, a spacing interval of 200 to 300 feet is associated with a substantial negative impact, amounting to 35%.
Likewise,
Figure 9 shows the long-term (EUR) impact on infill wells’ future performance. The trend line, sloping downward, reveals a strong inverse correlation, suggesting that increased spacing correlates with a reduced long-term negative impact on the child wells. With an R-squared value of 0.7993, this model indicates that nearly 80% of the variance in long-term impact is explained by the distance between wells. As the offset increases, the plot shows a clear trend of diminishing impact, affirming the hypothesis that greater distances between wells mitigate the negative effects on productivity over the long term. It is noteworthy that while the negative impact is not as pronounced in the long term as it is in the short term, it still persists, ranging between 20 and 25%. In this study, child wells were grouped according to the timing of their infill completions to facilitate a deeper understanding of the impact of well spacing on production performance over time. Although variations in completion times were present, a clear relationship was identified between the spacing of wells and their subsequent production outcomes.
The effect of the time interval between the drilling of parent and child wells on well performance was examined. The productivity of child wells appears to be significantly influenced by the duration that has elapsed since the nearby parent wells were initially drilled. When a parent well commences production, it induces a decline in pressure within the surrounding rock formations. Drilling a child well shortly after the parent well may lead to diminished productivity due to the continued pressure depletion within the reservoir. This reduction in productivity arises from the depletion effect, which causes a decrease in fluid availability within the system and the formation of low-pressure zones and localized pressure sinks, consequently reducing formation stress. Lower formation stress can cause fractures to propagate preferentially toward the parent well, following paths of least resistance. Previous studies have shown that increasing the time between infill operations tends to intensify the depletion effect, thereby adversely affecting child well performance.
Figure 10 and
Figure 11 illustrate the impact of infill timing on both the short-term and long-term productivity of child wells.
Figure 10 shows that the production performance of child wells remains unaffected for up to five months, after which the impact progressively increases with a wider time gap. This pattern reveals a strong correlation between infill timing and child well performance, mirroring the effects observed with well spacing. These findings underscore the importance of minimizing the time difference between parent and child wells to reduce adverse impacts. Notably, a time gap of 40 to 50 months is associated with a 30–40% reduction in short-term (next 12 months) production performance.
Figure 11 represents the long-term negative impact on child well performance related to the infill timing difference between parent and child wells. Similarly to
Figure 10, there is a clear trend indicating that longer time gaps between the drilling of parent and child wells tend to correlate with higher long-term impacts on the child wells’ production performance. The negative impact on the EUR performance of child wells is less significant than the impact on short-term (next 12 months) production. Over the long term, the negative impact generally accumulates within the range of 20–30%.
The analysis focused on the interaction between parent and child wells specifically within the Niobrara and Codell Formations in the DJ Basin, utilizing the detailed data available in the Enverus database. Wells were identified based on their geologic formation, enabling a closer examination of parent–child relationships within these specified formations. This approach provided insights into the performance of wells in the Niobrara and Codell Formations, offering a clearer picture of how these formations respond to parent–child well interactions in the DJ Basin.
Figure 12 shows the normalized EUR based on the formation levels. Due to the extensive data for Niobrara B-C and Codell Formations, we determined the long-term impact on child wells using cumulative and EUR data.
Figure 13 illustrates the long-term impact on child wells within the Niobrara B and Niobrara C Formations, while
Figure 14 highlights the effects on the Codell Formation. For long-term impacts, Niobrara B shows variations ranging from 4 to 25%, whereas Niobrara C demonstrates impacts from negligible to 14%. It is important to note that Niobrara B has a higher number of parent–child well pairs compared to Niobrara C. Similarly, the Codell Formation experiences up to an 8% negative impact on the long-term production performance of child wells.
In
Figure 15, the b-factor derived from decline curve analysis is shown, illustrating its use for parent and child wells in the DJ Basin. This aligns with our calculations, which indicate that for child wells, the b-factor ranges from 0.89 to 0.99, while for parent wells, it ranges from 0.94 to 1.02.
In summary,
Figure 16 illustrates both the short-term and long-term effects of the parent well on the child well. Meanwhile,
Figure 17 quantifies the impact on the parent well resulting from the presence of a child well, detailing both short-term and long-term production outcomes.
Figure 16 presents the short- and long-term production impacts on child wells. In
Figure 16a, which illustrates the short-term impact over the next 12 months, child wells show a significant decline in production, with changes ranging from a 45.00% decrease to a minor 3.00% increase. The median short-term impact is a 16.00% decrease, indicating that most child wells underperform shortly after being drilled compared to existing parent wells. In the long term, depicted in
Figure 16b, the estimated ultimate recovery (EUR) impact on child wells remains negative, with declines from 4.48% to 48.20% and a median long-term decrease of 18.88%. These results emphasize that child wells, particularly in the DJ Basin, face substantial production challenges, with consistent underperformance relative to parent wells both in the short and long term. This suggests that child wells often struggle to achieve similar recovery levels as parent wells, potentially due to competition for resources or drainage effects within the reservoir.
Figure 17 illustrates the short- and long-term production impacts on parent wells in the presence of infill (child) wells. In the short term, represented by
Figure 17a, parent wells exhibit a wide range of production changes over the next 12 months, with impacts varying from a 36% decrease to a 58% increase. The median short-term change is a 4.71% increase, suggesting that, on average, parent wells tend to see a production boost shortly after infill drilling, likely due to increased reservoir pressure or resource redistribution. Conversely, the long-term effects, shown in
Figure 17b, reveal a smaller and often negative impact on the estimated ultimate recovery (EUR) of parent wells. While some parent wells experience no long-term change, others suffer up to a 10% reduction in EUR. This phenomenon suggests that, over time, resource competition or drainage from infill wells can detract from the parent well’s recovery potential. Together, these figures highlight the nuanced and often contrasting effects of infill wells, with potential short-term gains but long-term trade-offs in resource recovery.