Search Results (14)

Machine learning models that only use data for training and forecasting oilfield production have a sense of disconnection from the physical background, while embedding development patterns in them can enhance interpretability and even improve accuracy. In this paper, a novel multi-well production forecasting model embedded with decline curve analysis (DCA) is proposed, enabling the machine learning model to incorporate physical information. Moreover, an improved particle swarm optimization algorithm is proposed to optimize the hyperparameters in the loss function of the model. These hyperparameters determine the importance of the overall DCA and each module in training, which traditionally requires expert knowledge to determine. Simulation results based on the benchmark reservoir model show that the model has better forecasting ability and generalization performance compared to typical machine learning methods. Full article

This study presents a new equation, the dynamic recovery factor (DRF), for evaluating the recovery factor (RF) in homogeneous and heterogeneous reservoirs. The DRF method’s outcomes are validated and compared using the decline curve analysis (DCA) method. Real measured field data from 15 wells in a homogenous sandstone reservoir and 10 wells in a heterogeneous carbonate reservoir are utilized for this study. The concept of the DRF approach is based on the material balance principle, which integrates several components (weighted average cumulative pressure drop (ΔP_cum), total compressibility (C_t), and oil saturation (S_o)) for predicting RF. The motivation for this study stems from the practical restrictions of conventional RF valuation techniques, which often involve extensive datasets and use simplifying assumptions that are not applicable in complex heterogeneous reservoirs. For the homogenous reservoir, the DRF approach predicts an RF of 8%, whereas the DCA method predicted 9.2%. In the heterogeneous reservoir, the DRF approach produces an RF of 6% compared with 5% for the DCA technique. Sensitivity analysis shows that RF is very sensitive to variations in C_t, ΔP_cum, and S_o, with values that vary from 6.00% to 10.71% for homogeneous reservoirs and 4.43% to 7.91% for heterogeneous reservoirs. Uncertainty calculation indicates that errors in C_t, ΔP_cum, and S_o propagate to RF, with weighting factor (W_i) uncertainties causing changes of ±3.7% and ±4.4% in RF for homogeneous and heterogeneous reservoirs, respectively. This study shows the new DRF approach’s ability to provide reliable RF estimations via pressure dynamics, while DCA is used as a validation and comparison baseline. The sensitivity analyses and uncertainty analyses provide a strong foundation for RF estimation that helps to select well-informed decisions in reservoir management with reliable RF values. The novelty of the new DRF equation lies in its capability to correctly estimate RFs using limited available historical data, making it appropriate for early-stage development and data-scarce situations. Hence, the new DRF equation is applied to various reservoir qualities, and the results show a strong alignment with those obtained from DCA, demonstrating high accuracy. This agreement validates the applicability of the DRF equation in estimating recovery factors through different reservoir qualities. Full article

The objective of this research is to examine the dynamics of parent/child well interaction in unconventional plays, an issue that has gained prominence as high-quality inventory reduces and the number of infill wells escalates. To achieve this, the research will identify and analyze the factors influencing the interaction between parent/child wells and quantify the impacts of time, distance, and geological formation within the context of the DJ basin. The short-term estimate, considered as the next 12 months of cumulative oil production, is forecasted using decline curve analysis (DCA), and the long-term estimates come from the estimated ultimate recovery (EUR) of oil. The impact of the interaction on the parent well is determined as the difference between the recovery of the pre-frac hit and the post-frac hit. The child wells are compared to unaffected wells from the same unit. The average distance between parent and child wells is kept constant, and the time gap between the pre-existing and infill wells is statistically compared to observe the impact of time. The same procedure is followed for distance, orientation, and formation. The findings indicate that stimulation of child wells can lead to a depletion-induced stress shadow around the parent wells, potentially resulting in asymmetrical fracture growth. Consequently, the proximity of parent wells may contribute to a decrease in the performance of the child wells. On the contrary, parent wells with frac hits experienced varied outcomes, including improved production, reduced production, or no noticeable change at all. When the distance between parent and child well decreases, the negative impact on child wells increases. Increasing the time gap between pre-existing wells and infill wells shows an adverse impact on child wells. The impact on child wells was not observed when the parent well had been producing for less than 5 months. An interesting pattern emerged when analyzing the orientation of wells; child wells drilled at a perpendicular angle to their parent wells did not exhibit changes in performance. Within the geological context, the Niobrara Formation was found to have a more substantial negative impact on well interactions than the Codell Formation. In conclusion, time and distance play a crucial role in parent/child well interaction. Despite the existence of studies on parent/child well interactions within the literature, a comprehensive and detailed analysis specifically targeting the DJ Basin—particularly focusing on the intricacies of well interactions within the Niobrara and Codell Formations—has not yet been undertaken. Full article

Background: Patients with multiple myeloma (MM) who have a suboptimal response to induction therapy or early relapse are classified as functional high-risk (FHR) patients and have been shown to have a dismal prognosis. The aim of this study was to establish a predictive nomogram for patients with non-transplanted FHR MM. Materials and Methods: The group comprised 215 patients in our center between 1 January 2006 and 1 March 2024. To identify independent risk factors, univariate and multivariate logistic regression analyses were performed, and a nomogram was constructed to predict non-transplant FHR MM. To evaluate the nomogram’s predictive accuracy, we utilized bias-corrected AUC, calibration curves, decision curve analysis (DCA), and clinical impact curves (CIC). Results: Multivariate logistic regression demonstrated that younger age at onset, a higher proportion of LDH (more than 220 U/L), pattern A + C of M protein decline patterns, a lower proportion of patients with induction treatment efficacy than VGPR, and those undergoing maintenance therapies were independent risk factors for patients with non-transplanted FHR MM. The AUC scores for the training and internal validation groups were 0.940 (95% CI 0.893–0.986) and 0.978 (95% CI 0.930–1.000). DCA and CIC curves were utilized to further verify the clinical efficacy of the nomogram. Conclusions: We developed a nomogram that enables early prediction of non-transplant FHR MM patients. Younger age at onset, LDH ≥ 220 U/L, an A + C pattern of M-protein decline, and induction therapy efficacy not reaching VGPR are more likely to be FHR MM patients. Patients who do not undergo maintenance therapy are prone to early progression or relapse. Full article

As a clean unconventional energy source, shale gas reservoirs are increasingly important globally. Accurate prediction methods for shale gas production capacity can bring significant economic benefits by reducing construction and operating costs. Decline curve analysis (DCA) is an efficient method that uses mathematical formulas to describe production trends with minimal reliance on geological or engineering parameters. However, traditional DCA models often fail to capture the complex production dynamics of shale gas wells, especially in complex environments. To overcome these limitations, this study proposes an Improved DCA method that integrates multiple base empirical DCA models through ensemble learning. By combining the strengths of individual models, it offers a more robust and accurate prediction framework. We evaluated this method using data from 22 shale gas wells in region L, China, comparing it to six traditional DCA models, including Arps and the Logistic Growth Model (LGM). The results show that the Improved DCA model achieved superior performance—with an mean absolute error (MAE) of 0.0660, an mean squared error (MSE) of 0.0272, and an $R^2$ value of 0.9882—and exhibited greater stability across various samples and conditions. This method provides a reliable tool for long-term production forecasting and optimization without extensive geological or engineering information. Full article

The decline curve analysis (DCA) technique is the simplest, fastest, least computationally demanding, and least data-required reservoir forecasting method. Assuming that the decline rate of the initial production data will continue in the future, the estimated ultimate recovery (EUR) can be determined at the end of the well/reservoir lifetime based on the declining mode. Many empirical DCA models have been developed to match different types of reservoirs as the decline rate varies from one well/reservoir to another. In addition to the uncertainties related to each DCA model’s performance, structure, and reliability, any of them can be used to estimate one deterministic value of the EUR, which, therefore, might be misleading with a bias of over- and/or under-estimation. To reduce the uncertainties related to the DCA, the EUR could be assumed to be within a certain range, with different levels of confidence. Probabilistic decline curve analysis (pDCA) is the method used to generate these confidence intervals (CIs), and many pDCA approaches have been introduced to reduce the uncertainties that come with the deterministic DCA. The selected probabilistic type of analysis (i.e., frequentist or Bayesian), the used DCA model(s), the type and the number of wells, the sampling technique of the data or the model’s parameters, and the parameters themselves undergo a probability distribution, and these are the main differences among all of these approaches and the factors that determine how each approach can quantify the uncertainties and mitigate them. In this work, the Bayesian and frequentist approaches are deeply discussed. In addition, the uncertainties of DCA are briefly discussed. Further, the bases of the different probabilistic analyses are explained. After that, 15 pDCA approaches are reviewed and summarized, and the differences among them are stated. The study concludes that Bayesian analysis is generally more effective than frequentist analysis, though with narrower CIs. However, the choice of DCA model and sampling algorithm can also affect the bounds of the CIs and the calculation of the EUR. Moreover, the pDCA approach is recommended for quantifying uncertainties in DCA, with narrower CIs that indicate greater effectiveness. However, the computational time and the number of iterations in sampling are also considered critical factors. That is why various assumptions and modifications have been made in the pDCA approaches, including the assumption of a certain probability distribution for the sampled parameters to improve their reliability of reserve estimation. The motivation behind this research was to present a full state-of-the-art review of the pDCA and the latest developments in this area of research. Full article

Shale gas reservoirs have huge amounts of reserves. Economically evaluating these reserves is challenging due to complex driving mechanisms, complex drilling and completion configurations, and the complexity of controlling the producing conditions. Decline Curve Analysis (DCA) is historically considered the easiest method for production prediction of unconventional reservoirs as it only requires production history. Besides uncertainties in selecting a suitable DCA model to match the production behavior of the shale gas wells, the production data are usually noisy because of the changing choke size used to control the bottom hole flowing pressure and the multiple shut-ins to remove the associated water. Removing this noise from the data is important for effective DCA prediction. In this study, 12 machine learning outlier detection algorithms were investigated to determine the one most suitable for improving the quality of production data. Five of them were found not suitable, as they remove complete portions of the production data rather than scattered data points. The other seven algorithms were deeply investigated, assuming that 20% of the production data are outliers. During the work, eight DCA models were studied and applied. Different recommendations were stated regarding their sensitivity to noise. The results showed that the clustered based outlier factor, k-nearest neighbor, and the angular based outlier factor algorithms are the most effective algorithms for improving the data quality for DCA, while the stochastic outlier selection and subspace outlier detection algorithms were found to be the least effective. Additionally, DCA models, such as the Arps, Duong, and Wang models, were found to be less sensitive to removing noise, even with different algorithms. Meanwhile, power law exponential, logistic growth model, and stretched exponent production decline models showed more sensitivity to removing the noise, with varying performance under different outlier-removal algorithms. This work introduces the best combination of DCA models and outlier-detection algorithms, which could be used to reduce the uncertainties related to production forecasting and reserve estimation of shale gas reservoirs. Full article

The present study shows how new Gaussian solutions of the pressure diffusion equation can be applied to model the pressure depletion of reservoirs produced with hydraulically multi-fractured well systems. Three practical application modes are discussed: (1) Gaussian decline curve analysis (DCA), (2) Gaussian pressure-transient analysis (PTA) and (3) Gaussian reservoir models (GRMs). The Gaussian DCA is a new history matching tool for production forecasting, which uses only one matching parameter and therefore is more practical than hyperbolic DCA methods. The Gaussian DCA was compared with the traditional Arps DCA through production analysis of 11 wells in the Wolfcamp Formation at Hydraulic Fracture Test Site-1 (HFTS-1). The hydraulic diffusivity of the reservoir region drained by the well system can be accurately estimated based on Gaussian DCA matches. Next, Gaussian PTA was used to infer the variation in effective fracture half-length of the hydraulic fractures in the HFTS-1 wells. Also included in this study is a brief example of how the full GRM solution can accurately track the fluid flow-paths in a reservoir and predict the consequent production rates of hydraulically fractured well systems. The GRM can model reservoir depletion and the associated well rates for single parent wells as well as for arrays of multiple parent–parent and parent–child wells. Full article

Determining the reliable values of the filtration parameters of productive reservoirs is the most important task in monitoring the processes of reserve production. Hydrodynamic studies of wells by the pressure build-up method, as well as a modern method based on production curve analysis (Decline Curve Analysis (DCA)), are some of the effective methods for solving this problem. This paper is devoted to assessing the reliability of these two methods in determining the filtration parameters of terrigenous and carbonaceous productive deposits of oil fields in the Perm Krai. The materials of 150 conditioned and highly informative (obtained using high-precision depth instruments) studies of wells were used to solve this problem, including 100 studies conducted in terrigenous reservoirs (C₁v) and 50 carried out in carbonate reservoirs (C₂b). To solve the problem, an effective tool was used—multivariate regression analysis. This approach is new and has not been previously used to assess the reliability of determining the filtration parameters of reservoir systems by different research methods. With its use, a series of statistical models with varying degrees of detail was built. A series of multivariate mathematical models of well flow rates using the filtration parameters determined for each of the methods is constructed. The inclusion or non-inclusion of these filtration parameters in the resulting flow rate models allows us to give a reasonable assessment of the possibility of using the pressure build-up method and the DCA method. All the constructed models are characterized by high statistical estimates: in all cases, a high value of the determination coefficient was obtained, and the probability of an error in all cases was significantly less than 5%. As applied to the fields under consideration, it was found that both methods demonstrate stable results in terrigenous reservoirs. The permeability determined by the DCA method and the pressure build-up curve does not control the flow of the fluid in carbonate reservoirs, which proves the complexity of the filtration processes occurring in them. The DCA method is recommended for use to determine the permeability and skin factor in the conditions of terrigenous reservoirs. Full article

We analyze the effect that the geometry of the Effective Propped Volume (EPV) has on the economic performance of hydrofractured multistage shale gas wells. We study the sensitivity of gas production to the EPV’s geometry and we compare it with the sensitivity to other parameters whose relevance in the production of shale gas is well known: porosity, kerogen content and permeability induced in the Stimulated Recovery Volume (SRV). To understand these sensitivities, we develop a high-fidelity 3D numerical model of shale gas flow that allows determining both the Estimated Ultimate Recovery (EUR) of gas as well as analyzing the decline curves of gas production (DCA). We find that the geometry of the EPV plays an important role in the economic performance and gas production of shale wells. The relative contribution of EPV geometry is comparable to that of induced permeability of the SRV or formation porosity. Our results may lead to interesting technological developments in the oild and gas industry that improve economic efficiency in shale gas production. Full article

A comprehensive overview and analysis of the productivity of 1216 recently abandoned multi-stage hydraulically fractured horizontal wells from five shale formations in the United States (US) is presented in this study. In this study, two decline curve analysis (DCA) methods were used to match actual production history data using least-squares fitting to find the best fit production parameters to reliably forecast production. The production history matching conducted resulted in very accurate matches (correlation coefficient of 0.99) between actual production data and the two DCA methods (Arps hyperbolic decline and stretched exponential production decline (SEPD) models). Using the outcomes from production history matching, universal averages of decline parameters for Arps hyperbolic decline and SEPD models were developed for each of the five formations. Furthermore, hindcasting was performed by matching a portion of the known production history and comparing the remaining portion of the known production history to the forecast. The Arps hyperbolic decline and SEPD methods were used to match production using only limited early production data (three months, six months, one year and two years). The main goals for fitting the DCA model to early production data was to estimate the optimum decline parameters that are then used to forecast production and estimate ultimate recovery. Production history matching using limited early production periods produced accurate production forecasts using as few as six months of production history (correlation coefficients between 0.85 and 0.94 using Arps hyperbolic decline). The main outcome of this study was a production analysis conducted on the production data of more than 1000 wells from five different shale formations to present the expected production behaviors of similar wells. Different production key performance indicators (KPIs) such as average well life, cumulative production volumes at different periods, average drop in production rate within the first year of production, average time to reach maximum flow rate, and the maximum flow rate were measured on all the wells from the five formations to provide an overview of the production performance of each formation. Full article

The development of prediction tools for production performance and the lifespan of shale gas reservoirs has been a focus for petroleum engineers. Several decline curve models have been developed and compared with data from shale gas production. To accurately forecast the estimated ultimate recovery for shale gas reservoirs, consistent and accurate decline curve modelling is required. In this paper, the current decline curve models are evaluated using the goodness of fit as a measure of accuracy with field data. The evaluation found that there are advantages in using the current DCA models; however, they also have limitations associated with them that have to be addressed. Based on the accuracy assessment conducted on the different models, it appears that the Stretched Exponential Decline Model (SEDM) and Logistic Growth Model (LGM), followed by the Extended Exponential Decline Model (EEDM), the Power Law Exponential Model (PLE), the Doung’s Model, and lastly, the Arps Hyperbolic Decline Model, provide the best fit with production data. Full article

A recent study by the Wall Street Journal reveals that the hydrofractured horizontal wells in shales have been producing less than the industrial forecasts with the empirical hyperbolic decline curve analysis (DCA). As an alternative to DCA, we introduce a simple, fast and accurate method of estimating ultimate recovery in oil shales. We adopt a physics-based scaling approach to analyze oil rates and ultimate recovery from 14,888 active horizontal oil wells in the Bakken shale. To predict the Estimated Ultimate Recovery (EUR), we collapse production records from individual horizontal shale oil wells onto two segments of a master curve: (1) We find that cumulative oil production from 4845 wells is still growing linearly with the square root of time; and (2) 6401 wells are already in exponential decline after approximately seven years on production. In addition, 2363 wells have discontinuous production records, because of refracturing or changes in downhole flowing pressure, and are matched with a linear combination of scaling curves superposed in time. The remaining 1279 new wells with less than 12 months on production have too few production records to allow for robust matches. These wells are scaled with the slopes of other comparable wells in the square-root-of-time flow regime. In the end, we predict that total ultimate recovery from all existing horizontal wells in Bakken will be some 4.5 billion barrels of oil. We also find that wells completed in the Middle Bakken formation, in general, produce more oil than those completed in the Upper Three Forks formation. The newly completed longer wells with larger hydrofractures have higher initial production rates, but they decline faster and have EURs similar to the cheaper old wells. There is little correlation among EUR, lateral length, and the number and size of hydrofractures. Therefore, technology may not help much in boosting production of new wells completed in the poor immature areas along the edges of the Williston Basin. Operators and policymakers may use our findings to optimize the possible futures of the Bakken shale and other plays. More importantly, the petroleum industry may adopt our physics-based method as an alternative to the overly optimistic hyperbolic DCA that yields an ‘illusory picture’ of shale oil resources. Full article

This paper advances a practical tool for production forecasting, using a 2-segment Decline Curve Analysis (DCA) method, based on an analytical flow-cell model for multi-stage fractured shale wells. The flow-cell model uses a type well and can forecast the production rate and estimated ultimate recovery (EUR) of newly planned wells, accounting for changes in completion design (fracture spacing, height, half-length), total well length, and well spacing. The basic equations for the flow-cell model have been derived in two earlier papers, the first one dedicated to well forecasts with fracture down-spacing, the second one to well performance forecasts when inter-well spacing changes (and for wells drilled at different times, to account for parent-child well interaction). The present paper provides a practical workflow, introduces correction parameters to account for acreage quality and fracture treatment quality. Further adjustments to the flow-cell model based 2-segment DCA method are made after history matching field data and numerical reservoir simulations, which indicate that terminal decline is not exponential (b = 0) but hyperbolic (with 0 < b< 1). The timing for the onset of boundary dominated flow was also better constrained, using inputs from a reservoir simulator. The new 2-segment DCA method is applied to real field data from the Eagle Ford Formation. Among the major insights of our analyses are: (1) fracture down-spacing does not increase the long-term EUR, and (2) fracture down-spacing of real wells does not result in the rate increases predicted by either the flow-cell model based 2-segment DCA (or its matching reservoir simulations) with the assumed perfect fractures in the down-spaced well models. Our conclusion is that real wells with down-spaced fracture clusters, involving up to 5000 perforations, are unlikely to develop successful hydraulic fractures from each cluster. The fracture treatment quality factor (TQF) or failure rate (1-TQF) can be estimated by comparing the actual well performance with the well forecast based on the ideal well model (albeit flow-cell model or reservoir model, both history-matched on the type curve). Full article