The present study provides a comprehensive set of new analytical expressions to help understand and quantify well interference due to competition for flow space between the hydraulic fractures of parent and child wells. Determination of the optimum fracture spacing is a key factor to improve the economic performance of unconventional oil and gas resources developed with multi-well pads. Analytical and numerical model results are combined in our study to identify, analyze, and visualize the streamline patterns near hydraulic fractures, using physical parameters that control the flow process, such as matrix permeability, hydraulic fracture dimensions and assuming infinite fracture conductivity. The algorithms provided can quantify the effect of changes in fracture spacing on the production performance of both parent and child wells. All results are based on benchmarked analytical methods which allow for fast computation, making use of Excel-based spreadsheets and Matlab-coded scripts. Such practical tools can support petroleum engineers in the planning of field development operations. The theory is presented with examples of its practical application using field data from parent and child wells in the Eagle Ford shale (Brazos County, East Texas). Based on our improved understanding of the mechanism and intensity of production interference, the fracture spacing (this study) and inter-well spacing (companion study) of multifractured horizontal laterals can be optimized to effectively stimulate the reservoir volume to increase the overall recovery factor and improve the economic performance of unconventional oil and gas properties.
This study is based on the premise that most of the trapped hydrocarbons can be produced, if we substitute them with another ‘acrificial’ fluid that has amplified interactions with organic pore walls, such as CO2. For the presented study, a downhole shale sample is analyzed in the laboratory to predict gas storage properties such as pore-volume, pore compressibility, and gas adsorption capacity. Then a series of pressure pulse decay measurements are performed to delineate transport mechanisms and predict stress-sensitive permeability. These coefficients are obtained as the calibration parameters of a simulation-based optimization for injection and production. Simulation model considers compositional gas flow in a deformable porous media and includes a multi-continuum porosity, with organic and inorganic pores, and micro-fractures. The experimental and simulation results show that most of the injected CO2 is adsorbed in the organic matrix and are not produced back. This is because CO2 molecules have significantly larger adsorption capacity when compared to methane. The strong adsorption of CO2 improves the release of natural gas from kerogen pores. This indicates that the separation of produced CO2 will be a minimal cost. Transport in kerogen has significant pore wall effects, and includes large mass fluxes of the adsorbed molecules by the walls due to surface diffusion. In essence, the adsorbed CO2 molecules significantly influence transport of methane. The results also show core-plug permeability is stress-sensitive due to presence of micro-fractures. Forward simulation results using optimum parameters indicate that closure stress developing near the fractures could significantly control the volume of CO2 injected. This raises operational issues on when to start injecting, and how to inject CO2. Using a simulation study of a production well with single-fracture, we show that fracture closure stress develops rapidly and production rate becomes a slave of the fracture geo-mechanics, e.g., strength of the proppants and the level of proppant embedment.
Methane hydrate is formed in a sand pack that undergoes cooling-heating cycles over a range of temperature. Five cycles are designed so that hysteresis can be observed in the sand pack. Each cycle has a different melting temperature which leads to varying intensity of temperature relaxation effect on the hysteresis. Evidence of hysteresis is observed in three separate temperature readings of thermocouples. Formation of hydrates is dependent on the thermal cooling rate of the sand pack, and the melting temperature of the previous cycle. A temperature increase is observed in the whole system, and this increase is driven by temperature peaks indicating significant hydrate formation near the thermocouples. These peaks have important effects on the whole system. By comparing each cycle's temperature peaks, hysteresis is clearly observed at the temperature readings of the short thermocouple. The same hysteresis pattern follows for the location of the temperature peaks. When significant hydrate formation occurs in the sand pack, a steepening of the pressure decline is observed, indicating a rapid loss of free gas in the system. The pattern that is observed in the temperature peaks is also identified in the pressure profiles, thus linking the gas saturation to hydrate formation. The time derivative of pressure corroborates these findings. A new model is proposed for the prediction of secondary hydrate formation time as a function of the melting temperature the porous medium experienced.
The objective of this study is to visualize the drained rock volume (DRV) and pressure depletion in hydraulically and naturally fractured reservoirs, using a high-resolution simulator to plot streamlines and time-of-flight contours that outline the DRV, based on computationally efficient complex potentials. A recently developed expression based on fast, grid-less Complex Analysis Methods (CAM) is applied to model the flow through discrete natural fractures with variable hydraulic conductivity. The impact of natural fractures on the local development of DRV contours and streamline patterns is analyzed. A sensitivity analysis of various permeability contrasts between natural fractures and the matrix is included. The results show that the DRV near hydraulic fractures is significantly affected by the presence of nearby natural fractures. The DRV location shifts according to the orientations, permeability and the density of the natural fractures. Reservoirs with numerous natural fractures result in highly distorted DRV shapes as compared to reservoirs without any discernable natural fractures. Additionally, the DRV shift due to natural fractures may contribute to enhanced well-interference by flow channeling via the natural fractures, as well as the creation of undrained rock volumes between the natural fractures. Complementary pressure depletion plots for each case show how the local pressure field changes, in a heterogeneous reservoir, due to the presence of natural fractures. The results from this study offer insights on how natural fractures affect the DRV and pressure contour plots. This study uses a fast grid-less and meshless high-resolution flow simulation tool based on CAM to simulate the flow in heterogeneous naturally fractured porous media. The CAM tool provides a practical/efficient simulation platform, complementary to grid-based reservoir simulators.
The objective of this paper is to propose an alternative data analysis approach to working with microseismic data. Modern machine learning techniques, such as MWCA (Multiway Component Analysis) and TD (Tucker Decomposition) can give the capability to efficiently work with complex high-dimensional microseismic data structures. Using this method, it was possible to restore hidden information about the signal, compress the data, and get insights about fractures without using conventional time-consuming simulations. Therefore, it is an important addition to the hydraulic fracturing quality assessment. It is a cost-effective technique providing a greater degree of automation in comparison to conventional methods.
The approach was tested on synthetic data and relevant real microseismic data provided by a service company. The data was integrated in a 3rd-order tensor form where modes are: seismic events time, receiver locations, and event locations. The tensor was then decomposed into a core tensor and three factor matrices by means of a special form of TD called HOSVD (Higher-Order Singular Value Decomposition). HOSVD is a multidimensional decomposition used to extract low rank approximations of tensors. The MWCA technique was utilized to impose constraints on TD. HOSVD showed potential as a tool for a rapid fractures analysis by observing decomposed tensor structure. Additionally, the technique helped reduce the original model by 73% (supercompression).
The proposed workflow is general and highly applicable to various plays. Since the applications of MWCA and TD are still emerging, future enhancements to this methodology are expected. In turn, this will reveal further insights from microseismic data, making it paramount to optimal fracturing and improved field management.
Rate transient analysis using log-log plots of rate-normalized pressure (RNP) and its derivative (RNP') versus material balance time have proven helpful in providing estimates of shale matrix permeability and SRV drainage volumes in multiple transverse fracture wells (MTFW's) (
We have constructed an analytical model of MTFW's that accurately predicts individual fracture flow performance for both constant and variable rate and constant bottom hole pressure inner boundary conditions. Using this model, we can accurately compute the pressure disturbance and rate change seen at the whole well and for individual fractures to quantify the degree of interference between fractures for any number of parallel, equally-spaced, and equally-sized fractures. This model has been validated by simulation using a commercial simulator. With both this analytical model and a series of numerical simulations, we investigated the fundamental mechanisms of flow in MTFW's and how the estimation of telf may be improved.
Previous authors have represented the progression of flow regimes in MTFW's as a linear flow period that transitions to a pseudo steady state (or apparently boundary-dominated) flow regime. We show that the same flow response is exhibited by a fully-infinite linear system, calling into question the nature of the "stimulated reservoir volume" (SRV) as a bounded reservoir system. In addition, we show telf can be detected and interpreted as the beginning of the onset of this fracture interference using the "limit of detectability" concept.
A high rate of penetration (ROP) is considered one of the most sought-after targets when drilling a well. While physics-based models determine the importance of drilling parameters, they fail to capture the extent or degree of influence of the interplay of the different dynamic drilling features. Parameters such as WOB, RPM, and flowrate, MSE, bit run distance, gamma ray for each rock formation in the Volve field in the North Sea were examined ensuring an adequate ROP while controlling the tool face orientation is quite challenging. Nevertheless, its helps follow the planned well trajectory and eliminates excessive doglegs that lead to wellbore deviations. Five different Machine Learning algorithms were preliminary implemented to optimize ROP and create a less tortuous borehole. The collected data was cleaned and preprocessed and used to structure and train Random Forest, Support Vector Regression, Ridge Regression, LASSO, and Gradient Boosting, XG boost among others and the appropriate hyperparameters were selected. A successful model was chosen based on maximized ROP, minimized deviation from planned trajectory, and lower CPF. An MAEP of 15% was achieved using GBM boost followed AdaBoost. The algorithms have demonstrated competence on the historical dataset, accordingly it will be further tested on blind data to serve as a real-time system for drilling optimization to enable a fully automated system.
The objective of this work is to develop a methodology to estimate the fraction of Reserves assigned to each Reserves category (1P, 2P, and 3P) of the PRMS resources classification matrix using a cumulative distribution function (CDF). Previous published work has often used Swanson's Mean (SM) as the basis for allocating Reserves to individual categories, but we found that this method, which relates the Reserves categories through a CDF for a normal distribution, is an inaccurate means to determine the relationship of the Reserves categories with asymmetric distributions, and our work identified a better method, Gaussian Quadrature (GQ).
Production data are lognormally distributed, regardless of basin type, and thus are not compatible with the SM concept. The GQ algorithm provides a methodology to estimate the fraction of Reserves that lie within the 1P, 2P, and 3P categories — known as their
We selected 38 wells from a Permian Basin dataset available to us, and we performed probabilistic decline curve analysis (DCA) using the Arps Hyperbolic model and Monte Carlo simulation (MCS) to obtain a probability distribution of the 1P, 2P, and 3P volumes. We considered this information to be our "truth case," to which we compared relative weights of different Reserves categories from the GQ and SM methodologies. We also performed probabilistic rate transient analysis (RTA) using the IHS
The probabilistic DCA results indicated that the SM method is an
Based on our results, we conclude that the GQ method is accurate and can be used to approximate the relationship between the relative weights of resources in PRMS categories. This relationship will aid entities in reporting Reserves of different categories to regulatory agencies because it can be recreated for any field, play, or region. These distributions of Reserves and Resources Other than Reserves (ROTR) are important for planning and for resource inventorying. The GQ method provides a measure of confidence in our prediction of the Reserves weights because of the relatively smaller percentage differences between the probabilistic DCA, RTA, and GQ weights than those implied by the SM method. For reference, our proposed methodology can be implemented in both conventional and unconventional reservoirs.
In this study, we have extended and applied the diffuse source upscaling methodology to sandstone and carbonate pore network models in order to evaluate their effective transmissibility and permeability. The proposed method allows us to find transmissibility values for sub-volumes of the pore network during the transition from transient to pseudo steady state flow. The pore network models utilize a lattice grid construction, consisting of nodes and bonds that connect the nodes. The Eikonal equation is solved on the lattice using Dijkstra's method to obtain the diffusive time of flight, which is then used to model the transition from transient to pseudo steady state flow. The solution uses the concept of a transient drainage volume, which increases with time as pressure propagates into the nodes of the pore network. The diffuse source upscaling approach allows us to calculate the transmissibility of the drainage volume as it increases with time. The calculated results can be compared to the analytical results, where the sample is assumed to be internally homogeneous. A synthetic model was created to illustrate how the calculated lattice model and the analytic reference results compare for a homogeneous model. The comparison of the carbonate analytical and calculated results showed that there exists a high degree of internal heterogeneity while the more homogeneous sandstone model showed a close agreement with the synthetic model. For both samples, the late time pseudo steady state permeability showed a good correspondence with other permeability evaluations. The diffuse source method has more directional information available than the steady state method. Hence, the new method of analysis can be viewed as an extension of pseudo steady state concepts of permeability to transient flow, with increased spatial resolution corresponding to the transient drainage volume. Instead of obtaining only the steady state transmissibility from a pore network model, the diffuse source approach provides us with the ability to better characterize the internal heterogeneity of a model and to explain the wide range of permeability values obtained by other approaches.
Numerical modeling of unconventional reservoirs, using commercial simulator, requires the construction of SRV that incorporates explicit geometries of primary and secondary fractures. Most of the time, during two phase flow, these models exhibit constant GOR. The method outlined in this paper eliminates the limitations of constant GOR being the only outcome and shows all other possible GOR responses that have a direct bearing on long term deliverability.
To overcome the drawback of numerical simulation, we make use of a dual porosity semi-analytical model. Using the concept of dimensional productivity index and its derivative, two-phase solutions are generated with the help of sandface pseudopressure. This model helps define all GOR variations of a ‘complete’ dual porosity system, wherein the fracture domain is assumed to contain part natural fracture and part induced hydraulic fracture. Apart from the impact of fluid variation, the other contributing factor in GOR variation is fracture density, which is addressed with the help of idealized fracture orientations such as the slab (planar 1D primary fracture only), the cylinder (non-planar 2D fracture with planar secondary fracture) and the sphere (non-planar 3D fracture with non-planar secondary fracture). These matrix shapes encompass all possible range of fracture densities (both natural and induced) that impact long-term performance.
The results of this method are shown for different fluids and for different idealized fracture orientations. It demonstrates that if the volume of fractures, in a given volume of SRV, is kept constant then the fluid type and fracture orientation are directly responsible for rate of pressure depletion that gives rise to these variations in GOR. It brings out the effect of different fracture orientations on the same fluid type and the effect of the same orientation on different fluid types. Additionally, with the help of published literature data, it is also demonstrated how GOR variation complements the conventional rate transient analysis for such unconventional reservoirs.
With the use of this method we can evaluate horizontal fractured well performance for different types of fluids and different fracture orientations in liquids-rich shale reservoirs. This GOR variation is important sensitivity parameter conveying the information about natural fractures present in the reservoir, information which is hard to get by from any other source, thus bringing out the significance of this method.