Multiple In-Situ Stress Measurements in Carbonate Reservoirs for CO2 Injection Capability Assessment and Far-Field Strain Calibrations

The scope of this work is to measure downhole fracture-initiation pressures in multiple carbonate reservoirs located onshore about 50 km from Abu Dhabi city. The objective of characterizing formation breakdown across several reservoirs is to quantify the maximum gas and CO2 injection capacity on each reservoir layer for pressure maintenance and enhance oil recovery operations. This study also acquires pore pressure and fracture closure pressure measurements for calibrating the geomechanical in-situ stress model and far-field lateral strain boundary conditions. Several single-probe pressure drawdown and straddle packer microfrac injection tests provide accurate downhole measurements of reservoir pore pressure, fracture initiation, reopening and fracture closure pressures. These tests are achieved using a wireline or pipe-conveyed straddle packer logging tool capable to isolate 3 feet of openhole formation in a vertical pilot hole across five Lower Cretaceous carbonate reservoirs zones. The fracture closure pressures are obtained from three decline methods during the pressure fall-off after fracture propagation injection cycle. The three methods are: (1) square-root of the shut-in time, (2) G-Function pressure derivative, and (3) Log-Log pressure derivative. The far-field strain values are estimated by multi-variable regression from the microfrac test data and the core-calibrated static elastic properties of the formations where the stress tests are done. The reservoir pressure across these carbonate formations are between 0.48 to 0.5 psi/ft with a value repeatability of 0.05 psi among build-up tests and 0.05 psi/min of pressure stability. The formation breakdown pressures are obtained between 0.97 and 1.12 psi/ft over 5,500 psi above hydrostatic pressure. The in-situ fracture closure measurements provide the magnitude of the minimum horizontal stress 0.74 - 0.83 psi/ft which is used to back-calculate the lateral strain values (0.15 and 0.72 mStrain) as far-field boundary condition for subsequent geomechanical modeling. These measurements provide critical subsurface information to accurately predict wellbore stability, hydraulic fracture containment and CO2 injection capacity for effective enhance oil recovery within these reservoirs. This in-situ stress wellbore data represents the first of its kind in the field allowing petroleum and reservoir engineers to optimize the subsurface injection plans for efficient field developing.

Characterization of the High-Pressure and High-Temperature Phase Diagram and Equation of State of Chromium

The high-pressure and high-temperature melting curve of chromium has been investigated both experimentally (in situ), using a laser-heated diamond-anvil cell technique coupled with synchrotron powder X-ray diffraction, and theoretically, using ab initio density-functional theory simulations. In the pressure–temperature range covered experimentally (up to 90 GPa and 4500 K, respectively) only the solid body-centred-cubic and liquid phases of chromium have been observed. Experiments and computer calculations give melting curves in agreement with each other, that can be described by a Simon–Glatzel equation Tm(P) = 2136K(1+P/25.9) 0.41. In addition, a quasi-hydrostatic equation of state at ambient temperature has been experimentally characterized up to 131 GPa and compared with the present simulations. Both methods give very similar third-order Birch-Murnaghan equations of state with a bulk modulus of 182-185 GPa and its pressure derivative of 4.74-5.15. According to the present calculations, the obtained melting curve and equation of state are valid at least up to 815 GPa, being the melting temperature at this pressure 9310 K. Finally, from the obtained results, it was possible to determine a thermal equation of state of chromium valid up to 65 GPa and 2100 K.

Shut-in Stabilization Time Optimization for Better Reservoir Pressure Monitoring Harnessing Neural Network Modeling

Stabilization time is an essential key for pressure measurement accuracy. Obtaining representative pressure points in build-up tests for pressure-sensitive reservoirs is driven by optimizing stabilization time. An artificial intelligence technique was used in the study for testing pressure-sensitive reservoirs using measuring gauges. The stabilization time function of reservoir characteristics is generally calculated using the diffusivity equation where rock and fluid properties are honored. The artificial neural network (ANN) technique will be used to predict the stabilization time and optimize it using readily available and known inputs or parameters. The values obtained from the formula known as the diffusion formula and the ANN technique are then compared against the actual values measured from pressure gauges in the reservoirs. The optimization of the number of datasets required to be fed to the network to allow for coverage over the whole range is essential as opposed to the clustering of the datasets. A total of about 3000 pressure derivative samples from the wells were used in the testing, training, and validation of the ANN. The datasets are optimized by dividing them into three fractional parts, and the number optimized through monitoring the ANN performance. The optimization of the stabilization time is essential and leads to the improvement of the ANN learning process. The sensitivity analysis proves that the use of the formula and ANN technique, compared to actual datasets, is better since, in the formula and ANN technique, the time was optimized with an average absolute relative error of 3.67%. The results are near the same, especially when the ANN technique undergoes testing using known and easily available parameters. Time optimization is essential since discreet points or datasets in the ANN technique and formula would not work, allowing ANN to work in situations of optimization. The study was expected to provide additional data and information, considering that stabilization time is essential in obtaining the pressure map representation. ANN is a superior technique and, through its superiority, allows for proper optimization of time as a parameter. Thus it can predict reservoir log data almost accurately. The method used in the study shows the importance of optimizing pressure stabilization time through reduction. The study results can, therefore, be applied in reservoir testing to achieve optimal results.

Deep Similarity Learning for Well Test Model Identification

Over the years, well test analysis or pressure transient analysis (PTA) methods have progressed from straight lines via type curve analysis to pressure derivatives and deconvolution methods. Today, analysis of the log-log (pressure and its derivative) response is the most used method for PTA. Although these methods are widely available through commercial software, they are not fully automated, and human interaction is needed for their application. Furthermore, PTA is described as an inverse problem, whose solution in general is non-unique, and several models (well, reservoir and boundary) can be found applicable to similar pressure-derivative response. This tends to always bring about confusion in choosing the correct model using the conventional approach. This results in multiple iterations that are time consuming and requires constant human interaction. Our approach automates the process of PTA using a Siamese neural network (SNN) architecture comprised of Convolutional neural network (CNN) and Long Short-Term Memory (LSTM) layers. The SNN model is trained on simulated experimental data created using a design of experiments (DOE) approach involving most common 14 interpretation scenarios across well, reservoir, and boundary model types. Across each model type, parameters such as permeability, horizontal well length, skin factor, and distance to the boundary were sampled to compute 560 different pressure derivative responses. SNN is trained using a self-supervised training strategy where the positive and negative pairs are generated from the training data. We use transformations such as compression and expansion to generate positive pairs and negative pairs for the well test model responses. For a given well test model response, similarity scores are computed against the candidates in each model class, and the best match from each class is identified. These matches are then ranked according to the similarity scores to identify optimal candidates. Experimental analysis indicated that the true model class frequently appeared among the top ranked classes. The model achieves an accuracy of 93% for the top one model recommendations when tested on 70 samples from the 14 interpretation scenarios. Prior information on the top ranked probable well test models, significantly reduces the manual effort involved in the analysis. This machine learning (ML) approach can be integrated with any PTA software or function as a standalone application in the interpreter's system. Current work using SNN with LSTM layers can be used to speed up the process of detecting the pressure derivative response explained by a certain combination of well, reservoir and boundary models and produce models with less user interaction. This methodology will facilitate the interpretation engineer in making the model recognition faster for detailed integration with additional information from sources such as geophysics, geology, petrophysics, drilling, and production logging.

Lattice Dynamical Study and Elastic Property of Europium Telluride (Eute) Crystal

In the present work authors are reporting complete lattice dynamical properties of Europium telluride (EuTe). The present model works on three body rigid ion model & three body rigid shell model (TRIM & TRSM). The short-range overlap repulsion is operative up to the second neighboring ions. An excellent agreement has been obtained between theory and experiment for their all-phonon properties of (EuTe) like phonon dispersion curves, Debye temperature variations, two-phonon IR/Raman spectra, third-fourth order lattice constant, pressure derivative and anharmonic elastic properties.

Delamination in Tibet: Deriving constraints from the density of eclogite

Tibet, which is characterized by collisional orogens, has undergone the process of delamination or convective removal. The lower crust and mantle lithosphere appear to have been removed through delamination during orogenic development. Numerical and analog experiments demonstrate that the metamorphic eclogitized oceanic subduction slab or lower crust may promote gravitational instability due to its increased density. The eclogitized oceanic subduction slab or crustal root is believed to be denser than the underlying mantle and tends to sink. However, the density of eclogite under high-pressure and high-temperature conditions and density differences from the surrounding mantle is not preciously constrained. Here, we offer new insights into the derivation of eclogite density with a single experiment to constrain delamination in Tibet. Using in situ synchrotron X-ray diffraction combined with diamond anvil cell, experiments focused on minerals (garnet, omphacite, and epidote) of eclogite are conducted under simultaneous high-pressure and high-temperature conditions, which avoids systematic errors. Fitting the pressure-temperature-volume data with the third-order Birch-Murnaghan equation of state, the thermal equation of state (EoS) parameters, including the bulk modulus (KT0), its pressure derivative (KT0′), the temperature derivative ((KT/T)P), and the thermal expansion coefficient (α0), are derived. The densities of rock-forming minerals and eclogite are modeled along with the geotherms of two types of delamination. The delamination processes of subduction slab breakoff and the removal of the eclogitized lower crust in Tibet are discussed. The Tibetan eclogite which containing 40–60 vol. % garnet and 37–64 % degrees of eclogitization can promote the delamination of slab break-off in Tibet. Our results indicate that eclogite is a major controlling factor in the initiation of delamination. A high abundance of garnet, a high Fe-content, and a high degree of eclogitization are more conducive to instigating the delamination.

Dual-phase flow in two-layer porous media: a radial composite Laplace domain approximation

The main purpose of this work is to present an interpretation method for injectivity test in a two-layer reservoir that can be extended to a multilayer approach, based on new analytical solutions to the well pressure response. The developed formulation uses a radially composite reservoir approach and considers that the water front propagation may be approximated by a piston-like flow displacement. The reservoir is assumed to be laterally infinite and properties such as permeability and porosity may be different in each layer. The solutions were developed in the Laplace domain and then inverted to real domain using the Stehfest Algorithm. The proposed formulation was then validated by comparison with a numerical flow simulator. Results showed a good agreement between the numerical simulator and the analytical model. Also, a sensitivity study was done by comparing the results of different scenarios varying oil viscosities and injection flow rate to assess how these properties affect the pressure and pressure derivative profiles.

A Well-Testing Approach for Diagnostics of Fracture Complexity with Well Interference

Owing to well interference, the fracture geometries of child wells are sometimes more complex than initially expected. Some approaches or methodologies have been developed to evaluate the complex fracture geometries, however, the fracture geometries are still poorly understood. This work uses the boundary element method to propose a new well testing approach to determine the complex fracture geometries of child wells with inter-well interference. It is found that the well interferences from Parent well on Child well mainly happen on the late stage, which can be physically expected. The flow regimes of Child well can be divided into: wellbore storage & skin effects, fracture bilinear flow, "fluid supply", formation linear flow, pseudo-boundary dominated flow, "well interferences", pseudo-radial flow, and boundary-dominated flow. The stage of "well interferences" occurs later with the increase in well spacing. The boundary-dominated flow is affected by the reservoir size and shape. When the reservoir size is fixed, the pressure curves in final stage of different-shape reservoirs overlap, which provides a tool to diagnose the reservoir size. While the reservoir size are variable, the occurrences of boundary-dominated flow are quite different. The smaller the reservoir, the quicker the boundary-dominated flow, which is in line with actual situations. It is also found that Parent-well rate mainly affects the flow regimes after pseudo-boundary dominated flow. That to say, after that flow regime, the performance of Child well is interfered by Parent well. The impact is more obvious with the increase in Parent-well rate, especially in pseudo-radial flow. In that flow stage, the horizontal value of pressure derivative also satisfies 0.5(qchd,D+qpar,D). In addition, when the Parent-well rate is negative, namely an injection well, the pressure derivatives of Child well decrease sharply, which means that the pressure depletion of Child well decreases and it is helpful to production of Child well. When the Parent-well rate is a positive and large value, the pressure depletion of Child well increase sharply and its production is harmed by the Parent well. Thus, there should be an optimized production strategies between Parent well and Child well. Finally, the model application on diagnostics of fracture complexity of an actual well is performed. This study provides a new way to identify the fracture geometries of child wells in unconventional plays.

Rate/Pressure Transient Analysis of a Variable Bottom Hole Pressure Multi-Well Horizontal Pad with Well Interference

Multi-well horizontal pads are common in unconventional reservoirs. With addition of infill wells and hydraulic fracturing, interference between multiple multi-fractured-horizontal wells (MFHWs) has become a serious issue. Current RTA workflows assume a single MFHW in the unconventional formation. This paper presents a new multi-MFHW solution and related analysis methodology to analyze targeted well rate performance in a multi-MFHW system. In this work, a semi-analytical equation describing multi-well pad in the Laplace domain with well interference is proposed. The proposed semi-analytical model can simulate the rate performance of a multi-well horizontal pad with variable BHP for a targeted well in the pad and different initial production durations for the offset well. From the constant BHP condition and Laplace transforms, we obtained multi-MFHW solutions for transient flow. We used superposition of various constant BHP solutions to study interference among various fractures and MFHWs. The variable BHP of the targeted well is achieved by a variable dimensionless BHP function in the Laplace domain without any convolution or deconvolution calculations. A systematic validation for the proposed method is conducted using a commercial numerical simulator for cases of different initial production times for offset MFHWs, multi-MFHWs with variable BHP. Through the total material balance of the multi-MFHW system, we can analyze a target well in the pad with this multi-MFHW analysis. Interference by offset wells often appears after pseudo-radial flow in the target well's hydraulic fracture. It causes the pressure derivative curve during elliptical and infinite-acting radial flow (IARF) to rise, as does the RNP derivative. The inverse semi-log derivative has the opposite trend. Well interference also makes the rate/pressure drop functions to deviate from initial straight lines in later stages. Sensitivity analysis of well spacing shows that "transition flow" will change from elliptical to formation linear flow between wells as well spacing increases and it can show the transitional flow characteristics in more common cases.

Pressure Transient Analysis of Wells in the Fault-Karst Carbonate Reservoirs with Vertical Beads-on-String Structure: Case Studies in Shunbei Oilfield, Tarim Basin of Northwestern China

The newly discovered the fault-karst carbonate reservoirs in Tarim Basin are formed by large-scale tectonic fault activities and multiple-stage karstification. The ground outcrop, seismic reflection and well logging show that the large caves, vugs, tectonic fractures and matrix coexist in the reservoirs. The fractures interconnecting with caves in series to form vertical beads-on-string structure is the most common pattern. It is found that conventional models are difficult to match the recorded pressure data. To fill this gap, this work summarizes three kinds of patterns for this structure and presents three novel models to estimate formation properties. The physical models of multi-fracture-region multi-cave-region series connection are established by simplifying vertical beads-on-string structure. The corresponding mathematical models are developed, in which the flow in fracture regions obey Darcy's law, while the flow in cave regions obeys free flow. Importantly, the gravity is considered due to the flow along vertical direction. Then typical flow regimes are analyzed and sensitivity analysis is conducted. Our work shows that pressure-derivative curves show similar ‘concave’ characteristic for the cave storage regime and vug/matrix interporosity flow regime. The difference is that the pressure derivative for cave storage regime is unit slope, while this slope is not equal to unity for vug/matrix interporosity flow regime. Therefore, large cave and vug/matrix medium can be distinguished by slope of pressure derivative. More than that, the typical characteristic of vertical beads-on-string structure on type curve is that the cave storage regimes and linear flow regimes alternately appear. This characteristic helps the engineers identify vertical beads-on-string structure. A novel finding is that gravity effect could lead to unit-slope pressure and pressure derivative at late times, which is traditional recognized as the presence of a closed boundary when it may not be the case. Lastly, this methodology is applied to two cases from Shunbei Oilfield in which it is difficult to obtain good fitting quality and interpretation results using traditional methods. Besides conventional properties, the proposed methodology allows us to estimate other properties (e.g., cave height, cave radius), which are not readily obtained from conventional methods.