Real-time drilling optimization is a topic of significant interest because of its economic value, and its importance increases particularly during periods of low oil prices. This paper evaluates different optimization strategies and algorithms for real-time optimization of an objective function (function to be optimized) specific to drilling. The objective function optimized here is derived from a data-driven (or machine-learning) model with an unknown functional form. A data-driven model has been used to calculate the objective function [rate of penetration (ROP)] because it has been shown to be more efficient in ROP prediction relative to deterministic models (Hegde and Gray 2017). The data-driven ROP model is built using machine-learning algorithms; measured drilling parameters [weight on bit (WOB), revolutions per minute (rev/min), strength of rock, and flow rate] are used as inputs to predict the ROP.
Real-time drilling optimization that is data-driven is challenging because of run-time constraints. This is perceived as a handicap for data-driven models because their functional form is unknown, making them more difficult to optimize. This paper evaluates algorithms depending on their ability to best maximize the objective (ROP) and their time effectiveness. Two simple yet robust algorithms, the eyeball method and the random-search method, are presented as plausible solutions to this problem. These methods are then compared with popular metaheuristic algorithms, evaluating the tradeoff between improvement in the objective (search for a global optimal) and the computational time of run.
Using results from the simulations conducted in this paper, we concluded that data-driven models can be used for real-time drilling despite their computational constraints by choosing the right optimization algorithm. The best tradeoff in terms of ROP increase as well as computational efficiency evaluated in this paper is the simplex algorithm. The ROP was improved by 30% on average with a variance of 2.5% in the test set over 14 formations that were tested.
Downhole temperature data obtained by either temperature logging or fiber-optic cables have been used to evaluate stimulation treatments and post-stimulation performance of horizontal wells with multiple fractures. Field cases qualitatively show capabilities of detecting creation of transverse fractures, poor zonal isolation, and inflow locations, although downhole temperature behavior in those wells is not fully understood from the theoretical modeling perspective.
In this study, we present comprehensive numerical flow and thermal models for a horizontal well with multiple fractures. The well experiences single-phase water flow during injection and shut-in, and gas/water two-phase flow during production. These models are formulated for reservoir and wellbore domains with consideration of their coupling. The reservoir models are formulated in 3D space using mass conservation of each component and thermal energy conservation with Darcy’s law in transient conditions. The wellbore models are also transient, and formulated for 1D space using mass conservation of each component, conservation of combined-phase momentum, and total energy conservation. The wellbore- and sandface-temperature profiles are obtained as solutions of these models. These models enable us to simulate field operations in multistage-fracturing treatment; injection and shut-in occur alternately for each stage from toe to heel with zonal isolation. After the stimulation treatments, these models are used to simulate temperature behavior during production in gas/water two-phase flow.
We show an example of a single fracture in which the developed model simulates temperature behavior during injection, shut-in, and production to show capabilities of the developed model. This study shows that injected fluid makes the fluid temperature in the fracture lower than the geothermal temperature even after 1 month of shut-in. This affects the temperature interpretation during production because the initial temperature is different from the geothermal temperature assumed as the initial temperature by most studies published previously. A synthetic case with five fractures demonstrates capabilities of detection of created-fracture locations from the shut-in temperature profile. In addition, we apply the model to a field case of distributed-temperature-sensor (DTS) temperature profiles during warmback after multistage hydraulic fracturing, and 30 days after the start of the production in this well. The good match obtained between this model and the DTS data from this well indicates how this modeling approach can be used to estimate the production from individual perforation clusters. The case studies illustrate qualitative interpretations in situations occurring in fields, such as warm-up behavior with multiple clusters during the shut-in period.
This paper provides insights from the theoretical modeling perspective for downhole temperature interpretation qualitatively performed at the current time. It also discusses the validity of the assumptions made in previous studies and precautions relevant to those assumptions.
In this study, we use a custom-designed visual cell to investigate nonequilibrium carbon dioxide (CO2)/oil interactions under high-pressure/high-temperature conditions. We visualize the CO2/oil interface and measure the visual-cell pressure over time. We perform five sets of visualization tests. The first three tests aim at investigating interactions of gaseous (g), liquid (l), and supercritical (sc) CO2 with a Montney (MTN) oil sample. In the fourth test, to visualize the interactions in the bulk oil phase, we replace the opaque MTN oil with a translucent Duvernay (DUV) light oil (LO). Finally, we conduct an N2(sc)/oil test to compare the results with those of CO2(sc)/oil test. We also compare the results of nonequilibrium CO2/oil interactions with those obtained from conventional pressure/volume/temperature (PVT) tests.
Results of the first three tests show that oil immediately expands upon injection of CO2 into the visual cell. CO2(sc) leads to the maximum oil expansion followed by CO2(l) and CO2(g). Furthermore, the rate of oil expansion in the CO2(sc)/oil test is higher than that in CO2(l)/oil and CO2(g)/oil tests. We also observe extracting and condensing flows at the CO2(l)/oil and CO2(sc)/oil interfaces. Moreover, we observe density-driven fingers inside the LO phase because of the local increase in the density of LO. The results of PVT tests show that the density of the CO2/oil mixture is higher than that of the CO2-free oil, explaining the density-driven natural convection during CO2(sc) injection into the visual cell. We do not observe either extracting/condensing flows or density-driven mixing for the N2(sc)/oil test, explaining the low expansion of oil in this test. The results suggest that the combination of density-driven natural convection and extracting/condensing flows enhances CO2(sc) dissolution into the oil phase, leading to fast oil expansion after CO2(sc) injection into the visual cell.
Yang, Xiangtong (PetroChina) | Pan, Yuanwei (Schlumberger) | Fan, Wentong (PetroChina) | Huang, Yongjie (Schlumberger) | Zhang, Yang (PetroChina) | Wang, Lizhi (Schlumberger) | Wang, Lipeng (Schlumberger) | Teng, Qi (PetroChina) | Qiu, Kaibin (Schlumberger) | Zhao, Meng (Schlumberger) | Shan, Feng (PetroChina)
The Keshen Reservoir is a naturally fractured, deep, tight sandstone gas reservoir under high tectonic stress. Because the reservoir matrix is very tight, the natural-fracture system is the main pathway for gas production. Meanwhile, stimulation is still required for most production wells to provide production rates that sufficiently compensate for the high cost of drilling and completing wells to access this deep reservoir. Large depletion (and related stress change) was expected during the course of the production of the field. The dynamic response of the reservoir and related risks, such as reduction of fracture conductivity, fault reactivation, and casing failure, would compromise the long-term productivity of the reservoir.
To quantify the dynamic response of the reservoir and related risks, a 4D reservoir/geomechanics simulation was conducted for Keshen Reservoir by following an integrated work flow. The work started from systematic laboratory fracture-conductivity tests performed with fractured cores to measure conductivity vs. confining stress for both natural fractures and hydraulic fractures (with proppant placed in the fractures of the core samples). Natural-fracture modeling was conducted to generate a discrete-fracture network (DFN) to delineate spatial distribution of the natural-fracture system. In addition, hydraulic-fracture modeling was conducted to delineate the geometry of the hydraulic-fracture system for the stimulated wells. Then, a 3D geomechanical model was constructed by integrating geological, petrophysical, and geomechanical data, and both the DFN and hydraulic-fracture system were incorporated into the 3D geomechanical model. A 4D reservoir/geomechanics simulation was conducted through coupling with a reservoir simulator to predict variations of stress and strain of rock matrix as well as natural fractures and hydraulic fractures during field production. At each study-well location, a near-wellbore model was extracted from the full-field model, and casing and cement were installed to evaluate well integrity during production.
The 4D reservoir/geomechanics simulation revealed that there would be a large reduction of conductivity for both natural fractures and hydraulic fractures, and some fractures with certain dip/dip azimuth will be reactivated during the course of field production. The induced-stress change will also compromise well integrity for those poorly cemented wellbores. The field-development plan must consider all these risks to ensure sustainable long-term production.
The paper presents a 4D coupled geomechanics/reservoir-simulation study applied to a high-pressure/high-temperature (HP/HT) naturally fractured reservoir, which has rarely been published previously. The study adapted several new techniques to quantify the mechanical response of both natural fractures and hydraulic fractures, such as using laboratory tests to measure stress sensitivity of natural fractures, integrating DFN and hydraulic-fracture systems into 4D geomechanics simulation, and evaluating well integrity on both the reservoir scale and the near-wellbore scale.
Hydraulic fractures act as conduits connecting a wellbore to nanodarcy-permeability unconventional reservoirs. Proppants are responsible for enhancing the fracture conductivity, and they help in maintaining high production rates. This study is focused on the measurement of long-term conductivity of proppant packs at simulated reservoir-temperature and pressure conditions. Various conductivity-impairment mechanisms such as proppant crushing, fines migration, embedment, and diagenesis are investigated.
Testing was performed with a conductivity cell that allows simultaneous measurement of fracture compaction and permeability. The proppant-pack performance during compression between metal and shale platens was compared. The proppant-filled fracture (concentration of 0.75-3 lbm/ft2) is subjected to axial load (5,000 psi) to simulate closure stress. Brine (3% NaCl + 0.5% KCl) is flowed through the pack at a constant rate (3 cm3/min) at 250°F during an extended duration of time (10-60 days). In this study, Ottawa sand proppant was used between platen facies fabricated from Vaca Muerta and Eagle Ford shales.
Testing between metal platens indicated that the reduction in permeability with 20/40-mesh Ottawa sand (˜30% during 12 days) was less than that of 60/100-mesh Ottawa sand, which suffered a 99% reduction in only 4 days.
Measurements with 20/40-mesh Ottawa sand between shale platens were conducted at 1.5 lbm/ft2. During a duration of 10 days, the Eagle Ford platens proppant pack exhibits a greater reduction in permeability, in comparison with Vaca Muerta platens. The normalized compaction for Eagle Ford shale platens is 20% more than Vaca Muerta platens because of greater proppant embedment. Particle-size analysis and scanning-electron-microscopy (SEM) images verify proppant crushing, fines migration, and embedment as dominant damage mechanisms. These factors are observed to depend on the testing of shales. The results suggest a substantial degradation of permeability during the initial 5 days of testing, after which the permeability appears to stabilize. Crushed proppant and dislodged shale-surface particles contribute to the fines generated; a greater concentration of fines is observed downstream.
In a separate study between Vaca Muerta platens, under similar closure stress and temperature conditions at 2-lbm/ft2 proppant concentration, the permeability reduced by almost three orders of magnitude during a duration of 60 days. It was also observed that growth of diagenetic smectite is accelerated by making the fluid more basic (pH of 10).
The authors of SPE-186093-PA [SPE J. 22 (5): 1487–1505. https://doi.org/10.2118/186093-PA] have submitted a correction to Eq. 11 on page 1493.
Zhang, Feifei (Yangtze University) | Kang, Yongfeng (Halliburton) | Wang, Zhaoyang (Halliburton) | Miska, Stefan (University of Tulsa) | Yu, Mengjiao (University of Tulsa) | Zamanipour, Zahra (University of Tulsa)
This paper identifies wellbore-stability concerns caused by transient swab/surge pressures during deepwater-drilling tripping and reaming operations. Wellbore-stability analysis that couples transient swab/surge wellbore-pressure oscillations and in-situ-stress field oscillations in the near-wellbore (NWB) zone in deepwater drilling is presented.
A transient swab/surge model is developed by considering drillstring components, wellbore structure, formation elasticity, pipe elasticity, fluid compressibility, fluid rheology, and the flow between wellbore and formation. Real-time pressure oscillations during tripping/reaming are obtained. On the basis of geomechanical principles, in-situ stress around the wellbore is calculated by coupling transient wellbore pressure with swab/surge pressure, pore pressure, and original formation-stress status to perform wellbore-stability analysis.
By applying the breakout failure and wellbore-fracture failure in the analysis, a work flow is proposed to obtain the safe-operating window for tripping and reaming processes. On the basis of this study, it is determined that the safe drilling-operation window for wellbore stability consists of more than just fluid density. The oscillation magnitude of transient wellbore pressure can be larger than the frictional pressure loss during the normal-circulation process. With the effect of swab/surge pressure, the safe-operating window can become narrower than expected. The induced pore pressure decreases monotonically as the radial distance increases, and it is limited only to the NWB region and dissipates within one to two hole diameters away from the wellbore.
This study provides insight into the integration of wellbore-stability analysis and transient swab/surge-pressure analysis, which is discussed rarely in the literature. It indicates that tripping-induced transient-stress and pore-pressure changes can place important impacts on the effective-stress clouds for the NWB region, which affect the wellbore-stability status significantly.
This paper investigates the effects of mudcake and formation multiporosity/multipermeability on the evolution of a safe-drilling mudweight window. The analytical poroelastic solutions for an inclined wellbore drilled through a multiporosity/multipermeability porous medium were derived, taking into account the mudcake buildup on the wellbore wall. A multiporosity/multipermeability porous medium consists of an overlapping of N distinct porous-continuum networks, each of which has its own geomechanical and petrophysical properties. Wellbore collapse and fracturing are investigated by studying a dual-porosity naturally fractured weak sandstone. The first porosity is matrix porosity, and the second porosity is the fractures. In addition, a triple-porosity source shale with multiple scales of natural fractures was modeled. The first porosity corresponds to the shale matrix one, and two scales of fracture distribution account for the other two sets of porosity.
The Drucker and Prager (1952) criterion is applied to analyze wellbore collapse and shear failure, whereas the tensile strengths of both formations are considered, conservatively, as negligible. The safe-drilling mud-weight window is calculated to illustrate the time-dependent effects of formation N-porosity/N-permeability nature and the wellbore-wall boundary conditions (with/without mudcake). On the one hand, natural fractures narrow the safe-drilling mud-weight window by degrading rock strength and facilitating hydraulic-pressure invasion. On the other hand, the mudcake leads to a wider safe-drilling mud-weight window by generating compressive effective radial stress on the wellbore wall and impeding hydraulic-pressure invasion. Mudcake thickness and mudcake permeability are found to have significant effects. The drilling-mud design to build a mudcake on the wellbore wall is essential when drilling through difficult naturally fractured formations.
Liu, Qing-You (Southwest Petroleum University and State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation) | Tao, Lei (Southwest Petroleum University and State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation) | Zhu, Hai-Yan (Southwest Petroleum University and State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation) | Lei, Zheng-Dong (PetroChina) | Jiang, Shu (China University of Petroleum (East China) and University of Utah) | McLennan, John D. (University of Utah)
Waterless fracturing for shale-gas exploitation using supercritical carbon dioxide (scCO2) is both effective and environmentally friendly, and has become an extensive research topic. Previous researchers have focused on the chemical and physical properties and microstructure of sandstone, carbonate, and shale caprock, rather than on the properties of shale-gas formations. The macroscale mechanical properties and microscale fracture characteristics of Wufeng Shale exposed to scCO2 (at greater than 31.8°C and 7.29 MPa) are still not well-understood. To study the macroscale and microscale changes of shale subjected to scCO2, we obtained Chinese Wufeng Shale crops (Upper Ordovician Formation) from Yibin, Sichuan Basin, China. The shale samples were divided into two groups. The first group was exposed to scCO2, and the second group was exposed to nitrogen (N2). Scanning-electron-microscope (SEM) and X-ray-diffraction (XRD) images were taken to study the original microstructure and mineral content of the shale. To study the macroscale mechanical changes of Wufeng Shale immersed in scCO2 or N2 for 10 hours, triaxial tests with controlled coring angles were conducted. SEM and XRD images were taken after the triaxial tests. In the SEM images, tight bedding planes and undamaged minerals (with sharp edges and smooth surfaces) were found in N2-treated samples both before and after testing, indicating that exposure to N2 did not affect the microstructures. However, the SEM images for the microstructure scCO2-treated samples before and after testing were quite different. The bedding planes were damaged, which left some connected microfractures and corrosion holes, and some mineral types were broken into small particles and left with uneven mineral surfaces. This shows that scCO2 can change rock microstructures and make some minerals (e.g., calcite) fracture more easily. The complex microscale fractures and the decrease in strength for scCO2-treated shale aid the seepage and gathering of gas, enhancing shale-gas recovery. Knowledge of the multiscale physical and chemical changes of shale exposed to scCO2 is not only essential for scCO2 fracturing, but it is also important for scCO2 jets used to break rock and for the geological storage of CO2.
Frank, Florian (Rice University) | Liu, Chen (Rice University) | Alpak, Faruk O. (Shell International Exploration and Production) | Berg, Steffen (Rice University) | Riviere, Beatrice (Shell Global Solutions International)
Advances in pore-scale imaging, increasing availability of computational resources, and developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multiphase flow on pore structures feasible. In this paper, we describe a two-phase-flow simulator that solves mass- and momentum-balance equations valid at the pore scale (i.e., at scales where the Darcy velocity homogenization starts to break down). The simulator is one of the key components of a molecule-to-reservoir truly multiscale modeling work flow.
A Helmholtz free-energy-driven, thermodynamically based diffuse-interface/phase-field method is used for the effective simulation of numerous advecting interfaces, while honoring the interfacial tension (IFT). The advective Cahn-Hilliard (CH) (mass-balance, energy dissipation) and Navier-Stokes (NS) (momentum-balance, incompressibility) equations are coupled to each other within the phase-field framework. Wettability on rock/fluid interfaces is accounted for by means of an energy-penalty-based wetting (contact-angle) boundary condition. Individual balance equations are discretized by use of a flexible discontinuous Galerkin (DG) method. The discretization of the mass-balance equation is semi-implicit in time using a convex/concave splitting of the energy term. The momentum-balance equation is split from the incompressibility constraint by a projection method and linearized with a Picard splitting. Mass- and momentum-balance equations are coupled to each other by means of operator splitting, and are solved sequentially.
We discuss the mathematical model and its DG discretization, and briefly introduce nonlinear and linear solution strategies. Numerical-validation tests show optimal convergence rates for the DG discretization, indicating the correctness of the numerical scheme and its implementation. Physical-validation tests demonstrate the consistency of the phase distribution and velocity fields simulated within our framework. Finally, two-phase-flow simulations on two real pore-scale images demonstrate the usefulness of the pore-scale simulator. The direct pore-scale numerical-simulation methodology rigorously considers the flow physics by directly acting on pore-scale images of rocks without remeshing. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problems.