Gas lift is one of the most widely used artificial lift methods, and the use of nodal analysis to generate the gas lift performance curve is well established. However, the optimal gas injection rate is often selected as the point with maximum liquid production, which neglects the cost of incremental injection gas volume. This paper investigates the determination of the optimal operational point using a multiobjective optimization technique by considering the trade-off between gas consumption and oil production. The indicator-based evolutionary algorithm transforms the multiobjective problem into a single objective one using the hypervolume metric computed in the objective space. For the gas lift problem, which is a bi-objective problem aimed at maximizing oil production while minimizing gas injection rate, the hypervolume metrics are identically equivalent to geometric hyperareas under the trade-off curve. The optimization is only applied to the monotonically increasing portion of the gas lift performance curve; thus, all trivial sub-optimal conditions are excluded. The optimal operational point of gas injection rate is determined by finding the maximum rectangular hyperarea under the performance curve. The proper determination of the optimal injection gas rate could not only improve the efficiency of the gas lift itself, but also reduce the burden on the maintenance of surface facilities. The method is also applied to the multi-well scenario where a novel multi-well gas lift performance curve is generated using multiobjective Genetic Algorithm, which could help determine the optimal gas allocation/distribution scenario. The described process is incorporated in an integrated workflow which further leads to fast delivery of analysis/results that enable production engineers to make smarter decisions faster in a repeatable way.
In-situ gelled acids have been used for acid diversion in heterogeneous carbonate reservoirs for more than two decades. Most of the gelled systems are based on an anionic polymer that has a cleaning problem after the acid treatments that leads to formation damage. This work evaluates a new cationic-polymer acid system with the self-breaking ability for the application as an acid divergent in carbonate reservoirs.
Experimental studies have been conducted to examine the rheological properties of the polymer-based acid systems. The apparent viscosities of the live and the partially neutralized acids at pH from 0 to 5 were measured against the shear rate (0 to 1,000 s-1). The impact of salinity and temperature (80 to 250°F) on the rheological properties of the acid system was also studied. The viscoelastic properties of the gelled acid system were evaluated using an oscillatory rheometer. Dynamic sweep tests were used to determine the elastic (G’) and viscous modulus (G") of the system. Single coreflood experiments were conducted on Indiana limestone cores to study the nature of diversion caused by the polymer-acid system. The impact of permeability contrast on the process of diversion was investigated by conducting dual coreflood experiments on Indiana limestone cores which had a permeability contrast of 1.5-20. CT scans were conducted to study the propagation of wormhole post acid injection for both single and dual corefloods.
The live acid system displayed a non-Newtonian shear-thinning behavior with the viscosity declining with temperature. For 5 wt% HCl and 20 gpt polymer content at 10 s-1, the viscosity decreased from 230 to 40 cp with temperature increasing from 88 to 250°F. Acid spending tests demonstrated that the acid generated a gel with a significant improvement in viscosity to 260 cp (at 250°F and 10 s-1) after it reached a pH of 2. The highly viscous gel plugged the wormhole and forced the acid that followed to the next higher permeability zone. The viscosity of gel continued to increase until it broke down to 69 cp (at 250°F and 10 s-1) at a pH of 4.8, which provides a self-breaking system and better cleaning. Coreflood studies indicated that the wormhole and the diversion process is dependent on the temperature and the flow rate. There was no indication of any damage caused by the system. The injected acid volume to breakthrough (PVBT) decreased from 2.2 to 1.4 when the temperature increased from 150 to 250°F.
The strong elastic nature of the gel (G’= 3.976 Pa at 1 Hz) formed by the partially neutralized acid system proves its suitability as a candidate for use as a diverting agent. This novel acid-polymer system has significant promise for usage in acid diversion to improve stimulation of carbonate reservoirs.
Xu, Zhengming (China University of Petroleum, Beijing) | Wu, Kan (Texas A&M University) | Song, Xianzhi (China University of Petroleum, Beijing) | Li, Gensheng (China University of Petroleum, Beijing) | Zhu, Zhaopeng (China University of Petroleum, Beijing) | Sun, Baojiang (China University of Petroleum, East China)
Energized fracturing fluids, including foams, carbon dioxide (CO2), and nitrogen (N2), are widely used for multistage fracturing in horizontal wells. However, because density, rheology, and thermal properties are sensitive to temperature and pressure, it is important to understand the flow and thermal behaviors of energized fracturing fluids along the wellbore. In this study, a unified steady-state model is developed to simulate the flow and thermal behaviors of different energized fracturing fluids and to investigate the changes of fluid properties from the wellhead to the toe of the horizontal wellbore. The velocity and pressure are calculated using continuity and momentum equations. Temperature profiles of the whole wellbore/formation system are obtained by simultaneously solving energy equations of different thermal regions. Temperature, pressure, and energized-fluid properties are coupled in both depth and radial directions using an iteration scheme. This model is verified against field data from energized-fluid-injection operations. The relative average errors for pressure and temperature are less than 5%. The effects of injection pressure, mass-flow rate, annulus-fluid type, foam quality, and proppant volumetric concentration on pressure and temperature distributions are analyzed. Influence degrees of these operating parameters on the bottomhole pressure (BHP) for different energized fracturing fluids are calculated. The required injection parameters at the surface to achieve designed bottomhole treating parameters for different energized fracturing fluids are compared. The results of this study might help field operators to select the most-suitable energized fluid and further optimize energized-fluid-fracturing treatments.
Seunghwan Baek and I. Yucel Akkutlu, Texas A&M University Summary Source rocks, such as organic-rich shale, consist of a multiscale pore structure that includes pores with sizes down to the nanoscale, contributing to the storage of hydrocarbons. In this study, we observed hydrocarbons in the source rock partition into fluids with significantly varying physical properties across the nanopore-size distribution of the organic matter. This partitioning is a consequence of the multicomponent hydrocarbon mixture stored in the nanopores, exhibiting a significant compositional variation by pore size-- the smaller the pore size, the heavier and more viscous the hydrocarbon mixture becomes. The concept of composition redistribution of the produced fluids uses an equilibrium molecular simulation that considers organic matter to be a graphite membrane in contact with a microcrack that holds bulk-phase produced fluid. A new equation of state (EOS) was proposed to predict the density of the redistributed fluid mixtures in nanopores under the initial reservoir conditions. A new volumetric method was presented to ensure the density variability across the measured pore-size distribution to improve the accuracy of predicting hydrocarbons in place. The approach allowed us to account for the bulk hydrocarbon fluids and the fluids under confinement. Multicomponent fluids with redistributed compositions are capillary condensed in nanopores at the lower end of the pore-size distribution of the matrix ( 10 nm). The nanoconfinement effects are responsible for the condensation. During production and pressure depletion, the remaining hydrocarbons become progressively heavier. Hence, hydrocarbon vaporization and desorption develop at extremely low pressures. Consequently, hydrocarbon recovery from these small pores is characteristically low. Introduction Resource shale and other source-rock formations with significant amounts of organic matter, such as mudstone, siltstone, and carbonate, have a multiscale pore structure that includes fractures, microcracks, and pores down to a few nanometers (Ambrose et al. 2012; Loucks et al. 2012). The total amount of hydrocarbons stored is directly proportional to the amount of organic matter.
Field data have shown the decline of fracture conductivity during reservoir depletion. In addition, refracturing and infill drilling have recently gained much attention as efficient methods to enhance recovery in shale reservoirs. However, current approaches present difficulties in efficiently and accurately simulating such processes, especially for large-scale cases with complex hydraulic and natural fractures.
In this study, a general numerical method compatible with existing simulators is developed to model dynamic behaviors of complex fractures. The method is an extension of an embedded discrete-fracture model (EDFM). With a new set of EDFM formulations, the nonneighboring connections (NNCs) in the EDFM are treated as regular connections in traditional simulators, and the NNC transmissibility factors are linked with gridblock permeabilities. Hence, manipulating block permeabilities in simulators can conveniently control the fluid flow through fractures. Complex dynamic behaviors of hydraulic fractures and natural fractures can be investigated using this method.
The proposed methodology is implemented in a commercial reservoir simulator in a nonintrusive manner. We first present one synthetic case study in a shale-oil reservoir to verify the model accuracy and then combine the new model with field data to demonstrate its field applicability. Subsequently, four field-scale case studies with complex fractures in two and three dimensions are presented to illustrate the applicability of the method. These studies involve vertical- and horizontal-well refracturing in tight reservoirs, infill drilling, and fracture activation in a naturally fractured reservoir. The proposed approach is combined with empirical correlations and geomechanical criteria to model stress-dependent fracture conductivity and natural-fracture activation. It also shows convenience in dynamically adding new fractures or extending existing fractures during simulation. Results of these studies further confirm the significance of dynamic fracture behaviors and fracture complexity in the analysis and optimization of well performance.
Brice Y. Kim and I. Yucel Akkutlu, Texas A&M University, and Vladimir Martysevich and Ronald G. Dusterhoft, Halliburton Summary The stress-dependent permeabilities of split shale core plugs from Eagle Ford, Bakken, and Barnett Formation samples are investigated in the presence of microproppants. An analytical permeability model is developed for the investigation, including the interactions between the fracture walls and monolayer microproppants under stress. The model is then used to analyze a series of pressure-pulsedecay measurements of the propped shale samples in the laboratory. The analysis provides the propped-fracture permeability of the samples and predicts a parameter related to the quality of the proppant areal distribution in the fracture. The proppant-placement quality can be used as a measure of success of the delivery of proppants into microfractures and to design stimulation experiments in the laboratory. Introduction Unconventional-oil/gas resources, such as tight gas/oil and resource shale, have low porosity and ultralow permeability. Creating a well-connected complex fracture network is a key component of increasing the permeability and accelerating production. The early era of hydraulic fracturing horizontal wells in unconventional formations was concerned with achieving long fractures with multistage treatments with large cluster spacing. However, recent trends in this type of well completion and stimulation involve fractures that are created in narrower clusters in much closer spacing, targeting larger surface areas. It is argued that the practice of hydraulic fracturing with narrow clusters in close spacing along a lateral wellbore creates fractures with significantly reduced sizes, but in a complex network (Rassenfoss 2017). The creation of a network of fractures includes major operational issues.
The standard model for relating bulk formation resistivity to porosity and water saturation was introduced to the petroleum industry in 1941; it remains the industry standard to this day. The model was discovered empirically by means of graphical analysis. Basically, G.E. Archie discovered that when the logarithm of formation resistivity factor was plotted against the logarithm of porosity the resulting trend could be fitted by a straight line. A similar relationship was discovered connecting the logarithms of resistivity index and water saturation. When these two power laws are combined into a single equation, it can be solved for water saturation (which is not observable from a borehole) in terms of bulk formation resistivity, interstitial brine resistivity, and porosity (all of which can be estimated from observations made in boreholes). This revolutionized log interpretation. There has always been a problem with the model in terms of its “explainability”. That is, it cannot be derived in any straightforward way from accepted first principles of physics. It does not contradict any first principle, but neither does it seem to follow ineluctably from them. However, since the model works, most formation evaluators have memorized the relationships that follow from the model and simply “get used to them”. That remains the situation to this day. However, there is a path around this obstacle to understanding formation resistivity at a fundamental level, and that way forward is to abandon the resistivity formulation in favor of its reciprocal, conductivity. It is surprising that such a seemingly trivial change could open a new vista into the relationships among formation electrical properties. A conductivity formulation permits the asking of questions about how a formation’s conductivity should respond to changes not only in brine conductivity, but also in the fractional amount of brine in a formation, and its geometrical configuration. By answering these questions in an obvious way, and with some analysis of data taken in the laboratory, an intuitively obvious model explaining bulk formation conductivity emerges. The model is not the same as the Archie model. However, when certain parameters are taken to their limiting values, and the model is converted into resistivity space, Archie’s power law model is revealed as an approximation to the limiting cases. Thus, from the conductivity formulation, an intuitive understanding of the Archie model emerges. Moreover, the conductivity model can be derived in at least three different ways, each yielding different insights into formation conductivity.
Significant research has been conducted on hydrocarbon fluids in the organic materials of source rocks, such as kerogen and bitumen. However, these studies were limited in scope to simple fluids confined in nanopores, while ignoring the multicomponent effects. Recent studies using hydrocarbon mixtures revealed that compositional variation caused by selective adsorption and nanoconfinement significantly alters the phase equilibrium properties of fluids. One important consequence of this behavior is capillary condensation and the trapping of hydrocarbons in organic nanopores. Pressure depletion produces lighter components, which make up a small fraction of the in-situ fluid. Equilibrium molecular simulation of hydrocarbon mixtures was carried out to show the impact of CO2 injection on the hydrocarbon recovery from organic nanopores. CO2 molecules introduced into the nanopore led to an exchange of molecules and a shift in the phase equilibrium properties of the confined fluid. This exchange had a stripping effect and, in turn, enhanced the hydrocarbon recovery. The CO2 injection, however, was not as effective for heavy hydrocarbons as it was for light components in the mixture. The large molecules left behind after the CO2 injection made up the majority of the residual (trapped) hydrocarbon amount. High injection pressure led to a significant increase in recovery from the organic nanopores, but was not critical for the recovery of the bulk fluid in large pores. Diffusing CO2 into the nanopores and the consequential exchange of molecules were the primary drivers that promoted the recovery, whereas pressure depletion was not effective on the recovery. The results for N2 injection were also recorded for comparison.
Viscoelastic surfactants (VES) are essential components in self-diverting acid systems. Their low thermal stability limits their application at elevated temperatures. The industry introduced new VES chemistries with modified hydrophilic functional groups, which enhances their thermal stability. These new chemistries are still challenged by the lack of compatibility with corrosion inhibitors (CI). This work aims to study the nature and the mechanism of the interaction between the VES and the corrosion inhibitors, which affects both the rheological and corrosion inhibition characteristics of the self-diverting acid system.
This study is based on rheology and corrosion inhibition tests, where combinations of VES and corrosion inhibitors are tested and complemented with chemical and microscopic analysis. Negatively charged thiourea and positively charged quaternary ammonium corrosion inhibitors were selected to study their impact on both cationic and zwitterionic VES systems. Each mixture of the corrosion inhibitor and the VES was blended in a 15 and 20 wt% HCl acid mixture, then assessed for its viscosity at different shear rates, CI concentrations, and temperatures up to 280°F in live and spent acid conditions. Each acid solution was assessed using Fourier-Transform-Infra-Red (FTIR) before and after each rheology and corrosion test to track the changes of the mixture functional groups. Each mixture was examined under a polarizing microscope to assess its colloidal nature. The corrosion inhibition effectiveness of selected acid mixtures was evaluated. N-80 steel coupons were immersed statically in the acid mixture for 6 hours at 150°F and 1,000 psi. The corrosion rate was evaluated by using metal coupon weight loss analysis followed by optical microscope examination for the metal surface.
The interaction between the CI and the VES surface charges and molecular geometries dictates both the rheological and the inhibitive properties of the acid mixtures. The use of a small molecular structure anionic CI with a cationic VES, results in a fine monodispersed CI particles in the VES-acid system. The opposite charges between the CI and the VES results in electrostatic attraction forces. Both the fine dispersion and the electrostatic attraction enhances the rheological performance of the mixture and packs the corrosion-inhibiting layer. The addition of a bulk and similarly charged CI with the VES results in a coarse polydispersed CI particles with repulsive nature with the VES. These properties increase the shear-induced structures and lower the packing of the inhibition layer deposited on the metal coupons, which decrease the rheological performance of the acid mixture and increase its corrosion rate. The FTIR analysis shows that there is no chemical reaction between the CIs and the VESs tested.
This work investigates the interactions between the corrosion inhibitors and the viscoelastic surfactants. It explains the impact of the surface charge of both corrosion inhibitors and VES on their rheological and corrosion inhibition characteristics. It adds a selection criterion for compatible VES and corrosion inhibitors.
The objective of this work is to design novel multi-layer neural network architectures for simulations of multi-phase flow taking into account the observed data (e.g., production data) and physical modeling concepts. Our approaches use deep learning concepts combined with model reduction methodologies to predict multi-phase flow dynamics. The use of reduced-order model concepts is important for constructing robust deep learning architectures. The reduced-order models provide fewer degrees of freedom and allow handling the cases relevant to reservoir engineering that is limited to production and near-well data.
Multi-phase flow dynamics can be thought as multi-layer networks. More precisely, the solution, pressures and saturations, at the time instant n+1 depends on the solution at the time instant n and input parameters, such as permeability, well rates, and so on. Thus, one can regard the solution as a multi-layer network, where each layer is a nonlinear forward map. The number of time steps is user-defined quantity, which will be treated as an unknown within our deep learning algorithms. We will rely on rigorous model reduction concepts to define unknowns and connections for each layer. Novel proper orthogonal basis functions will be constructed such that the degrees of freedom have physical meanings (e.g., represent the solution values at selected locations) and basis functions have limited support, which will allow localizing the forward dynamics. This will allow writing the forward map for the solution values at selected locations with pre-computed neighborhood structure that will be used in deep learning algorithms.
In each layer, our reduced-order models will provide a forward map, which will be modified (trained) using available data. It is critical to use reduced-order models for this purpose, which will identify the regions of influence and the appropriate number of variables. Because of the lack of available data, the training will be supplemented with computational data as needed and the interpolation between data-rich and data-deficient models. We will also use deep learning algorithms to train the elements of the reduced model discrete system.
In this case, deep learning architectures will be employed to approximate the elements of the discrete system and reduced-order model basis functions.
The numerical results will use deep learning architectures to predict the solution and reduced-order model variables. Trained basis functions will allow interpolating the solution between the observation points. We show how network architecture, which includes the neighborhood connection, number of layers, and neurons, affect the approximation. Our results show that with a fewer number of layers, the multi-phase flow dynamics can be approximated. The proposed approach uses physical model concepts and deep learning methods to design a novel forward map, which combines the available data and physical models. This will benefit to develop a fast and data-based algorithms for reservoir simulations.