Water chemistry has been shown to affect oil recovery by affecting surface charge and rock dissolution. The single-well chemical-tracer (SWCT) test is a field method to measure residual oil saturation (Sor), in which hydrolysis reaction of an ester has been known as a key process that could displace the equilibrium state of a reservoir by changing formation-water (FW) composition.
Because oil mobilization during the SWCT tests causes an error in the measurement of Sor, changes in water chemistry might be a concern for the accuracy of Sor measurements. In our previous work, the extent to which different reservoir parameters might change water composition and the effect of water-chemistry changes on the calcite dissolution and the oil liberation from the carbonate-rock surfaces were extensively evaluated. In this study, the effect of water-chemistry changes on surface-charge alteration at the carbonate/brine interface has been studied by constructing and applying a surface-complexation model (SCM) that couples bulk aqueous and surface chemistry. We present how the pH drop induced by the displacement of the equilibrium state and changes in water chemistry in the formation affect surface charge in a pure-calcite carbonate rock during the SWCT tests.
The results show that a pH drop during the SWCT tests while calcium concentration is held constant in the FW by ignoring calcite dissolution yields a less-positive/more-negative surface charge so that wettability of carbonate rock might be altered to a less-oilwetting state, when the oil is negatively charged. In reality, however, calcite dissolves by water-chemistry changes during the SWCT tests, which leads to an increasing calcium concentration in the FW. Consequently, an SWCT test in carbonates is accompanied by increasing calcium concentration while pH drops, which yields an increase in the surface charge of carbonate rocks. Therefore, the pH drop does not directly affect the surface charge of carbonate rock during an SWCT test, and calcium concentration increased from calcite dissolution could control the surface charge more significantly.
Production data from hydraulically fractured horizontal wells in ultralow-permeability reservoirs have been observed to exhibit a half-slope straight line on a log-log plot of rate vs. time. Using these observations, many analytical models of linear flow have been developed to analyze the well performance in these reservoirs. However, it is relatively complicated to solve these models with the Laplace transform and numerical inversion. In this paper, a new analytical solution of a triple-porosity model is derived for unconventional oil reservoirs. The partial-differential equations (PDEs) are transformed into ordinary-differential equations (ODEs) by integration, instead of the Laplace transform. A rate-vs.-time solution in real-time space can be obtained, bypassing the numerical inversion for the Laplace transform. Our model is validated by comparison with both the numerical-model and Laplace-transform solutions. The physical meanings of the model parameters are analyzed through sensitivity analysis. The new model is then applied to field-production data for history matching and forecasting. Besides matching the production data, the pore volume (PV) of the matrix and fracture media can be estimated, which helps quantitative analysis of unconventional reservoirs.
Shi, Juntai (China University of Petroleum, Beijing) | Wang, Shan (China University of Petroleum, Beijing) | Xu, Xianglin (China University of Petroleum, Beijing) | Sun, Zheng (China University of Petroleum, Beijing) | Li, Jing (China University of Petroleum, Beijing) | Meng, Ye (China University of Petroleum, Beijing)
Vertically fractured wells are used widely to achieve efficient development of low-permeability reservoirs and unconventional tight reservoirs. Currently, there are some commonly adopted productivity models for a fractured vertical well, including the Giger (1985) model, the Economides model (Economides et al. 1989), the Joshi (1991) model, the Guo model (Guo and Evans 1993), the Zhang (1999) model, and others. However, these models are only suitable for either short fractures or long fractures, and thus cannot satisfy the need for arbitrary-length fracture selection. In addition, these models have certain requirements for boundary conditions, and few models consider the nonuniform flow in actual hydraulic factures. Therefore, it is desirable to establish a productivity model for vertically fractured wells with arbitrary fracture length under complex boundary conditions.
In this paper, first, we evaluate the existing fractured-vertical-well productivity models in detail. After that, on the basis of the potential superposition principle and mirror-image method, we develop the productivity model for a fractured vertical well with arbitrary fracture length under different boundary conditions. Grounded in this model, further considering the frictional pressure drop caused by fracture-flow nonuniformity, we establish the productivity equation of a finite-conductivity-fracture vertical well with nonuniform flow in the fracture. Finally, after comparing with the existing model under certain conditions, the reliability of the proposed model is verified successfully.
Results show that the Giger model assumes that the boundary in the fracture-extension direction is impermeable, and the pressure wave reaches the boundary earlier than the constant-pressure boundary, which is perpendicular to the extension direction of the fracture, whereas both the Economides model and the Joshi model assume that the boundary in the fracture-extension direction is far, and is always farther than the boundary perpendicular to the direction of the fracture extension. The results forecast by the previous models will deviate greatly from actual well-production performance, if the real field case cannot meet the requirements of these models. The proposed model is not only in good agreement with the previous models at given conditions, but is also suitable for fractured vertical wells under arbitrary-length fractures and complex boundary conditions. Compared with the existing models, the correctness and reasonableness of the model are shown, and the application of the proposed model is broadened.
For the development of low-permeability and unconventional tight oil and gas reservoirs with fractured vertical wells or fractured horizontal wells, the establishment and application of this model have great theoretical significance and application value for production prediction. This model can be a foundation or reference for productivity prediction of low-permeability and unconventional tight oil and gas reservoirs with fractured vertical wells or fractured horizontal wells.
The objective of this paper is to revisit currently used techniques for analyzing reservoir performance and characterizing the horizontal-well productivity index (PI) in finite-acting oil and gas reservoirs. This paper introduces a new practical and integrated approach for determining the starting time of pseudosteady-state flow and constant-behavior PI. The new approach focuses on the fact that the derivative of PI vanishes to zero when pseudosteady-state flow is developed. At this point, the derivative of transient-state pressure drop and that of pseudosteady-state pressure drop become mathematically identical. This point indicates the starting time of pseudosteady-state flow as well as the constant value of pseudosteady-state PI. The reservoirs of interest in this study are homogeneous and heterogamous, single and dual porous media, undergoing Darcy and non-Darcy flow in the drainage area, and finite-acting, depleted by horizontal wells. The flow in these reservoirs is either single-phase oil flow or single-phase gas flow.
Several analytical models are used in this study for describing pressure and pressure-derivative behavior considering different reservoir configurations and wellbore types. These models are developed for heterogeneous and homogeneous formations consisting of single and dual porous media (naturally fractured reservoirs) and experiencing Darcy and non-Darcy flow. Two pressure terms are assembled in these models; the first pressure term represents the time-dependent pressure drop caused by transient-state flow, and the second pressure term represents time-invariant pressure drop controlled by the reservoir boundary. Transient-state PI and pseudosteady-state PI are calculated using the difference between these two pressures assuming constant wellbore flow rate. The analytical models for the pressure derivatives of these two pressure terms are generated. Using the concept that the derivative of constant PI converges to zero, these two pressure derivatives become mathematically equal at a certain production time. This point indicates the starting time of pseudosteady-state flow and the constant behavior of PI.
The outcomes of this study are summarized as the following:
The novel points in this study are the following:
Li, Xiaojiang (China University of Petroleum, Beijing and Sinopec Research Institute of Petroleum Engineering) | Li, Gensheng (China University of Petroleum, Beijing) | Yu, Wei (Texas A&M University) | Wang, Haizhu (China University of Petroleum, Beijing) | Sepehrnoori, Kamy (University of Texas at Austin) | Chen, Zhiming (China University of Petroleum, Beijing) | Sun, He (University of Texas at Austin) | Zhang, Shikun (China University of Petroleum, Beijing)
Liquid/supercritical carbon dioxide (L/SC-CO2) fracturing is an emerging technology for shale gas development because it can effectively overcome problems related to clay swelling and water scarcity. Recent applications show that L/SC-CO2 fracturing can induce variations in temperature. Understanding of this phenomenon is rudimentary and needs to be carefully addressed to improve the understanding of CO2 thermodynamic behavior, and thus helps to optimize CO2 fracturing in the field.
In this paper, we develop a numerical model to assess the impact of thermal effect on fracture initiation during CO2 fracturing. The model couples fluid flow and heat transfer in the fracture, and is verified by a peer-reviewed solution and observation in laboratory experiments. The velocity, pressure, and temperature are calculated at various time to demonstrate the thermodynamic behavior during fracture initiation. A pseudo shock wave is observed, associated with a compression wave and an expansion wave, which finally leads to an increase in temperature in the new fracture and a decrease in temperature in the initial fracture. The thermal stress is derived to investigate the difference between hydraulic fracturing and CO2 fracturing. The results show that thermal stress, resulting from CO2 fracturing initiation, is comparable to the rock strength, which will help induce microfractures, and thus promote the fracture complexity. The formation pressure after CO2 fracturing is also calculated to evaluate the pressure-buildup potential. This work highlights the importance of CO2 expansion during and after fracturing. It is one of the unique features that differs from hydraulic fracturing. For field-design recommendations, to enhance the thermal effect of CO2 fracturing, it is a good strategy to pump CO2 at high pressure and low temperature into the reservoirs with high Young’s modulus, low Poisson’s ratio, low permeability, and high geothermal temperature (or large depth).
This paper does not address the dynamics of fracture propagation under the influence of thermal effect. Rather, it intends to demonstrate the potential of the thermal effect of CO2 fluid in assisting the fracture propagation, and the importance of incorporating the compressibility of CO2 into fracture modeling and operation design. Failing to account for this thermal effect might underestimate the fracture complexity and stimulated reservoir volume.
Li, Caoxiong (Institute of Mechanics, Chinese Academy of Sciences and School of Engineering Science, University of Chinese Academy of Sciences) | Lin, Mian (Institute of Mechanics, Chinese Academy of Sciences and School of Engineering Science, University of Chinese Academy of Sciences) | Ji, Lili (Institute of Mechanics, Chinese Academy of Sciences) | Jiang, Wenbin (Institute of Mechanics, Chinese Academy of Sciences) | Cao, Gaohui (Institute of Mechanics, Chinese Academy of Sciences and School of Engineering Science, University of Chinese Academy of Sciences)
Shale possesses abundant micro/nanopores. Most micro/nanopores that exist in organic-rich shale are organic pores and mainly developed in organic matter. The pore distribution in matrix space significantly affects gas percolation and diffusion. Pore-size distribution possesses a self-similar, or fractal, property. The pore space and gas permeability of shale can be easily rebuilt and evaluated, respectively, using fractal theory. In this work, a 3D intermingled-fractal model (3D-IFM) is successfully built using scalable scanning-electron-microscopy (SEM) images of shale samples. 3D-IFM is made up of several components, including organic pores in organic matter and in pyrites, inorganic pores, slits, and matrix. An improved pore-connective-calculation method is also introduced to evaluate the apparent gas permeability of the shale model. The proposed 3D-IFM rapid-permeability-evaluation method for organic-rich shale is valid and useful and considers the main components of shale. This method can rapidly evaluate apparent gas permeability and simplify the apparent-gas-permeability-calculation process. Thus, the method provides a promising means of rapidly evaluating apparent gas permeability.
A new method is proposed to estimate the compliance and conductivity of induced unpropped fractures as a function of the effective stress acting on the fracture from diagnostic-fracture-injection-test (DFIT) data. A hydraulic-fracture resistance to displacement and closure is described by its compliance (or stiffness). Fracture compliance is closely related to the elastic, failure, and hydraulic properties of the rock. Quantifying fracture compliance and fracture conductivity under in-situ conditions is crucial in many Earth-science and engineering applications but is very difficult to achieve. Even though laboratory experiments are used often to measure fracture compliance and conductivity, the measurement results are influenced strongly by how the fracture is created, the specific rock sample obtained, and the degree to which it is preserved. As such, the results may not be representative of field-scale fractures.
During the past 2 decades, the DFIT has evolved into a commonly used and reliable technique to obtain in-situ stresses, fluid-leakoff parameters, and formation permeability. The pressure-decline response across the entire duration of a DFIT reflects the process of fracture closure and reservoir-flow capacity. As such, it is possible to use these data to quantify changes in fracture conductivity as a function of stress. In this paper, we present a single, coherent mathematical framework to accomplish this. We show how each factor affects the pressure-decline response, and the effects of previously overlooked coupled mechanisms are examined and discussed. Synthetic and field-case studies are presented to illustrate the method. Most importantly, a new specialized plot (normalized system-stiffness plot) is proposed, which not only provides clear evidence of the existence of a residual fracture width as a fracture is closing during a DFIT, but also allows us to estimate fracture-compliance (or stiffness) evolution, and infer unpropped fracture conductivity using only DFIT pressure and time data alone. It is recommended that the normalized system-stiffness plot (NS plot) be used as a standard practice to complement the G-function or square-root-of-time plot and log-log plot because it provides very valuable information on fracture-closure behavior and the properties of fracture-surface roughness at a field-scale, information that cannot be obtained by any other means.
Hydraulic fractures propagate perpendicular to the horizontal-well axis whenever the drilling direction is parallel to the minimum-principal-stress direction. However, operators frequently drill horizontal wells parallel to lease boundaries, resulting in hydraulic-fracture vertical planes slanted at angles less than 90° from the well axis.
The stimulated-rock-volume (SRV) dimensions are defined by fracture height, well length, and fracture length multiplied by the sine of the angle between fracture planes and the horizontal-well axis (fracture angle). The well productivity index (PI) under boundary-dominated flow (BDF) is given by the PI for one fully penetrating fracture multiplied by the number of fractures. An extension of the unified-fracture-design (UFD) approach for rectangular drainage areas enables determination of the unique number of fractures that will maximize well productivity under BDF conditions given the formation permeability, proppant mass, fracture angle, and well spacing. Fracture length and width vary depending on the fracture angle, but the total-propped-fracture volume remains constant.
Because the likely reason for drilling at an angle to the minimum-stress direction is to better cover a lease area with north/south and east/west boundaries, the smallest fracture angle will be 45°, corresponding to northwest/southeast or northeast/southwest minimum-stress direction. This results in the need to lengthen fractures by at most 40% to preserve the SRV for a given horizontal-well length and spacing. For the same sufficiently large proppant mass, this will reduce fracture conductivity by the same factor. However, because the flow area has increased, the result will be greater well productivity.
This study shows a simple strategy for designing wells to maximize productivity even when not drilled in the minimumstress direction.
Nitrate used to control reservoir souring in oil fields contains nitrite impurities. Nitrite is a strong oxidizer, and when used in souring-treatment fluids, the flow path often includes carbon-steel piping. Vanadium, also an oxidizer, is at times found in oilfield-production streams that commingle with souring-treatment fluids. The interactions between nitrite and vanadium and their effects on carbon steel X65 corrosion were investigated.
The effect of nitrite on corrosion was investigated using synthetic brine to simulate produced water [rich in carbon dioxide (CO2), pH value of approximately 5] and seawater (negligible CO2, pH value of approximately 7). Tests were conducted with carbon steel X65 exposed to synthetic brine at 25, 60, and 80°C using a rotating cylinder electrode (RCE). The test results demonstrate the following:
Field-scale simulations of complex processes often suffer from long simulation times. One of the main reasons is that the Newton-Raphson (NR) process used to solve each simulation timestep requires many iterations and small timestep sizes to converge. Because the selection of solution variables affects the nonlinearity of the equations, it is attractive to have a practical method to rapidly explore the use of alternative primary variables in general-purpose reservoir simulators.
Many reservoir simulators use pressure, saturations, and temperature in each gridblock as the primary solution variables, which are referred to as natural variables. There is also a class of reservoir simulators that uses pressure, total component masses (or moles), and internal energy in each gridblock as primary variables. These simulators are referred to as mass-variable-based reservoir simulators. For a given choice of primary variables, most simulators have dedicated, highly optimized procedures to compute the required derivatives and chain rules required to build the Jacobian matrix. Hence, it is usually not possible to switch between mass and natural variables. In this work, however, we establish a link at the numerical-solution level between natural- and mass-variable formulations and design a novel (nonlinear) block-local method that transforms mass-variable shifts (computed at each NR iteration) into equivalent natural-variable shifts.
We demonstrate on a number of simulation models of varying complexity that by use of the proposed approach, a mass-variable-based flow simulator can still effectively use natural variables, where the change of variables can be made locally per gridblock. Results indicate that in some models the total number of NR iterations, linear-solver (LS) iterations, and timestep-size cuts (caused by the nonconvergence of the NR procedure, also known as backups) are reduced when using natural variables instead of mass variables. However, the improvement is relatively modest and not generally observed. Our findings also signify that depending on the specific characteristics of the simulation problem at hand, mass-variable-based simulators may perform comparably or outperform natural-variable-based simulators.
The proposed variable-switching method can be used effectively to evaluate the effect of using different primary solution variables on problem nonlinearity and solver efficiency. With this method, the effect of interchanging primary solution variables on problem nonlinearity can be rapidly evaluated.