type curve
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2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xin Zhao ◽  
Donghe Pei

The evolutoid of a regular curve in the Lorentz-Minkowski plane ℝ 1 2 is the envelope of the lines between tangents and normals of the curve. It is regarded as the generalized caustic (evolute) of the curve. The evolutoid of a mixed-type curve has not been considered since the definition of the evolutoid at lightlike point can not be given naturally. In this paper, we devote ourselves to consider the evolutoids of the regular mixed-type curves in ℝ 1 2 . As the angle of lightlike vector and nonlightlike vector can not be defined, we introduce the evolutoids of the nonlightlike regular curves in ℝ 1 2 and give the conception of the σ -transform first. On this basis, we define the evolutoids of the regular mixed-type curves by using a lightcone frame. Then, we study when does the evolutoid of a mixed-type curve have singular points and discuss the relationship of the type of the points of the mixed-type curve and the type of the points of its evolutoid.


Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2852
Author(s):  
Xin Zhao ◽  
Donghe Pei

In this paper, we consider the pedal curves of the mixed-type curves in the Lorentz–Minkowski plane R12. The pedal curve is always given by the pseudo-orthogonal projection of a fixed point on the tangent lines of the base curve. For a mixed-type curve, the pedal curve at lightlike points cannot always be defined. Herein, we investigate when the pedal curves of a mixed-type curve can be defined and define the pedal curves of the mixed-type curve using the lightcone frame. Then, we consider when the pedal curves of the mixed-type curve have singular points. We also investigate the relationship of the type of the points on the pedal curves and the type of the points on the base curve.


2021 ◽  
Author(s):  
Mohammad Reza ◽  
Riezal Arieffiandhany ◽  
Debby Irawan ◽  
S Shofiyuddin ◽  
Darmawan Budi Prihanto

Abstract Manifestation of Low Resistivity Pay (LRP) Existences in ONWJ Area because of Fine Grained, Superficial Microporosity, Laminated Shaly Sand and Electronic Conduction. Water saturation petrophysical analysis for LRP Case due to those reason above can be solved by electrical parameter determination with Type Curve. But to overcome the LRP caused by Laminated Shaly Sand, the use of high resolution resistivity logs that are close to the resolution of thin bed reservoir is a must. Alternative solutions, conventional high resolution resistivity logs, namely Micro Spherical Focused Log (MSFL) are used to interpret thin bed reservoirs that have the hydrocarbon potential. This intergrated petrophysical analysis is called MAINE Petrophysical Method The Petrophysical MAINE method is the development of the TECWAL (Type Curve, Core and Water Analysis) method which leaves question marks on Laminated Shaly Sand Reservoir and the possibility of variations in the Electrical Parameter and Water Saturation Irreducible (SWIRR) dependent on Rocktype. The Basis of the MAINE Method is the Worthington Type Curve with some assumptions such as Each rocktype has a different value of Bulk Volume of Water (BVW) and BVW can be used to determine the SWIRR value of each rocktype and Each rocktype has different electrical parameter m and n. In the process, the use of J-Function and Buckles Plot is applied to help determinet Rocktype and BVW values. The rocktype will be the media in distributing the value of Electrical Parameter generated by the Type Curve and the value will be used in water saturation calculation. In Laminated Shaly Sand Reservoir, Rocktyping will be analyzed more detail using the High Resolution Conventional Log, Micro Spherical Focused Log (MSFL). The expected final result of this analysis is the more reliable Water Saturation (SW) and the integration of water saturation values in the Buckles Plot which can help in determining the transition zone in order to avoid mistakes in determining the perforation zone. Through the MAINE Petrophysical Method, there is a decrease in water saturation from an average value 86% to 66% or a decrease 23%. This result is quite significant for the calculation of reserves in the LRP zone. By integrating this method with the Buckles Plot, it can help the interpreter to determine the perforation interval in order to avoid water contact or the transition zone


2021 ◽  
Author(s):  
Helmi Pratikno ◽  
W. John Lee ◽  
Cesario K. Torres

Abstract This paper presents a method to identify switch time from end of linear flow (telf) to transition or boundary-dominated flow (BDF) by utilizing multiple diagnostic plots including a Modified Fetkovich type curve (Eleiott et al. 2019). In this study, we analyzed publicly available production data to analyze transient linear flow behavior and boundary-dominated flow from multiple unconventional reservoirs. This method applies a log-log plot of rate versus time combined with a log-log plot of rate versus material balance time (MBT). In addition to log-log plots, a specialized plot of rate versus square root of time is used to confirm telf. A plot of MBT versus actual time, t, is provided to convert material balance time to actual time, and vice versa. The Modified Fetkovich type curve is used to estimate decline parameters and reservoir properties. Applications of this method using monthly production data from Bakken and Permian Shale areas are presented in this work. Utilizing public data, our comprehensive review of approximately 800 multi-staged fractured horizontal wells (MFHW) from North American unconventional reservoirs found many of them exhibiting linear flow production characteristics. To identify end of linear flow, a log-log plot of rate versus time alone is not sufficient, especially when a well is not operated in a consistent manner. This paper shows using additional diagnostic plots such as rate versus MBT and specialized plots can assist interpreters to better identify end of linear flow. With the end of linear flow determined for these wells, the interpreter can use the telf to forecast future production and estimate reservoir properties using the modified type curve. These diagnostic plots can be added to existing production analysis tools so that engineers can analyze changes in flow regimes in a timely manner, have better understanding of how to forecast their wells, and reduce the uncertainty in estimated ultimate recoveries related to decline parameters.


2021 ◽  
Author(s):  
Fengyuan Zhang ◽  
Hamid Emami-Meybodi

Abstract This study presents a new type-curve method to characterize hydraulic fracture (HF) attributes and dynamics by analyzing two-phase flowback data from multi-fractured horizontal wells (MFHWs) in hydrocarbon reservoirs.The proposed method includes a semianalytical model, as well as a workflow to estimate HF properties (i.e., initial fracture pore-volume and fracture permeability) and HF closure dynamics (through iterating fracture compressibility and permeability modulus).The semianalytical model considers the coupled two-phase flow in the fracture and matrix system, the variable production rate at the well, as well as the pressure-dependent reservoir and fluid properties. By incorporating the contribution of fluid influx from matrix into the fracture effective compressibility, a new set of dimensionless groups is defined to obtain a dimensionless solution for type-curve analysis. The accuracy of the proposed method is tested using the synthetic data generated from six numerical simulation cases for shale gas and oil reservoirs. The numerical validation confirms the unique behavior of type curves during fracture boundary dominated flow and verifies the accuracy of the type-curve analysis in the characterization of fracture properties. For field application, the proposed method is applied to two MFHWs in Marcellus shale gas and Eagle Ford shale oil.The agreement of interpreted results between the proposed method and straight-line analysis not only demonstrates the practicality in field application but also illustrates the superiority of the type-curve method as an easy-to-use technique to analyze two-phase flowback data. The analysis results from both of the field examples reveal the consistency in the estimated fracture properties between the proposed method and long-term history matching.


2021 ◽  
Author(s):  
Loc Luong

Abstract In this study, an extended version of the fractional decline model is analytically developed for gas flow in fracture reservoir using the anomalous diffusion equation incorporated with the fractional calculus and equation of state. The model can represent the heterogeneity of complex fracture networks and can further be used to interpret reservoir properties by performing type-curve matching of flow rate and cumulative production from multi-fractured horizontal wells in unconventional reservoirs. To address the limitations of conventional planar fracture idealization, the hydraulic fractures in this present study are integrated with the fracture network, and the fractional diffusivity is solved for a horizontal wellbore. Upon establishing and solving the governing equation in the Laplace domain, the solutions are converted back to the real-time and space domain by performing numerical Laplace inversion. A set of distinctive type curves is generated on the basis of an infinite conductivity horizontal well model, considering early and middle times, in order to capture the heterogeneity of the fractal network in the reservoir model. Application of this new model is demonstrated through type-curve matching of two synthetic cases of simulation data obtained from commercial software; the cases cover orthogonal evenly and unevenly distributed networks. Results from these examples show an acceptable match between the fractional decline model and synthetic data and, hence, showcase the applicability of this model to capture the transient flow in heterogeneous fractured reservoirs.


2021 ◽  
Vol 73 (09) ◽  
pp. 8-10
Author(s):  
Justin Hayes

If you talk to a typical subsurface professional working on unconventionals today (e.g., a reservoir engineer, completion engineer, geologist, petrophysicist, etc.) as I have in person and through media such as LinkedIn, you will find that many lament one key thing: Our sophisticated models have been reduced too much. Of course, I am generalizing and those are not the words they use; the lamentations come in many forms. The dissatisfaction with oversimplification is most easily observed as dis-taste for the type curve, the simplified model we use to predict upcoming new drills. (Yes, I know many of you will want to refer to them by their “proper” name: type well curve; I will be sticking with the colloquial version.) A simple meme posted on LinkedIn about type curves garnered one of the most engaged conversations I have seen amongst technical staff. The responses varied from something like “Thank God someone finally said this out loud” to comments such as “I don’t know anything better than type curves.” Most comments were closer to the former than the latter. What is even more remarkable is that our investors feel the same. In personal conversations, many of them refer to our type curves simply as “lies.” This perception, coupled with the historical lack of corporate returns, led investors away from our industry in droves. Many within the industry see it differently and want to blame the exodus on other factors such as oil and gas prices, climate change, competition from renewables, other environmental, social, and governance (ESG) issues, the pandemic, or OPEC’s unwillingness to “hold the bag” any longer. If you ask them, though, investors will tell you a simple answer: The unconventional business destroyed way too much capital and lied too much through the type curves. Why is it that both investors and technical staff are unhappy with our ability to accurately model future performance? Why can’t we deliver returns? The typical unconventional-focused oil and gas company has two models that are critical to the business. First is the subsurface model, with which we are all intimately familiar in its various forms, and the second is the corporate financial model, which is focused on cash flows, income, and assets/liabilities. It is unfortunate that the two models are separate. It means we must simplify one or both so they can communicate with each other. How can you observe this oversimplification while it is happening? It is happening when the finance staff say, “Please just give me a simple type curve and well count; I need to model, optimize, and account for debt/leverage, equity, and cash flows.” Meanwhile, the technical staff say, “Please just give me a CAPEX budget or a well count; I need to model, optimize, and account for well spacing, completion design, land constraints, and operational constraints.” Looking back, we know that the winner in this tug-of-war of competing needs was the type curve.


Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Minbo Zhang ◽  
Zhen Zhang ◽  
Dangyu Zhang ◽  
Delong Zou ◽  
Jinlei Du ◽  
...  

The microscopic pore and fissure structure is the key factor affecting the exploitation, storage, and migration of coalbed methane and coal spontaneous combustion tendency. For further research of the microstructure of deep soft coal rock, such as pores and fissures, the coal samples from the Yangdong mining area were qualitatively and quantitatively analyzed in terms of morphological characteristics, pore shape, pore specific surface area, pore volume, and pore diameter by a scanning electron microscope (SEM) and a low-temperature liquid nitrogen adsorption experiment. The results show that there are three major categories and five minor categories of pores with different genetic types, including metamorphic pore, exogenous pore, and mineral pore, and there are endogenous fissures, exogenous tensile fissures, and exogenous shear fissures developed in the coal body. According to the results of the low-temperature liquid nitrogen adsorption experiment, the hysteresis curves of coal samples can be divided into two types. The I type curve produces a loop. There is a “hysteresis loop” which is obvious, and there is an inflection point that is not obvious. The pore system is mainly composed of open pores. The II type curve has no adsorption back line and no obvious inflection point. The pore structure is mainly composed of an impermeable hole closed at one end. The BET specific surface area of coal samples ranges from 0.2810 to 4.7569 m2/g, with an average of 1.27984 m2/g. The BJH pore volume ranges from 0.002864 to 0.007377 cm3/g, with an average of 0.0041246 cm3/g. The average BJH pore diameter of coal samples ranges from 4.3935 to 20.1501 nm, with an average of 16.0313 nm. The pore specific surface area of coal is mainly contributed by micropores, and the transition pores contribute the most to pore volume. The distribution of pore volume in each pore section of a coal sample has the rule that the transition pore is larger than the micropore, and the micropore is larger than the mesopore, and the maximum ratio is 66.2%. The distribution of pore specific surface area has the rule that the micropore is larger than the transition pore, and the transition pore is larger than the mesopore. The maximum ratio is 91.2%.


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