scholarly journals A PROPERTY OF CLOSED FINITE TYPE CURVES

2008 ◽  
Vol 77 (1) ◽  
pp. 145-149
Author(s):  
MIROSLAVA PETROVIĆ-TORGAŠEV

AbstractIn the paper we prove that any closed finite type curve in the Euclidean space En(n≥2) lies in a null-space of a non-trivial polynomial P=P(x1,…,xn) of variables x1,…,xn, and thus lies on a surface of finite degree.

2019 ◽  
Vol 485 (1) ◽  
pp. 7-10
Author(s):  
А. N. Agadzhanov

Peano-type curves in multidimensional Euclidean space are considered in terms of number theory. In contrast to curves constructed by D. Hilbert, H. Lebesgue, V. Sierpinski, and others, this paper presents results showing that each such curve is a continuous image of universal (shared by all curves) nowhere dense perfect subsets of the interval [0, 1] with a zero s-dimensional Hausdorff measure that consist of only Liouville numbers. An example of a problem in which a pair of continuous functions controlling the behavior of an oscillating system generates a Peano-type curve in the plane is given.


Author(s):  
P. Noverri

Delta Mahakam is a giant hydrocarbon block which is comprised two oil fields and five gas fields. The giant block has been considered mature after production for more than 40 years. More than 2,000 wells have been drilled to optimize hydrocarbon recovery. From those wells, a huge amount of production data is available and documented in a well-structured manner. Gaining insight from this data is highly beneficial to understand fields behavior and their characteristics. The fields production characterization is analyzed with Production Type-Curve method. In this case, type curves were generated from production data ratio such as CGR, WGR and GOR to field recovery factor. Type curve is considered as a simple approach to find patterns and capture a helicopter view from a huge volume of production data. Utilization of business intelligence enables efficient data gathering from different data sources, data preparation and data visualization through dashboards. Each dashboard provides a different perspective which consists of field view, zone view, sector view and POD view. Dashboards allow users to perform comprehensive analysis in describing production behavior. Production type-curve analysis through dashboards show that fields in the Mahakam Delta can be grouped based on their production behavior and effectively provide global field understanding Discovery of production key information from proposed methods can be used as reference for prospective and existing fields development in the Mahakam Delta. This paper demonstrates an example of production type-curve as a simple yet efficient method in characterizing field production behaviors which is realized by a Business Intelligent application


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.


2019 ◽  
Vol 9 (1) ◽  
pp. 206
Author(s):  
Guofeng Han ◽  
Yuewu Liu ◽  
Wenchao Liu ◽  
Dapeng Gao

Pressure communication between adjacent wells is frequently encountered in multi-stage hydraulic fractured shale gas reservoirs. An interference test is one of the most popular methods for testing the connectivity of a reservoir. Currently, there is no practical analysis model of an interference test for wells connected by large fractures. A one-dimensional equation of flow in porous media is established, and an analytical solution under the constant production rate is obtained using a similarity transformation. Based on this solution, the extremum equation of the interference test for wells connected by a large fracture is derived. The type-curve of pressure and the pressure derivative of an interference test of wells connected by a large fracture are plotted, and verified against interference test data. The extremum equation of wells connected by a large fracture differs from that for homogeneous reservoirs by a factor 2. Considering the difference of the flowing distance, it can be concluded that the pressure conductivity coefficient computed by the extremum equation of homogeneous reservoirs is accurate in the order of magnitude. On the double logarithmic type-curve, as time increases, the curves of pressure and the pressure derivative tend to be parallel straight lines with a slope of 0.5. When the crossflow of the reservoir matrix to the large fracture cannot be ignored, the slope of the parallel straight lines is 0.25. They are different from the type-curves of homogeneous and double porosity reservoirs. Therefore, the pressure derivative curve is proposed to diagnose the connection form of wells.


SPE Journal ◽  
2012 ◽  
Vol 18 (01) ◽  
pp. 97-113 ◽  
Author(s):  
Ayala H Luis F. ◽  
Peng Ye

Summary Rate-time decline-curve analysis is the technique most extensively used by engineers in the evaluation of well performance, production forecasting, and prediction of original fluids in place. Results from this analysis have key implications for economic decisions surrounding asset acquisition and investment planning in hydrocarbon production. State-of-the-art natural gas decline-curve analysis heavily relies on the use of liquid (oil) type curves combined with the concepts of pseudopressure and pseudotime and/or empirical curve fitting of rate-time production data using the Arps hyperbolic decline model. In this study, we present the analytical decline equation that models production from gas wells producing at constant pressure under boundary-dominated flow (BDF) which neither employs empirical concepts from Arps decline models nor necessitates explicit calculations of pseudofunctions. New-generation analytical decline equations for BDF are presented for gas wells producing at (1) full production potential under true wide-open decline and (2) partial production potential under less than wide-open decline. The proposed analytical model enables the generation of type-curves for the analysis of natural gas reservoirs producing at constant pressure and under BDF for both full and partial production potential. A universal, single-line gas type curve is shown to be straightforwardly derived for any gas well producing at its full potential under radial BDF. The resulting type curves can be used to forecast boundary-dominated performance and predict original gas in place without (1) iterative procedures, (2) prior knowledge of reservoir storage properties or geological data, and (3) pseudopressure or pseudotime transformations of production data obtained in the field.


2010 ◽  
Vol 47 (6) ◽  
pp. 1163-1170 ◽  
Author(s):  
Cetin Camci ◽  
H. Hilmi Hacisalihoglu

2020 ◽  
Vol 17 (06) ◽  
pp. 2050088 ◽  
Author(s):  
Tongchang Liu ◽  
Donghe Pei

In this paper, we study mixed-type curves in Minkowski 3-space. Mixed-type curves are regular curves, and there are both non-lightlike points and lightlike points in a mixed-type curve. For non-lightlike curves and null curves in Minkowski 3-space, we can study them by a Frenet frame or a Cartan frame, respectively. But for mixed-type curves, the two frames will not work. As far as we know, no one has yet given a frame to study them in Minkowski 3-space. So, we give the lightcone frame in order to provide a tool for studying this type curves in mathematical and physical research. As an application of the lightcone frame, we define an evolute of a mixed-type curve. We also give some examples to show the evolutes.


Symmetry ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1076 ◽  
Author(s):  
Sun Mi Jung ◽  
Young Ho Kim ◽  
Jinhua Qian

In studying spherical submanifolds as submanifolds of a round sphere, it is more relevant to consider the spherical Gauss map rather than the Gauss map of those defined by the oriented Grassmannian manifold induced from their ambient Euclidean space. In that sense, we study ruled surfaces in a three-dimensional sphere with finite-type and pointwise 1-type spherical Gauss map. Concerning integrability and geometry, we set up new characterizations of the Clifford torus and the great sphere of 3-sphere and construct new examples of spherical ruled surfaces in a three-dimensional sphere.


2011 ◽  
Vol 105-107 ◽  
pp. 1539-1546
Author(s):  
Chun Yan Zhao ◽  
Guo Yong Zheng

Based on dynamic triaxial test results of saturated soft clay, influence factors and variations on accumulated deformation were analyzed. The Parr’s equation on accumulated deformation was modified to create an attenuation-type curve model on accumulated deformation of saturated normal consolidation clay. In this model, dynamic strength was introduced and a new parameter called equivalent dynamic stress level was added. Besides, based on comparative analysis on variations between failure-type and attenuation-type curves, a failure-type curve model was created on accumulated deformation of saturated normal consolidation clay. The two models can take cycle number, coupling of static and dynamic deviator stress, consolidation way into consideration. The models were verified by test results. The correlation coefficients are more than 0.96 for optimization of test results based on the two models, and there is good agreement between optimized and test curves, which show that the two models are suitable to predict variations of accumulated deformation under different loading cases and consolidation ways. In order to improve prediction accuracy, it is suggested that loading cases and consolidation ways should be consistent with in-situ conditions when dynamic triaxial tests being used to determine the constants in the models.


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