Methods for horizontal well spacing calculation in tight gas reservoirs are still adversely affected by the complexity of related control factors,such as strong reservoir heterogeneity and seepage mechanisms.In this s...Methods for horizontal well spacing calculation in tight gas reservoirs are still adversely affected by the complexity of related control factors,such as strong reservoir heterogeneity and seepage mechanisms.In this study,the stress sensitivity and threshold pressure gradient of various types of reservoirs are quantitatively evaluated through reservoir seepage experiments.On the basis of these experiments,a numerical simulation model(based on the special seepage mechanism)and an inverse dynamic reserve algorithm(with different equivalent drainage areas)were developed.The well spacing ranges of Classes I,II,and III wells in the Q gas field are determined to be 802–1,000,600–662,and 285–400 m,respectively,with their average ranges as 901,631,and 342.5 m,respectively.By considering both the pairs of parallel well groups and series well groups as examples,the reliability of the calculation results is verified.It is shown that the combination of the two models can reduce errors and provide accurate results.展开更多
Multi-stage hydraulic fracturing of horizontal wells is the main stimulation method in recovering gas from tight shale gas reservoirs, and stage spacing deter- mination is one of the key issues in fracturing design. T...Multi-stage hydraulic fracturing of horizontal wells is the main stimulation method in recovering gas from tight shale gas reservoirs, and stage spacing deter- mination is one of the key issues in fracturing design. The initiation and propagation of hydraulic fractures will cause stress redistribution and may activate natural fractures in the reservoir. Due to the limitation of the analytical method in calculation of induced stresses, we propose a numerical method, which incorporates the interaction of hydraulic fractures and the wellbore, and analyzes the stress distri- bution in the reservoir under different stage spacing. Simulation results indicate the following： （1） The induced stress was overestimated from the analytical method because it did not take into account the interaction between hydraulic fractures and the horizontal wellbore. （2） The hydraulic fracture had a considerable effect on the redis- tribution of stresses in the direction of the horizontal wellbore in the reservoir. The stress in the direction per- pendicular to the horizontal wellbore after hydraulic frac- turing had a minor change compared with the original in situ stress. （3） Stress interferences among fractures were greatly connected with the stage spacing and the distance from the wellbore. When the fracture length was 200 m, and the stage spacing was 50 m, the stress redistribution due to stage fracturing may divert the original stress pat- tern, which might activate natural fractures so as to generate a complex fracture network.展开更多
A flow mathematical model with multiple horizontal wells considering interference between wells and fractures was established by taking the variable width conductivity fractures as basic flow units.Then a semi-analyti...A flow mathematical model with multiple horizontal wells considering interference between wells and fractures was established by taking the variable width conductivity fractures as basic flow units.Then a semi-analytical approach was proposed to model the production performance of full-life cycle in well pad and to investigate the effect of fracture length,flow capacity,well spacing and fracture spacing on estimated ultimate recovery(EUR).Finally,an integrated workflow is developed to optimize drilling and completion parameters of the horizontal wells by incorporating the productivity prediction and economic evaluation.It is defined as nested optimization which consists of outer-optimization shell(i.e.,economic profit as outer constraint)and inner-optimization shell(i.e.,fracturing scale as inner constraint).The results show that,when the constraint conditions aren’t considered,the performance of the well pad can be improved by increasing contact area between fracture and formation,reducing interference between fractures/wells,balancing inflow and outflow between fracture and formation,but there is no best compromise between drilling and completion parameters.When only the inner constraint condition is considered,there only exists the optimal fracture conductivity and fracture length.When considering both inner and outer constraints,the optimization decisions including fracture conductivity and fracture length,well spacing,fracture spacing are achieved and correlated.When the fracturing scale is small,small well spacing,wide fracture spacing and short fracture should be adopted.When the fracturing scale is large,big well spacing,small fracture spacing and long fracture should be used.展开更多
In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical...In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .展开更多
基金the Major Science and Technology Project of Southwest Oil and Gas Field Company(2022ZD01-02).
文摘Methods for horizontal well spacing calculation in tight gas reservoirs are still adversely affected by the complexity of related control factors,such as strong reservoir heterogeneity and seepage mechanisms.In this study,the stress sensitivity and threshold pressure gradient of various types of reservoirs are quantitatively evaluated through reservoir seepage experiments.On the basis of these experiments,a numerical simulation model(based on the special seepage mechanism)and an inverse dynamic reserve algorithm(with different equivalent drainage areas)were developed.The well spacing ranges of Classes I,II,and III wells in the Q gas field are determined to be 802–1,000,600–662,and 285–400 m,respectively,with their average ranges as 901,631,and 342.5 m,respectively.By considering both the pairs of parallel well groups and series well groups as examples,the reliability of the calculation results is verified.It is shown that the combination of the two models can reduce errors and provide accurate results.
基金supported by the Natural Science Foundation of China (Grant No. 51490653, Basic Theoretical Research of Shale Oil and Gas Effective Development)
文摘Multi-stage hydraulic fracturing of horizontal wells is the main stimulation method in recovering gas from tight shale gas reservoirs, and stage spacing deter- mination is one of the key issues in fracturing design. The initiation and propagation of hydraulic fractures will cause stress redistribution and may activate natural fractures in the reservoir. Due to the limitation of the analytical method in calculation of induced stresses, we propose a numerical method, which incorporates the interaction of hydraulic fractures and the wellbore, and analyzes the stress distri- bution in the reservoir under different stage spacing. Simulation results indicate the following： （1） The induced stress was overestimated from the analytical method because it did not take into account the interaction between hydraulic fractures and the horizontal wellbore. （2） The hydraulic fracture had a considerable effect on the redis- tribution of stresses in the direction of the horizontal wellbore in the reservoir. The stress in the direction per- pendicular to the horizontal wellbore after hydraulic frac- turing had a minor change compared with the original in situ stress. （3） Stress interferences among fractures were greatly connected with the stage spacing and the distance from the wellbore. When the fracture length was 200 m, and the stage spacing was 50 m, the stress redistribution due to stage fracturing may divert the original stress pat- tern, which might activate natural fractures so as to generate a complex fracture network.
基金Supported by the China National Science and Technology Major Project(2016ZX05037,2017ZX05063).
文摘A flow mathematical model with multiple horizontal wells considering interference between wells and fractures was established by taking the variable width conductivity fractures as basic flow units.Then a semi-analytical approach was proposed to model the production performance of full-life cycle in well pad and to investigate the effect of fracture length,flow capacity,well spacing and fracture spacing on estimated ultimate recovery(EUR).Finally,an integrated workflow is developed to optimize drilling and completion parameters of the horizontal wells by incorporating the productivity prediction and economic evaluation.It is defined as nested optimization which consists of outer-optimization shell(i.e.,economic profit as outer constraint)and inner-optimization shell(i.e.,fracturing scale as inner constraint).The results show that,when the constraint conditions aren’t considered,the performance of the well pad can be improved by increasing contact area between fracture and formation,reducing interference between fractures/wells,balancing inflow and outflow between fracture and formation,but there is no best compromise between drilling and completion parameters.When only the inner constraint condition is considered,there only exists the optimal fracture conductivity and fracture length.When considering both inner and outer constraints,the optimization decisions including fracture conductivity and fracture length,well spacing,fracture spacing are achieved and correlated.When the fracturing scale is small,small well spacing,wide fracture spacing and short fracture should be adopted.When the fracturing scale is large,big well spacing,small fracture spacing and long fracture should be used.
文摘In contrast to the solutions of applied mathematics to Zeno’s paradoxes, I focus on the concept of motion and show that, by distinguishing two different forms of motion, Zeno’s apparent paradoxes are not paradoxical at all. Zeno’s paradoxes indirectly prove that distances are not composed of extensionless points and, in general, that a higher dimension cannot be completely composed of lower ones. Conversely, lower dimensions can be understood as special cases of higher dimensions. To illustrate this approach, I consider Cantor’s only apparent proof that the real numbers are uncountable. However, his widely accepted indirect proof has the disadvantage that it depends on whether there is another way to make the real numbers countable. Cantor rightly assumes that there can be no smallest number between 0 and 1, and therefore no beginning of counting. For this reason he arbitrarily lists the real numbers in order to show with his diagonal method that this list can never be complete. The situation is different if we start with the largest number between 0 and 1 (0.999…) and use the method of an inverted triangle, which can be understood as a special fractal form. Here we can construct a vertical and a horizontal stratification with which it is actually possible to construct all real numbers between 0 and 1 without exception. Each column is infinite, and each number in that column is the starting point of a new triangle, while each row is finite. Even in a simple sine curve, we experience finiteness with respect to the y-axis and infinity with respect to the x-axis. The first parts of this article show that Zeno’s assumptions contradict the concept of motion as such, so it is not surprising that this misconstruction leads to contradictions. In the last part, I discuss Cantor’s diagonal method and explain the method of an inverted triangle that is internally structured like a fractal by repeating this inverted triangle at each column. The consequence is that we encounter two very different methods of counting. Vertically it is continuous, horizontally it is discrete. While Frege, Tarski, Cantor, Gödel and the Vienna Circle tried to derive the higher dimension from the lower, a procedure that always leads to new contradictions and antinomies (Tarski, Russell), I take the opposite approach here, in which I derive the lower dimension from the higher. This perspective seems to fail because Tarski, Russell, Wittgenstein, and especially the Vienna Circle have shown that the completeness of the absolute itself is logically contradictory. For this reason, we agree with Hegel in assuming that we can never fully comprehend the Absolute, but only its particular manifestations—otherwise we would be putting ourselves in the place of the Absolute, or even God. Nevertheless, we can understand the Absolute in its particular expressions, as I will show with the modest example of the triangle proof of the combined horizontal and vertical countability of the real numbers, which I developed in rejection of Cantor’s diagonal proof. .
