Semi-analytical model of multiple fractured horizontal well across a discontinuity in a linear composite reservoir

Many geologic settings can be treated as linear composite (LC) reservoirs, where linear discontinuities divide the formation into multiple zones with different properties. Although there have been many studies on pressure behavior of production wells in an LC reservoir, most of the studies focus on vertical wells. The modeling of multiple fractured horizontal (MFH) wells in an LC reservoir remains limited. The goal of the present work is to propose a general semi-analytical model of an MFH well situated anywhere in a two-zone LC reservoir. This model can take into account the situation where the horizontal well intersects with the discontinuity and hydraulic fractures are distributed in both the two zones. According to the point-source function method, the semi-analytical solution for an MFH well in LC reservoirs is derived by using superposition principle, fracture discrete scheme and numerical inversion algorithm of Laplace transformation. Type curves of MFH wells far away from a discontinuity and across a discontinuity in an LC reservoir are drawn and analysed, respectively. Furthermore, the effects of some parameters on pressure behavior and rate response of an MFH well across a discontinuity are studied. This research finds that the pressure behavior and rate response of an MFH well across a discontinuity are significantly affected by the well location, properties of hydraulic fractures and formation properties.

Pressure Transient Analysis for a Finite-Conductivity Fractured Vertical Well Near a Leaky Fault in Anisotropic Linear Composite Reservoirs

Geologic discontinuities usually exist in subsurface permeable formations, where multiple reservoir regions with distinct properties are separated by linear leaky faults. This kind of heterogeneous reservoir is usually called a linear composite reservoir. Although many analytical/semi-analytical linear composite models have been established to investigate the pressure behavior for linear composite reservoirs, almost all of these models were aimed at vertical wells without hydraulic fracturing and there are few analytical/semi-analytical models of fractured vertical wells in linear composite reservoirs. This paper first derives the Laplace-space point source solution for anisotropic linear composite systems separated by a partially communicating fault. Then, superposition principle and fracture discrete scheme are employed to acquire the semi-analytical solution for finite-conductivity fractured vertical (FCFV) wells in anisotropic linear composite reservoirs with a fault. The proposed solution is validated against numerical solutions under different reservoir scenarios. The characteristic of the pressure behavior for an FCFV well in anisotropic linear composite reservoirs with a fault is discussed in detail. The proposed model can be employed to obtain accurate pressure response with high computational efficiency. It is a good start to further develop analytical/semi-analytical models for other complex well types in an anisotropic linear composite reservoir with a fault.

The Inverse Precise Placement of Numbers Based at Pythagoras 1:3 and the Precise Configuration of Numbers as the Basis of a Unified Theorem That Binds the Physics of Mass, Space, Energy and the Torque Power (Inertia) That Sustains the Finite Universe.

This paper is based on the precise inverse cone of Pythagoras 1:3. As in section 1 of this paper, all mathematics presented in this paper is by precise mathematics equations and the author has maintained by proof that the base numbers constant from which all physics constants can be derived are -1 to 19 ( the value 6 is as per this paper is the constant for expansion of all bounded space and 19 is the patent “end value” of the base constant numbers as shown in section 1 and referenced in this section11). Numbers as created and as placed at the cone of Pythagoras 1:3 are precise manifestation of the numbers of linear composite. However, this paper shows that the invention of designated angles (Trigonometry) is an approximate arbitrary arrangement invented by man, based on the created fixed angle of 90 degrees and is certainly flawed as shown here in this paper. Likewise, any attempts to measure curvature by linear numbers is fraught with much error. The author maintains that “If the atomic density and structure of meteorites from far space have the same configuration as those found on this earth, then by all created logic , these numbers configuration presented in these two papers and the book (The God of Papa Einstein and Sir Isaac Newton) are a constant unified theorem of all the space and mass ( Quantum mechanics) in the universe”. Einstein’s Theory of relativity and all other interstellar phenomena are not addressed in the context of this paper because all this is observed science phenomena and not a physical science, and this paper deals with precise numbers configuration as in the section 1 of the paper. Einstein’s relativity is a real observed natural phenomenon, not science by itself, it is a natural aberration of the fact that observed relativity is due to inherent curvature and linear relationship between any two points in the universe and because of the spiral progression of curved space. Neither does light bend it appears to bend, nor does time really dilate in real terms even though it is a real observed phenomenon, neither numbers or distances dilate by any continuum, unfortunately, that is why Einstein’s misconception about time dilation is a Theory and will always be Theory.