Layered petroleum reservoirs with cross-flows

Studied is a cylindrical reservoir consisting of three layers: a water-containing bottom layer, and two oil-containing top layers from whose upper layer oil is produced. For its solution, a corrected version of the finite Hankel transform for Neumann-Neumann boundary conditions was used together with numerical inversion of the Laplace transform. The effects of the water zone on the unsteady state pressure in the reservoir were evaluated at distances away from the well and at the well-bore itself. We found that the vertical pressure drop increases gradually with time and is more significant in the vicinity of the well-bore. For constant production and at any time t, smaller reservoirs experience higher pressure drops than larger ones. For the reservoir investigated, we found that for nondimensional time t _Dw <10⁴ the presence of a second fluid (water) has no effect on the pressure drop. Of all the formation and fluid properties investigated, porosity has the largest effect on pressure.Nomenclature c ₁, c ₂ Oil and water compressibilities, vol/vol/atm, vol/vol/psi - h Height of water zone from bottom of reservoir, cm, ft - h _D h/r _w , non-dimensional - H Height of reservoir, cm, ft - H _D H/r _w, non-dimensional - J ₀, J ₁ Bessel functions of the first kind, zero and first-order - K _r2, K _r1 Oil and water zones, horizontal permeabilities, darcies, md - K _z2, K _z1 Oil and water zones, vertical permeabilities, darcies, md - k ₁ n=1, 2, 3... - k ₂ n=1, 2, 3... - k _1,0 - k _2,0 - p(r, z, t) P(r, z, 0)–P(r, z, t), atm, psi - P(r, z, t) Pressure at any layer in the reservoir, atm, psi - P(r, z, 0) Initial pressure at any layer in the reservoir, atm, psi - P _D , non-dimensional - q Constant production rate of well, cc/sec, barrels/day - r Radius of reservoir, cm, ft - r _D r/r _w , non-dimensional - r _e Drainage radius, cm, ft - r _eD re/r _w , non-dimensional - r _w Well-bore radius, cm, ft - t Time, sec, hr - _Dw (k _r2 t)/( _{2 2} c ₂ r _w ² ), non-dimensional - Y ₀, Y ₁ Bessel functions of the second kind, zero and first-order - z Distance z measured vertically upward from bottom of reservoir, cm, ft - Z _D z/r _w , non-dimensional - z ₁ Height of the bottom of the producing layer, cm, ft - z _1D z ₁/r _w , non-dimensional - z ₂ Height of the top of the producing layer, cm, ft - z _2,D z ₂/r _w , non-dimensional - _n nth positive root of equation (18) - ₁ k _z1/k _r1, non-dimensional - ₂ k _z2/k _r2, non-dimensional - _{1 1 1} c ₁/k _r1, hydraulic diffusivity of layer I - _{2 2 2} c ₂/k _r2, hydraulic diffusivity of layers II and III - ₂, ₁ Viscosity of oil and water, cp, cp - _{n n} /r _w , l/cm, l/ft - ₂, ₁ Porosity of oil and water-filled zones, fraction - ( ₁/ ₂) (k _z2/k _z1), non-dimensional     

Synthesis and photochemical degradation of N-arylmethyl derivatives of the herbicide 3-amino-1,2,4-triazole

Reaction of an arylmethyl halide with 3-amino-1,2,4-triazole ( 1 ) allows the preparation of the three N-aryl-methyl derivatives of 1 bearing the substituent on the heterocyclic nitrogen atoms. In basic medium (methoxide anion in DMF or methanol, or in benzene by phase transfer catalysis), the isomers 3 and 5 substituted at N-1 and N-2 respectively are obtained, while the isomer 4 is isolated from neutral medium (DMF). The isomers 3 and 4 may be also prepared by cyclization of appropriate formylguanidinium derivatives. 3-Arylmethylamino-1,2,4-triazoles 2 may be obtained through reaction of 3-chloro-1,2,4-triazole ( 6 ) with arylmethylamines. Photolysis of the N-arylmethyl-3-amino-1,2,4-triazoles 2-5 in methanol or water-methanol mixture, induces homolytic and heterolytic cleavage of the arylmethyl-C-N bond giving rise to 3-amino-1,2,4-triazole ( 1 ). Thus, compounds 2-5 with arylmethyl groups able to absorb solar light may be considered as potential photoactivatable herbicides.     

q-Analogue of the Watanabe Unitary Transform Associated to the q-Continuous Gegenbauer Polynomials

We associate a family of Hilbert spaces H _q ^2;(D) of analytic functions on the unit disk D=z :|z|<1 the q-continuous Gegenbauer polynomials C _n (x;q) on the interval]–1;1[ and give a q-analogue of the unitary integral transform that Watanabe constructed from the Hilbert space L ²(]–1;1[;(1–x ²)^– dx onto the weighted Hilbert space H ^2;(D).     

Intra-Channel Collision of Dual-Power Law Optical Solitons

The intra-channel collision of optical solitons, with dual-power law nonlinearity, is studied in this paper by the aid of quasi-particle theory. The perturbation terms that are considered in this paper are the nonlinear gain and saturable amplifiers along with filters. The suppression of soliton-soliton interaction, in presence of these perturbation terms, is acheived. The numerical simulations support the quasi-particle theory. OCIS codes: 060.2310; 060.4510; 060.5530; 190.3270; 190.4370.     

Singular Value Decomposition Solution of the Schrödinger Equation in the Presence of Exchange Terms

A new numerical method of solving integro-differential equations appearing in the theory of atomic and nuclear scattering systems has been devised. It is termed Singular Value Decomposition Method (SVD). It consists in expanding the exchange kernel into a number of separable terms by means of the Singular Value Decomposition and then iterating over the remainder. In this paper, we extend our SVD method to the scattering of low energy electron-helium which has been the subject of interest, both theoretically and experimentally. We compare our results with the Moments Method which is widely used. The Moments Method consists of making an expansion of the solution into an especially favorable basis that takes care of the non-exchange part of the Hamiltonian.     

Photocatalytic degradation of an azo reactive dye,Reactive Yellow 84, in water using an industrial titanium dioxide coated media

The photocatalytic degradation of an azo reactive dye, Reactive Yellow 84 (RY84), in aqueous solutions using industrial titanium dioxide coated non-woven paper was studied. The experiments were carried out to investigate the factors that influence the dye photocatalytic degradation, such as adsorption, initial concentration of dye, temperature, and solution pH. The experimental results show that adsorption is an important parameter controlling the apparent kinetics constant of degradation. The photocatalytic degradation rate was favored by a high concentration of solution in respect to Langmuir–Hinshelwood model. The degradation was enhanced by the temperature and was favored in acidic pH range.     

Das Picard-Prinzip und verwandte Fragen bei Störung von harmonischen Räumen

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