... displacement experiment nonuniformity fluid dynamics dimensionless time upstream oil & gas pressure-drop profile injection rate relative permeability analytical solution displacement rock property nonuniformity core sample porosity detecting rock property nonuniformity pressure drop...

... expression for the dimensionless time, t D . Variables of this type have been called similarity variables by several authors. 9 Substitution of Eqs. 2 through 4 into Eq. 1 yields 9 , 19 Figure 1 Radial flow toward spherical sink wellbore. (11) q s f q...

... Copyright 1985, Society of Petroleum Engineers type-curve match production control compressibility linear flow drillstem testing average reservoir pressure dimensionless time production monitoring production rate viscosity equation traverse configuration reserves evaluation drillstem...

... line source finite-radius source reservoir 1 pressure transient analysis pressure response relative size dimensionless time line-source reservoir superposition artificial intelligence bessel function constant-pressure subregion finite-radius reservoir Pressure interference between...

... 28 9 1983 1 6 1985 1 6 1985 Copyright 1985, Society of Petroleum Engineers boundary flow regime 3 drillstem testing buildup data dimensionless time upstream oil & gas semilog straight line flow regime 4 straight line mbh function reservoir flow regime 2...

..., the first line having a slope of one-half, the second with a slope of two-thirds of the late-time trend. Specifically, they indicated that the half-slope occurs around the dimensionless time of (1) ( t D ) H = 5 ω e γ · λ . The results of our calculation...

... response during this period is given by the following expression: Figure 2 Dimensionless pressure vs. dimensionless time for k 1 / k 2 = 100; s 1 = s 2 = 0, and s 1 = s 2 = 5. (22) p w D ( t D ) = 1.151     log     t D + 0.4045. Eq. 22...

... in Appendix A . The dimensionless time of breakthrough in the first layer, t D 1 , is given by (10) t D 1 = ( γ γ − 1 ) [ 1 − ∑ i = 1 n Δ V p i · 1 − ( γ 2 − 1 γ 2 ) k d i k d 1...

... fracture system observation well matrix system well response early time type curve warren approximation reservoir characterization hydraulic fracturing production monitoring dimensionless time reservoir surveillance complex reservoir reservoir drillstem/well testing production control...

... wall and sensible heat requirements within the zone, it is possible to estimate the channel size from the time of steam breakthrough at a producer. 10 3 1983 29 11 1983 26 8 1983 1 10 1984 1 10 1984 Copyright 1984, Society of Petroleum Engineers dimensionless time...

... optimal injection policy costate equation dimensionless distance capillary number artificial intelligence boundary condition oil saturation viscosity dimensionless time surfactant concentration flow in porous media fluid dynamics chemical cost injection policy oil recovery equation...

... characteristic velocity reservoir simulation petroleum engineer journal flow rate production monitoring dimensionless time Gas injection is increasingly being applied as a secondary or tertiary recovery technique. In many applications injection gas is not directly miscible...

... kpa compressibility grid system gridblock icvf fracture source sink hydraulic fracturing ellipse psia equation upstream oil & gas flow rate dimensionless time flow in porous media numerical reservoir simulation drillstem/well testing reservoir boundary reservoir simulation...

... in porous media dimensionless time fracture conductivity dimensionless fracture conductivity constant-conductivity solution well response petroleum engineer journal fracture permeability samaniego-v early time pressure transient analysis unequal wing length conductivity agarwal upstream oil...

... of a fracture. The existence of the fracture would have to be known a priori or from independent measurements such as single-well tests. The dimensionless time is defined as (3) t D L f = 3.6 × 10 − 6 k t ϕ c t μ L f 2 , where ϕ is porosity...

... of the internal boundary ellipse). Tabular and graphical forms of the dimensionless cumulative water influx and influx rate are presented as a function of the dimensionless time for various internal boundary geometries ranging from a e /b e = 1, which corresponds to a circle, to a a e /b e = ∞, which corresponds...

... 1980 28 1 1981 25 2 1981 1 6 1981 1 6 1981 Copyright 1981, Society of Petroleum Engineers flow in porous media drillstem/well testing fracture length constant-pressure production hydraulic fracturing fluid dynamics dimensionless time drillstem testing one-quarter...

.... 2 is a graph of the dimensionless flow rate vs. dimensionless time computed with the wellbore radius corrected to an effective radius for positive skin factor. For very small flow times ( t D < 10), the type-curve match would be in error for wells with nonzero skin. Figure 2...

... regarding the determination of the drainage volume by type-curve matching appear to be unrealistic. 16 7 1979 3 10 1980 17 7 1979 1 2 1981 1 2 1981 Copyright 1981, Society of Petroleum Engineers Figure 2 Dimensionless wellbore pressure drop vs. dimensionless time...

...Heber Cinco L.; F. Samaniego V.; N. Dominguez A. A mathematical model was developed to study the transient behavior of a well with a finite-conductivity vertical fracture in an infinite slab reservoir. For values of dimensionless time of interest, to >10, the dimensionless wellbore pressure, p...