System for computing the radius of investigation in a radial, composite reservoir system

摘要

A system for calculating the radius of investigation of a radial, composite reservoir has a processor with a clock, a display, and an electronic input coupled to the processor. The system divides the reservoir into a predetermined number (n) of concentric regions, and the processor is programmed to calculate periodically the radius of investigation based a starting time or elapsed time, and data relating to the reservoir rock, fluids, and geometries of each of the n regions. The processor computes the radius of investigation using at least one of Equations (1), (2), and (6) through (12) set forth in the specification, if using the System of U.S. Oilfield Units, or using an equivalent equation if using other units. These equations account for the effects of variations of both permeability and storativity in composite reservoirs on the radius of investigation with elapsed time.

主权项

1. A system for calculating the radius of investigation of a radial, composite reservoir, said system comprising:
a processor, a memory electronically coupled to said processor, a clock for providing a starting time and an elapsed time to the processor, a display electronically coupled to said processor, and an electronic input, coupled to said processor, for entering data; wherein said processor is programmed (a) to divide the reservoir into a predetermined number (n) of concentric regions; (b) to store in memory, for each region (n), data relating to the reservoir rock, fluids, and geometries of each of the n regions; and (c) to calculate the current radius of investigation in the reservoir for a plurality of selected regions (n) based upon the stored data for each such region (n) and a starting elapsed time, using at least one of Equations (1), (2), and (6) through (12) as expressed in the following:rij=ηj[∑I=1j-2⁢RI(1ηI+1-1ηI)]+Rj-1⁡(1-ηjηj-1)+C⁢ηj⁢Δ⁢⁢t(1)where:
rij is the radius of investigation (ft.) which is located in the jth concentric region; η is the total number of concentric regions in a composite system; ηj is the hydraulic diffusivity in the jth concentric region, determined by equation (3) below; Rj is the location of the boundary between the jth and the (j+1)th concentric regions; j is an arbitrary region (the boundary of the region of influence is located in the jth region; ηI and ηI+1 are the hydraulic diffusivities in the Ith and (I+1)th concentric regions; I is an indexing (also known as dummy) variable, which is temporarily utilized while performing the calculations in the summation loop in Equation (1); Rj−1 is the location of the boundary between the (j−I)th and the jth concentric regions; ηj−1 is the hydraulic diffusivity in the (j−I)th region; C is a constant (0.0566950796 in the case of the System of Oilfield Units); and Δt is the elapsed time in hours since the disturbance has been initiated at the well due to production or injectionORri⁢⁢j=ηj⁡[R1⁡(1η2-1η1)+R2⁡(1η3-1η2)+…+Rj-2⁡(1ηj-1-1ηj-2)]+Rj-1⁡(1-ηjηj-1)+C⁢ηj⁢Δ⁢⁢t(2)ORri⁢,j=MjFj⁡[∑I=1j-2⁢RI⁡(FI+1FI+1-FIMI)]+Rj-1⁡(1-MjFj⁢Fj-1Mj-1)+C⁢Mj⁢Δ⁢⁢tFj(6) ORri⁢,j=MjFj⁡[R1⁡(F2M2-F1M1)+R2⁡(F3M3-F2M2)+…+Rj-2⁡(Fj-1Mj-1-Fj-2Mj-2)]+Rj-1⁡(1-MjFj⁢Fj-1Mj-1)+C⁢Mj⁢Δ⁢⁢tFj(7)ORri⁢⁢1=C⁢η1⁢Δ⁢⁢t=C⁢M1⁢Δ⁢⁢tF1(8)ORri⁢⁢2=R1⁡(1-η2η1)+C⁢η2⁢Δ⁢⁢t=R1⁡(1-M2F2⁢F1M1)+C⁢M2⁢Δ⁢⁢tF2(9)ORri⁢⁢3=⁢R1⁢η3⁢(1η2-1η1)+R2⁡(1-η3η2)+C⁢η3⁢Δ⁢⁢t=⁢R1⁢M3F3⁢(F2M2-F1M1)+R2⁡(1-M3F3⁢F2M2)+C⁢M3⁢Δ⁢⁢tF3(10)ORri⁢⁢4=⁢η4⁡[R1⁡(1η2-1η1)+R2⁡(1η3-1η2)]+⁢R3⁡(1-η4η3)+C⁢η4⁢Δ⁢⁢t=⁢M3F3⁡[R1⁡(F2M2-F1M1)+R2⁡(F3M3-F2M2)]+⁢R3⁡(1-M4F4⁢F3M3)+C⁢M4⁢Δ⁢⁢tF4(11)ORΔ⁢⁢TRj=1C2⁡[R1η1+∑I=2j⁢RI-RI-1ηI]2=1C2⁡[R1⁢F1M1+∑I=2j⁢{(RI-RI-1)⁢FIMI}]⁢.(12)