Page 375 - Petrophysics 2E

PORE SIZE DISTRIBUTION 343

TABLE 5.1 B
LEAST SQUARES CALCULATION OF Pc(Y) AS A FUNCTION OF S(AVE) (x). THE EQUATION
IS: Y = (A + B-X)/(l + C*X)
N = 13
X Y x x Y XA2 YA2 XXYA2 XA2XY XA2 xYA2
0.827 4.135 3.418 0.683 17.099 14.134 2.825 11.683
0.769 4.865 3.740 0.591 23.664 18.192 2.875 13.986
0.711 5.879 4.180 0.505 34.557 24.569 2.972 17.468
0.653 7.071 4.619 0.427 50.004 32.661 3.017 21.334
0.595 8.284 4.932 0.354 68.624 40.857 2.936 24.325
0.566 9.885 5.600 0.321 97.722 55.357 3.172 31.358
0.538 11.843 6.366 0.289 140.248 75.394 3.422 40.530
0.480 15.293 7.337 0.230 233.866 112.202 3.520 53.831
0.422 18.370 7.751 0.178 337.450 142.392 3.271 60.085
0.393 23.818 9.362 0.154 567.316 222.991 3.680 87.650
0.364 35.518 12.934 0.133 1261.557 459.411 4.710 167.300
0.306 49.769 15.247 0.094 2476.926 758.827 4.671 232.473
0.277 79.219 21.980 0.007 6275.611 1741.210 6.098 483.110
NUM(1) = sum(X"2) x [sum(X x Y) x sums x Y"2) - sumY x sum(X"2 x YA2)] + sum(X x
Y) x sum^ x sum(X"2 x Y x 2) - sum@ x Y) x sum(~"2 x Y)] + sum(~"2 x Y) x [sumy x
sum(~"2 x Y) - sum^ x sum(X x ~"2)]
NUM(2) = N x [sum(X"2 x Y) x sum(X x Y"2) - sum(X x Y) x sum(X"2 x YA2)] + sumX x
sum^ x sum(~"2 x ~"2) -sum@ x Y) x sum@ x Y"')] + sum(X x Y) x [sum(X x Y) x sum(X x
Y) - sumY x sum(X"2 x Y)]
NUM(3) = N x [sum(X"2) x sum(X x Y"2) - sum(X x Y) x sum(X"2 x Y)] + sumX x [sumY x
sum(~"2 XY)-SU~X sum@ x ~"2)]+sum(x x Y) x [sud x sum(X x Y)-sumY x sum(~"2)]
x
DENOM= Nx[sum(XA2xY)xsum(X"2xY)-sum(XA2)xsum(XA2xYA2)]+sumXx[sumXx
sum(~"2 XY"~)] -sum[(X XY) xsum(x"2 x~)]+[sum(~ XY) xsum(X"2)-sumXxsum(~"2 XY)]
A NUM(l)/DENOM = -25.5296
B = NUM(Z)/DENOM = 17.6118
C = NUM(3)DENOM = -4.5064

Ritter and Drake developed the theory for the penetration of a
non-wetting phase into a porous medium [24]. Burdine et al. applied it
to reservoir rocks using mercury-injection capillary pressure curves [25].
The surface average area distribution of the pore, D(fi), by definition, is:

D(~)dr = dv, = Vpd& (5.54)

Differentiating Equation 5.54 and rearranging to obtain dr:

dr = (2) dPc (5.55)