PNG 301
Introduction to Petroleum and Natural Gas Engineering Hyperbolic Decline (0<b<1)


If b is in the range, 0<b<1 , then the integration of Equation 4.68 and Equation 4.69 results in the rate-time relationship:

q o = q oi ( 1+b D i t ) ( 1 b )
Equation 4.73

While a second integration with respect to time results in the rate-cumulative production relationship:

q o ( 1b ) = q oi ( 1b ) N p D i ( 1b ) q oi b
Equation 4.74

When the constant b is in the range 0<b<1 , we refer to the resulting production decline as Hyperbolic Decline. In hyperbolic decline, we have all three parameters, q oi , D i , and b , with which to match the field data.