A new concept f-or transient pressure buildup analysis is developed based upon the following:
A different method for calculating pressure drop in a reservoir and across the skin.
Any measured buildup curve is matched (after wellbore and storage effects have died out) with a rectangular hyperbolic equation specific for that buildup.
The asymptote to the time axis of the specific hyperbolic equation is final static buildup pressure.
The maximum slope of the MDH plot using the calculated points from the rectangular hyperbolic equation is taken to be m.
A direct relationship is developed between the buildup time to maximum slope on the calculated pH plot and the actual distance to the radius of drainage at the time of shutin.
The methods for determining m and the calculated distance to the effective drainage radius at the time of shutin are empirical.
A new concept for transient pressure behavior is presented whereby in a producing well the total presented whereby in a producing well the total pressure drawdown from the radius of drainage to the pressure drawdown from the radius of drainage to the wellbore is divided into two parts:
the pressure drop from the drainage radius to the wellbore (described by Darcy's Law and the basic buildup equation) and
the pressure drop near the wellbore which is caused by an end effect phenomenon called "skin", which is the result of possible turbulent flow, damage by various causes as a result of drilling and completing the well, and the percentage of the reservoir that has been perforated or open for production.
Therefore, at any instant of time: Delta p +Delta p = Delta, where the Delta p's are the pressure drops and the subscript r, s and w are reservoir, skin and wellbore respectively
The key equation is obtained by combining Darcy's Law with the basic equation: kh=162.6 quB/m, which gives: (4)
Once Delta p is calculated and knowing Delta p, Delta p is determined by difference. The actual drainage radius for a radial flow system at shut in time can be calculated by the empirical equation (A) in which r is directly related to time to maximum slope on the calculated MDH plot and indirectly related to the viscosity of the movable reservoir fluid. In the case of DST's and initial tests on wells, r calculated by equation (A) can be compared to that calculated by equation (8).
It has been found in buildups that when the wellbore and storage effects have died out, the measured time, pressure points can be described on a linear plot by a rectangular hyperbolic equation. It is plot by a rectangular hyperbolic equation. It is possible to derive a specific hyperbolic equation for possible to derive a specific hyperbolic equation for a particular buildup using three time, pressure points in this portion of the curve. The asymptote points in this portion of the curve. The asymptote to the time axis on an MDH plot at infinite shutin time appears to be the static buildup pressure within the developed drainage area of the well. It has also been found that when these time, pressure points (calculated from the hyperbolic equation) are plotted on an MDH plot, the maximum slope of the curve (the MDH plot is always an S type curve) appears to be m. Therefore, m would be unique for any particular buildup. Also, the shutin time on the MDH plot at which the slope is maximum (m)appears to be directly related to the distance from the wellbore to the radius of drainage at the time of shutin. A relation ship, based upon limited data, has been observed between log r and the factor log (m /u) where u is viscosity. This empirical equation is:
(A)
The phenomenon of anomalous pressure behavior is more prevalent than here to fore accepted. Any time oil and free gas are flowing together in a vertical column, there is a tendency for the gas bubbles to rise faster than the oil. When this column is closed at the top, gas bubbles will continue to rise causing excess bottomhole pressure.
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