Radial flow equations and matrix volumetric calculations can be used toaccurately predict reservoir performance. These same formulas can also be usedto mathematically design the necessary stimulations to be performed on thosereservoirs. Well productivity can be accurately monitored and plotted versusits own model profile to predict optimized production rates. Permeabilityimpairment resulting in reduced productivity can be accurately defined and thefluid volume requirements for matrix acid stimulation are readily calculated.Volume requirement calculations are based on formation damage analysis andindividual well production history. Analysis of the pre-damage and post-damageproduction data permits both skin damage factor and the radial depth of damageto be determined. Accurate volume requirements and radial extent of acidemplacement in the matrix are calculated, thus adopting an engineering approachto acid stimulation design and replacing the rule of thumb acid application formatrix stimulation. The new, simple and rapid technique guarantees noundertreatment and no overtreatment, thus effectively removing guess work fromstimulation technology. Several field programs have been performed withexcellent results using this technique. This paper presents the easy to followacid volume requirements calculation procedure and discusses some of the fieldresults. In order to understand the derivation of this system, we will firstexplore the field of well performance from a reservoir engineering standpointand then follow through with introduction of the theory developed there andapplied to the stimulation of both oil and gas wells.
Production of reservoir fluids into the wellbore and the rate of thatproductivity depends upon several factors as denoted by the flow rate formulabelow:
List of flow rate formula (Available in full paper)
Where:
q = flow rate, bpd
k = effective permeability, md
h = sand thickness, ft
Pe = reservoir pressure, psi
Pw = pressure at wellbore, psi
µ = viscosity, cp
re = drainage radius, ft
rw = wellbore radius, ft
We must evaluate each factor to determine its relationship to the productionefficiency of the well.
There are only two variables which affect well productivity:
K = permeability
Pw = sandface pressure (pressure at the wellbore)
Pw is directly proportional to K and therefore, the permeability isthe subject which must be addressed in order that we are able to evaluateproduction efficiency.
As production is initiated and continued, only Pe and Pwshould change unless Pe drops below the bubble point at which time,µ will also change. In many reservoirs, the well responds as predicted by thetheoretical calculations; however, there are others that are dramaticallydifferent than the theoretical. These are the situations which we wish toaddress; moreover, we must first understand those wells which react aspredicted in order that we gain an insight into why some wells do not react aspredicted.
As in Fig. #1, at a radius r1 from the wellbore, a radiusr2 = r1 + 1" with a height of 1 foot has a calculablepore volume of:
