Use of Cumulative-Production Type Curves in Fracture Design
- J.L. Elbel (Dowell Schlumberger) | P.A. Sookprasong (Dowell Schlumberger)
- Document ID
- Society of Petroleum Engineers
- SPE Production Engineering
- Publication Date
- August 1987
- Document Type
- Journal Paper
- 191 - 198
- 1987. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 5.4.2 Gas Injection Methods, 5.5 Reservoir Simulation, 5.7.5 Economic Evaluations, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 2.5.2 Fracturing Materials (Fluids, Proppant), 2.5.1 Fracture design and containment, 4.3.4 Scale, 2.4.3 Sand/Solids Control, 3 Production and Well Operations
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Summary. When a fracture treatment is designed, the expected increase in productivity or production rate is usually considered. Because production productivity or production rate is usually considered. Because production rate varies with time, an economic evaluation based on a production rate increase at a given time can be misleading. A better method of economic evaluation would use the cumulative production after some time period. This can be determined by reservoir simulators that incorporate the effect of propped hydraulic fractures. These simulators are not readily accessible to everyone, however, and are time consuming and expensive to run. Several authors have stated that cumulative-production type curves can he made with data generated by dimensionless-pressure type curves for a fractured well with infinite fracture conductivity. This paper shows how cumulative-production type curves for finite fracture conductivity can be generated from published dimensionless reciprocal-rate type curves or from reservoir simulators. A simple graphic procedure can then be used to give the combinations of fracture lengths and dimensionless fracture conductivity that will show the desired cumulative production or production rate at some particular time. Charts and simple equations also are given that will allow a quick estimate of the proppant volume required for the various fracture geometries needed for the desired production. This would form the basis for optimizing the fracture treatment. When used with methods to determine fracture fluid volumes for various fracture lengths, the minimum cost for any desired production can be made.
There are many paths to follow in designing a hydraulic fracture treatment, and probably no single method will be satisfactory in meeting all the various requirements and in overcoming various limitations. A common procedure in design optimization is to estimate production increases and the costs required to achieve various fracture lengths and then to make some evaluation on the basis of economics. This method limits itself to the number of cases that can be investigated because investigating the effect of a large number of combinations of fracture lengths and conductivities can be very time-consuming. Some available methods compare productivity increases on the basis of steady-state folds of increase and some decline plots of production after the boundary effects are present. In low-permeability reservoirs, however, large volumes of hydrocarbon can be produced before the boundary effect is reached, therefore, using predictions based on pseudosteady-state conditions can be misleading in pseudosteady-state conditions can be misleading in economic studies if this volume is not taken into consideration.
A technique has been developed that can determine the various combinations of fracture lengths and proppant volumes required for a desired cumulative production after a certain period of time. This technique uses a cumulative type curve with various dimensionless fracture conductivities and an overlay that is scaled to fracture length. Equations and charts have been developed that can be used to calculate proppant volumes, costs, and limiting conditions in the design. These equations include dimensionless fracture conductivity, FCD, and fracture half-length, Lxf. This inclusion is noteworthy because certain values of FCD and L, f are often used in rule-of-thumb guidelines.
Cumulative-Production Type Curve
Several authors have used cumulative-production type curves in fracture design and evaluation. Holditch et al. showed that when dimensionless time is divided by dimensionless pressure, the result will be dimensionless cumulative production, which has the following relationship for constant-rate or constant-pressure cases.
Dimensionless time, tD, is defined as
A finite-difference, two-dimensional reservoir simulator was used to calculate production rate, q, and cumulative production, Vc, at various times, t, with a constant flowing bottomhole pressure (BHP). The cumulative production was calculated with production was calculated with (3)
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