Considerations for Optimum Fracture Geometry Design

Abstract

Summary. This paper gives production forecasts forvarious equal-proppant-volume fracture geometries with various formation permeabilities,equal fracture lengths with different proppant volumes, andequal fracture lengths and proppant volumes with various proppant distributions. It shows conditions when Prats' relationship for maximum productivity is true and when higher values of dimensionless fracture productivity is true and when higher values of dimensionless fracture conductivity are beneficial. These should give the design engineer useful tools when optimizing fracture design. Introduction Hydraulic fracturing has been successful in increasing the productive reserves in many oil and gas reservoirs. As wells are completed in formations of lower permeability, larger fracturing treatments are required for economical recovery. Therefore, the fracturing design engineer wants to design the optimum fracturing geometry. Prats I addressed this problem by showing that for a given fracture Prats I addressed this problem by showing that for a given fracture volume (proppant volume), there is a fracture-width-to-fracture-length relationship for achieving maximum productivity. He showed that this relationship was 2L /b= 1.59k /k. Prats findings are valid after long producing times or for cases of high formation permeability. In formations producing times or for cases of high formation permeability. In formations with low permeability, Morse and Von Gonten showed that early transient production rates before a pseudosteady-state condition is reached can be production rates before a pseudosteady-state condition is reached can be important in determining the economics of hydraulic fracturing treatments. More recently, Cinco-Ley et al. and Agarwal et al. published dimensionless type curves that show the relationship of production rates for various fracture conductivities with time. These curves show that for a constant fracture length, higher fracture conductivities are beneficial and a rule of thumb of C = 10 to 30 has been proposed as the desired dimensionless fracture conductivities. The C is defined as (1) Prats' optimum fracture-width-to-fracture-length relationship for Prats' optimum fracture-width-to-fracture-length relationship for maximum productivity corresponds to a dimensionless fracture conductivity, C, of 1.26. This shows that for a given volume of proppant, the optimum fracture conductivity, k b, should equal proppant, the optimum fracture conductivity, k b, should equal 1.26 times the product of fracture length, L, and formation permeability, k, or k b = 1.26kL . This relationship is true for permeability, k, or k b = 1.26kL . This relationship is true for cumulative production after long periods of time (10 to 20 years) and for the cases studied by Prats. In low-permeability formations, however, higher values of C will result in more production during the early-time periods. In the fracturing of deeper formations with potential high closure stress on the proppants, more expensive proppants are often required to maintain fracture conductivity. In these cases, the proppant cost becomes a higher proportion of the treatment cost, and proppant cost becomes a higher proportion of the treatment cost, and proppant volume has some limiting effect on treatment sizing. When proppant volume has some limiting effect on treatment sizing. When fluid costs are relatively high, fluid volume or fracture length is the limiting parameter. This paper evaluates two conditions: equal-length and equalvolume fractures. The design engineer may design for a certain fracture length and try to obtain C = 10+. This would require a certain fracture volume that, according to Prats' study, would be better when distributed over a greater length, resulting in C = 1.26. To evaluate the guidelines using C in fracture-design optimization, production was simulated for various conditions with a finite-difference, two-dimensional, single-phase, reservoir simulator. This simulator can model the performance of a well containing a fracture of constant width with different conductivities in various fracturelength segments. This would be the same as constant proppant permeability with different fracture widths when nondarcy effects are permeability with different fracture widths when nondarcy effects are ignored. Three situations were simulated. The first situation was for a constant or predetermined fracture volume with five different fractur lengths in four reservoirs of different permeabilities. The second was for a constant or predetermined fracture length but with different proppant volumes. The third was for a situation having a constant proppant volumes. The third was for a situation having a constant fracture length and propped volume but with the propped width varying over the length. The first two situations were to test the validity of the guidelines mentioned previously; the last was to examine the differences between the constant-propped-width constraint of the type curves and the varying widths, which may be more common in practice. The term "optimization" in this paper is based solely on maximum production and is not meant to take the place of the proper economic optimization that would consider well spacing, formation thickness, porosity, production, and treatment cost. Equal-Fracture-Volume, Varying-Length Cases. Table 1 gives the reservoir properties used for the various simulations. It can be noted that the properties may seem unrealistic in their combination of dimensions. The thickness was varied to maintain a constant formation kh product, which allowed all the combinations to have the same proppant volume and the same combination of C and fracture penetration. This resulted in the use of some unusually low fracture conductivities for the simulations; however, because the study was performed to evaluate C, a dimensionless term, the conclusions should not be affected. A 900-acre [364-ha] spacing was used to accommodate the 2,898-ft [883-m] fracture penetration. Note that the formation porosity is decreased as the penetration. Note that the formation porosity is decreased as the permeability is decreased, and although this will affect the transient permeability is decreased, and although this will affect the transient time, it was done to give more realistic conditions. Table 2 shows the combination of C and L that will be obtained for equal proppant volumes for the cases in table 1. These combinations will always be the same in this constant-volume study because the kh is the same for all cases. Fig. 1 shows the cumulative production for Reservoir A having a permeability of 1 md with the five different combinations of fracture length and C . The same conclusion as given by Prats-that for a constant-volume fracture, C = 1.26 is the optimum-can be made. Of interest is the order of optimization of the combinations of C and L in Table 3. Fig. 2 shows the effect of early-time transient behavior for Reservoir B having a formation permeability of 0.1 md. It shows thafor the first 180 days, the order of C for maximum productivity is 5, 3, 10, 1.26, and 0.6. After 500 days, the order is 3, 5, 1.26, 10, and 0.6. It is interesting that the 2,898-ft [883-m] fracture having a C of 0.6 is better than the 710-ft [216-m] fracture having a C of 10. After about 15 years, the order is the same as with Formation A and agrees with Prats' conclusion. SPEPE P. 323