TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractWe have established the concept of Unified Fracture Design (UFD) to maximize the dimensionless productivity index (J D ) following a hydraulic fracture treatment. For a given mass of proppant there is a specific dimensionless fracture conductivity, which we called the optimum, at which the J D becomes maximum. The Proppant Number is a seminal quantity unifying the propped fracture and the drainage volumes and the two permeabilities, those of the proppant pack and the reservoir.
IN1RODUCTION Well stimulation procedures are designed to reduce the restrictions to flow from the reservoir into the wellbore and increase productivity.1 Hydraulic fracturing in low permeability reservoirs is an important and successful stimulation methodology widely used by the petroleum industry. The design of the optimum fracture treatment has three basic steps. The first step involves calculating fracture dimensions and conductivity for various fracture fluid pumping schedules. The second step is determining the oil and gas production rates and recoveries using the values of propped fracture length obtained from the fracture treatment design. The third step requires one to determine the optimum fracture treatment design by maximizing the economic benefit of the treatment. Since a fracture treatment design involves selection of fracturing fluids, additives, proppant materials, injection rate, pump schedule, and fracture dimensions, the determination of the optimum combination of all variables can be quite complicated. In this research, we have developed two methods to investigate reasonable combinations of design and treatment parameters to determine the most profitable fracture treatment design. Depending upon the post-fracture treatment production rates, the related expenses, and the economic constraints, the optimum treatment can be easily determined. The first optimization method is based on a mathematical technique called Mixed Integer Linear Programming (MILP).2 This method can be used to minimize or maximize a desired objective function subject to certain constraints. For this work, we have chosen the objective function to be the discounted net present value due to a fracture treatment. The constraints are related to the fracture dimensions and other items necessary to linearize the fracture design problem.3
Summary Hydraulic fracturing has been widely used in stimulating tight carbonate reservoirs to improve oil and gas production. Improving and maintaining the connectivity between the natural and induced microfractures in the far-field and the primary fracture networks are essential to enhancing the well production rate because these natural and induced unpropped microfractures tend to close after the release of hydraulic pressure during production. This paper provides a conceptual approach for an improved hydraulic fracturing treatment to enhance the well productivity by minimizing the closure of the microfractures in tight carbonate reservoirs and enlarging the fracture aperture. The proposed improved fracturing treatment was to use the mixture of the delayed acid-generating materials along with microproppants in the pad/prepad fluids during the engineering process. The microproppants were used to support the opening of natural or newly induced microfractures. The delayed acid-generating materials were used in this strategy to enlarge the flow pathways within microfractures owing to degradation introduced under elevated temperatures and interaction with the calcite formation. The feasibility of the proposed approach is evaluated by a series of the proof-of-concept laboratory coreflood experiments and numerical modeling results. First, one series of experiments (Experiments 1–3) was designed to investigate the depth of the voids on the fracture surface generated by the solid delayed acid-generating materials under different flow rates of the treatment fluids and different temperatures. This set of tests was conducted on a core plug assembly that was composed of half-core Eagle Ford Sample, half-core hastelloy core plug, and a mixture of solid delayed acid-generating materials [polyglycolic acid (PGA)] along with small-sized proppants sandwiched by two half-cores. Surface profilometer was used to quantify the surface-etched profile before and after coreflood experiments. Test results have shown that PGA materials were able to create voids or dimples on the fracture faces by their degradation under elevated temperature and the chemical reaction between the generated weak acid and the calcite-rich formation. The depth of the voids generated is related to the treatment temperature and the flow rate of the treatment fluids. Experiment 4 was conducted using two half-core splits to quantify the improvement factor of the core permeability due to the treatment with mixed sand and PGA materials. Simulations of fluid flow through proppant assembly (inside of the microfractures) using the discrete element method (DEM)–lattice Boltzmann method (LBM) coupling approach for three different scenarios (14 cases in total) were further conducted to evaluate the fracture permeability and conductivity changes under different situations such as various gaps between proppant particulates and different depths of voids generated on fracture faces: (1) fluid flow in a microfracture without proppant, (2) fluid flow in a microfracture with small-sized proppants, and (3) fluid flow in a microfracture supported by small-sized proppants and generated voids on the fracture walls. The simulation results show that with proppant support (Scenario 2), the microfracture permeability can be increased by tens to hundreds of times in comparison to Scenario 1, depending on the gaps between proppant particles. The permeability of proppant-supported microfracture (Scenario 3) can be further enhanced by the cavities created by the reactions between the generated acid and calcite formation. This work provides experimental evidence that using the mixture of the solid delayed acid-generating materials along with microproppants or small-sized proppants in stimulating tight carbonate reservoirs in the pad/prepad fluids during the engineering process may be able to effectively improve and sustain permeability of flow pathways from microfractures (either natural or induced). These findings will be beneficial to the development of an improved hydraulic fracturing treatment for stimulating tight organic-rich carbonate reservoirs.
Gaining an understanding of the well to well interference during hydraulic fracturing and subsequently production interference is paramount in optimizing the costs associated with field development. Much work has been done in the industry to better understand the interference during hydraulic fracturing and production among adjacent wells. This paper presents an analysis that employed both a pressure interference analysis and chemical tracer analysis to gain a better understanding of the fracture interference in a well pad in the Jafurah field. The subject pad consists of 4 wells. Two of which run parallel in a north direction and the other two run parallel in the southern direction. All four wells were hydraulically fractured with slickwater design. Adjacent to the subject pad is another pad that had been previously stimulated with crosslink design and was used for pressure monitoring. The distance between the laterals was relatively similar (X ft) with one exception (2 × ft). Initially, one well from both directions was stimulated with 33 stages each of slickwater design and the plugs were subsequently milled out. Afterwards, the other two wells were stimulated with 33 stages of slickwater each. In 7 of the 33 stages of the later wells, 20 oil and 20 water tracers were injected in sequence in an attempt to study the physical extent of the fractures generated. While the latter two wells were being stimulated, the wellhead pressure on the parallel wells was being monitored and recorded along with the wellhead pressures on the adjacent pad. During flowback, the southern wells were flowed back simultaneously and flowback samples were collected to be analyzed for tracers. Subsequently, the northern wells were opened up to flowback in the same manner and flowback samples were also collected for tracer analysis. Wellhead pressure was monitored on the adjacent pad during flowback of all the wells. The pressure data during the fracturing operation indicated for distance × ft and the size of stimulation stages pumped, a level of communication which was further verified by the production interference analysis as well as the tracer data.
Engineers use boundary-dominated productivity equations for fracture designs in medium permeability formations. These equations are critical to optimize fracture designs and are different for primary depletion and formations under waterflooding processes. This paper presents two new models to calculate the dimensionless productivity index, JD, of finite-conductivity fractured wells producing either at pseudo-steady or steady state conditions. These models use a new "definition" of the equivalent wellbore radius to incorporate the finite conductivity and fracture penetration dependency of the solution. New easy-to-use correlations (from 1500 numerical simulation runs) to calculate consistent shape factors and f-functions for fractured wells are also presented in the paper. The f-functions are an extension to PSS and SS conditions from the Cinco-Ley's original work. These equations are used to regenerate JD type curves of a finite-conductivity fractured well under pseudo-steady or steady state conditions. A comparison of the JD type curves of SS versus PSS is also presented. The maximum JD value, for fully penetrated infinite conductivity fractured well was 4/PI for SS versus 6/PI for the same case under PSS. These productivity equations are also used to understand more post-fracturing production performance and to push the limits in hydraulic fracturing by injecting very large volumes of proppant of very large retained permeability. The paper will present the production results of the evolution of this hydraulic fracturing technique in these turbidite formations in Russia. It will be shown how the dimensionless productivity indices have been improving as the proppant volume per foot and proppant size has been increased. Statistics has shown how productivity index JD has increased from 0.3 to 0.55 when proppant concentration is increased from 4 tons/meter to 8 tons/meter. Definitely, pushing the fracturing limits in Russia has had a great impact on the production increase on these turbidite formations. Introduction In 1949 Van Everdingen and Hurts1 presented the PSS solution (Eqn. 1) of the diffusivity equation for a cylindrical reservoir.Equation 1 In 1971, Ramey and Cobb2 showed that this linear relationship between PD and tDA at pseudo-steady state of an unfractured well could be represented by Eqn. 2 for any closed reservoir of any shape,Equation 2 Where tDA dimensionless time is based on drainage area, A is the drainage area, and CA is the shape factor for a particular drainage shape and well location. Eqn 2 became also the definition for the shape factor, CA.
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