SPE Membersopyright 1986, Society of Petroleum Engineers rhis paper was prepared for presentation at the 5Sth Califomis Regional Meeting of the Society of Petroleum Engineers held m Oakland, CA, April 24, !9ss, rhis pa~r was selected for presentation by an SPE Program Commmes following review of mlormation contained in an abstract submitted by the suthor(a). Contents of the psper, as presented, have not bean reviewad by the Sosiefy of Petroleum Enginaare and are aubjact to correction by tha guthor(a). The material, aa presented, doas not necessarily reflect any poaifion of the $ociaty of Petroleum Engineers, its offiiere, or members. Papera praaentad at SPE meetings are subject to publication review by Editorial Committees of the Socialy of Petroleum Enginaera. Permission to copy is restricted to an abstract of not more than 200 words, Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where nndby whom the pa~r is presented. Write Publicatiina Manager, SPE, P.O. Sox 83SSSS,FUchardaon, TX 7S0S3-3S3S. Telex, 7309S9, SPEDAL. AbstractIntroduction A new comprehensive model of hydraulic fracturing is presented which has been developed for the Gas Research Institute A substantial amount of effort has been invested, espe-(GRI) mobile fracture monitoring and analysis facility. The cially over the past decade, in the development of models for design and analysis of hydraulic fracturing. The resulting modmain purpose of the model is to simulate the hydraulic fracturing process in real-time, that is on+ite during the fracturing els have varied in at least three major aspects: realism and operation, but the model can also be used for pre-fracture de-generality of the assumptions made in formulating the modsign and post-fracture analysis. Sensor data obtained during ela; complexity of the resulting computer codes and machine the course of the job -requirements; and flexibility of the input-output characteriesuch as wellhead pressure, flow rates, tics, especially in relation to real job conditions and operator frac-fluid viscosity, and proppant staging -can be received . directly by the model se input, superseding the pre-frac job interfacing. Although some good progress haa been made by design schedule, and making possible more accurate model es-many groups, there have not been any models which were satisfactory in all of the three important areas, and most models timatea of current fracturing conditions and predictions of final h fracture geometry, as the job proceeds.ave, at beet, been adequate in one aspect only.The overall model haa four major components describing: Examples of previous work may be found in the consid--flow of fluids and slurry in tubular goods erable literature which has evolved on this subject. The sim-creation and propagation of the hydraulic fracture plest models, assuming 2D geometry with a constant specified -transport of proppant, deposition, and fracture closure height, were those of Christianovich, Geertsma, de Klerk and -heat and fluid exchange between frac...

Summary A new, fully integrated model of hydraulic fracturing can be used to compare measured and calculated pressures for parameter determination during the fracture treatment to improve the prediction of hydraulic fracture geometry. Sensor data obtained during the course of the treatment - such as wellhead flow rates, fracturing-fluid viscosity, and proppant concentration - are received directly by this model, which takes into account all the essential physical phenomena that influence the pressure response associated with hydraulic fracture growth. At any point during the treatment, the model can be rerun, faster than real time, changing reservoir and treatment parameters until the difference between calculated and measured wellhead or bottomhole pressure (BHP) histories is minimized. Updated predictions of final propped fracture geometry can then be made by running the model faster than real time, using the remaining treatment scheduled as input and adopting the parameters that correspond to the best history match; these predictions may differ substantially from that of the job design, thus providing field personnel with an improved estimate of the final fracture geometry before the treatment is completed, while remedies can still be implemented. Results show history matches of the pressure response and associated fracture geometries for three treatments performed in the Travis Peak formation of east Texas and one performed on a coal seam in the Piceance Creek basin near Collbran, in western Colorado. In addition, this work is contrasted with previous efforts to deduce fracture geometry from pressure-response profiles. Introduction A great number and variety of hydraulic fracturing models have been developed over the past 3 decades.1–7 Many have been applied in various ways to the design and analysis of treatments carried out on a commercial basis by the industry. Nonetheless, routine optimization of hydraulic fracture treatments - namely, the achievement of the greatest production possible for the smallest investment - remains a very elusive and desirable goal. Shortcomings in several areas have hindered the improvement of the fracturing process:the models used for design and analysis in many cases lack adequate descriptions of the physical phenomena;reservoir characteristics and fracturing-fluid rheology, which strongly influence fracture geometry, are often unknown or uncertain;inadequate monitoring of the fracturing treatment may diminish quality control; andinformation that becomes available during the course of the treatment is generally not used for updating the design prediction of final fracture geometry, which is usually generated from limited prefracture information. It is certainly true that substantial progress has been made over the past decade or so: fracture modeling has evolved from the early specialized constant-height formulations (Khristianovich-Geertsma-de Klerk1,2 and Perkins-Kern-Nordgren3,4) to the more general, fully three-dimensional (3D) simulators,5–7 as described in Ref. 8; minifracture and microfracture tests are occasionally performed to determine reservoir characteristics, such as in-situ stress distributions and the extent of fluid leakoff9–11; service companies have updated their on-site monitoring capabilities to ensure better execution of treatment designs11,12; and certain aspects of fracture creation (e.g., fracture-height containment) are determined from the pressure response during the treatment.9 These efforts have doubtless produced some improvements in treatment effectiveness. But even the most modern comprehensive simulators cannot accurately predict fracture geometry if pertinent reservoir characteristics are unknown; nor can the extent of fracture containment be inferred from the pressure response if rheological changes and sand staging are not taken into account. The optimization of hydraulic fracture treatments, therefore, requires substantive across-the-board improvements in which all the relevant capabilities in fracture modeling, data acquisition and interpretation, and field operations are synthesized into one coordinated system. Therefore, we propose a comprehensive methodology to improve hydraulic fracture prediction and to provide the basis for intelligent decision-making during the treatment. This methodology essentially involves detailing monitoring and real-time simulation and analysis of the fracturing process.13 It is based on the premise that the actual treatment record, and the information inferred primarily from the pressure response during the treatment, can be used to improve estimates of fracture geometry significantly over those derived from prefracture data and schedules. The essential aspects of this methodology can be summarized as follows.Detailed treatment monitoring (e.g., pressures, flows, rheology, and sand scheduling) and accounting of deviations from job design.Use of monitored sensor data as input to real-time hydraulic fracture models.Determination of unknown reservoir/treatment parameters and affirmation of known quantities by the history matching of observed and predicted response pressures.Best estimation of current fracture geometry using prefracture information, the history-matched parameters, and the real-time data flows.Updated predictions of future job status based on the best current fracture estimates and the remaining (or alternative) treatment schedule.Identification of any treatment pathologies and recommendation of possible remedies. Central to the analysis of the fracturing process during treatment is the real-time model of hydraulic fracturing and the history-matching procedure to determine unknown parameters. A summary of the fracture model is provided; its technical details are thoroughly described in Ref. 8. The major purpose of this paper is to describe the history-matching procedures and to show comparisons with actual field data, emphasizing the application of the model to the improvement of field fracturing operations.

The character of fluid flow in and around wellbores, cavities, and fractures in para-elastic media can significantly affect resource extraction operations in underground reservoirs. Reasonable estimations of hydraulic fracture profiles and propagation rates cannot be made without considering fluid exchange, especially for high leak-off; well production rates greatly depend on the flow rates into fractures; and reservoir properties are often strongly stress-sensitive.In this paper, the fluid loss and the subsequent "backs tress" (i. e. induced reservoir stress) caused by it are characterized for stationary and propagating fractures, and the model is applied to three cases: 1) a single fluid in the reservoir and fracture; 2) two fluids: a reservoir fluid and a fracture fluid that has penetrated some distance into the reservoir; 3) a production model where the crack has been propped and the reservoir fluid flows out of the well.The fluid exchange between fracture and reservoir is found by solving an integral representation of the flow in the reservoir. Since the pressure distribution in the reservoir is governed by a diffusion process, the flow out of (or into) the fracture and the backstress are rather simply calculated by integrating along the fracture the influcence function for the pressure due to each component of fluid exchange, specifying the pressure at each point on the fracture or closing the system by some other means such as solving simultaneously the flow equations in the fracture, and solving for the fluid exchange inside the integral. Then backs tress can then be found from the fluid exchange. Preliminary computational results for plane fractures have been obtained that compare well with existing special analytical and numerical solutions (e.g., those of Cinco and Samaniego). More general results are provided for moving fractures and induced stresses, and the broader capabilities of the methodology are outlined.References and illustrations at end of paper.

This paper presents some derivations and results of lumped numerical models which describe the growth and final geometry of hydraulic fractures. Using generally averaged reservoir and fracture parameters the model employs simple numerical routines to solve coupled non-linear ordinary differential equations for the pressure and dimensions of the fracture. Results of more complex models are included as a data-base in the spatial lumping process; thus the models represent all the essential features of fully 3-D, physically realistic hydraulic fractures. The present model provides a consistent description of fracture growth provides a consistent description of fracture growth and includes the effects of mechanisms such as fluid loss, backstress, heat transfer, proppant and variable fracture geometry. Results are presented the general usefulness of these models for fracture design and on -site interpretation of observed versus predicted downhole pressures. predicted downhole pressures. Introduction The literature on hydraulic fracturing modeling is extensive and abounds with different approaches to the various parts of this complex problem. Some of the earliest models problem. Some of the earliest models are universally used in the industry; some of the newer models are increasingly used. In previous papers we presented the basis previous papers we presented the basis for the analytical framework of the levels and techniques used in these numerical models. The three motivations of this present paper are: simplification, unification, and development of comprehensive practical simulators. These are all achieved by means of so-called "simple lumped models," which employ spatial averaging to reduce the problem to manageable form while retaining generality for the incorporation of other more complicated models. The underlying philosophy in developing the lumped models has been to incorporate as many of the significant mechanisms controlling fracture growth in as simple a numerical scheme as possible. As a consequence, the lumped models are possible. As a consequence, the lumped models are comprehensive descriptions, designed to allow the incorporation of results from more general models as reference data bases. The variable fracture geometry capability presented here allows generalized fracture shapes, from equiaxed to either well or poorly contained fractures. Fluid/reservoir effects such as fluid loss, backstress, thermo-rheology, and proppant transport can be accounted for with simplified versions of general 2-D and 3-D models. The simple lumped models presented in this paper include results from several of these models, specifically the P3DH cross-sectional simulations and from simple 3-D models results from more general models can be incorporated as they become available. The result is a fairly simple, efficient numerical routine that captures the essential features of the problem and seems to lead to reasonable predictions of fracture pressures and dimensions in our experiments. An earlier paper presented a description and some basic fracture growth equations; in this paper we present other extensions of the lumped models such as variable fracture geometry and fluid/reservoir interactions. p. 507