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Keywords: pressure transient analysis

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–26, 2013

Paper Number: SPE-164500-MS

... included in the paper for several numerical examples.

**pressure****transient****analysis**Upstream Oil & Gas hhfd 1 early radial flow Drillstem Testing vertical hydraulic fracture hhfd 0 hydraulic fracturing drillstem/well testing hxfd transition flow vertical transverse hydraulic fracture...
Abstract

Horizontal wells with multiple hydraulic fractures have become a common occurrence in the oil and gas industry, especially in tight formations. Published models assume that hydraulic fractures are fully penetrating the formations. However, studies have shown that fractures are not always fully penetrating the formations. This paper introduces a new technique for analyzing the pressure behavior of a horizontal well with multiple vertical and inclined partially penetrating hydraulic fractures. The hydraulic fractures in this model could be longitudinal or transverse, vertical or inclined, symmetrical or asymmetrical. The fractures are propagated in isotropic or anisotropic formations and considered having different dimensions and different spacing. This technique, based on pressure and pressure derivative concept, can be used to calculate various reservoir parameters, including directional permeability, fracture length and percentage of penetration. The study has shown that the pressure behavior of small penetration rate is similar to the horizontal wells without hydraulic fractures. A type curve matching technique has been applied using the plots of the pressure and pressure derivative curves. A set of type curves, which will be included in the paper, have been generated for the partially penetrating hydraulic fractures associated to the horizontal wells with different penetration rates. A step-by-step procedure for analyzing pressure tests using these type curves is also included in the paper for several numerical examples.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–26, 2013

Paper Number: SPE-164499-MS

... attentions were focused on the study of

**pressure****transient****analysis**of hydraulically fractured wells; there are few studies about the effects of the partially penetrating fractures. Raghavan et al (1978) were the first presented an analytical model that examines the effect of the fracture height...
Abstract

Abstract Hydraulic fracturing process is an important stimulation technique that has been widely used in conventional and unconventional oil and gas reservoirs. The technique involves creation of fracture or fracture system in porous medium to overcome wellbore damage, to improve oil and gas productivity in low permeability reservoirs or to increase production in secondary recovery operations. This paper introduces a new technique for interpreting pressures behavior of a horizontal well with multiple hydraulic fractures. The well extends in multi-boundary reservoirs having different configurations. The hydraulic fractures in this model can be longitudinal or transverse, vertical or inclined, symmetrical or asymmetrical. The fractures are propagated in isotropic or anisotropic formations and considered having different dimensions and different spacing. The study has shown that pressure responses and flow regimes are significantly influenced by both reservoir's boundaries and fractures' dimensions. Different flow regimes have been observed for different conditions. New flow regimes have been introduced in this study. The first one is the early radial flow regime which represents the radial flow around each fracture in the vertical plane resulted due to the partial vertical penetration of hydraulic fractures. The second one is the second linear flow regime which represents the linear flow toward each fractures in the vertical plane normal to the wellbore resulted due to the long spacing between fractures. Third one is the third linear flow regime which represents the linear flow in the vertical plane parallel to the wellbore after the pressure pulse reaches the upper and lower impermeable boundaries.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 27–29, 2011

Paper Number: SPE-142316-MS

... transient testing finite reservoir pressure behavior time limit upstream oil & gas approximation plane source infinite reservoir

**pressure****transient****analysis**flow regime spe 142316 permeability time approximation drillstem/well testing type curve state flow gringarten horizontal well...
Abstract

Horizontal wells can greatly increase the contact area of the wellbore and the pay zone; so they are commonly applied in oil reservoirs to enhance the production and ultimate recovery, especially in low permeability formations. The purpose of this study is to develop a technique for the interpretation of transient pressure based on dimensionless pressure and pressure derivative. Type curve matching is one of the techniques that can be used to interpret the pressure data of horizontal wells in finite reservoirs. Starting from very short horizontal wells to extra-long wells, the pressure behavior of the wells has been analyzed for different conditions. The effect of the outer boundaries of the reservoir on the pressure behavior of the horizontal wells has been investigated for different configurations. Rectangular shape reservoirs with different dimensions have been used to study the pressure response in the well. Five flow regimes have been observed for regular length horizontal wells; early radial, early linear flow, pseudo radial flow, channel flow or late linear flow, and pseudo-steady state flow. While only four flow regimes have been observed for the extra-long wells; linear flow, pseudo radial flow, channel flow, and pseudo-steady state or boundary affected flow. Of course, those flow regimes do not always take place under all conditions. Pseudo-steady state flow is expected to occur after long producing time. A pressure drawdown test was solved using the proposed type curve matching technique. The study has shown that the effect of the boundary on the pressure response of the horizontal wells and the type of flow regimes depend on the length of the horizontal wells and the distance to the nearest boundary.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, April 4–8, 2009

Paper Number: SPE-120106-MS

... Abstract Currently in the oil industry, a field usually contains several wells producing from the same drainage domain, and each well will have an effect on the pressure at other wells. For an infinite-acting multiple wells system,

**pressure****transient****analysis**is already done by using...
Abstract

Abstract Currently in the oil industry, a field usually contains several wells producing from the same drainage domain, and each well will have an effect on the pressure at other wells. For an infinite-acting multiple wells system, pressure transient analysis is already done by using superposition principle. This paper presents pressure drawdown equations of a multiple wells system in a circular cylinder reservoir with constant pressure outer boundary. The proposed equations provide fast analytical tools to evaluate the performance of multiple wells, which are located arbitrarily in a circular cylinder reservoir, and are producing at different rates. This paper examines the pressure drawdown response of a specific well located in a system of producing wells. The interference effects of nearby producing wells on the pressure drawdown response are investigated. The proposed equations are illustrated by numerical examples. It is concluded that, for a given multiple wells system in a circular cylinder reservoir, well pattern, well spacing, skin factor, flow rates and well off-center distances have significant effects on single well pressure transient behaviour. Because the reservoir is under edge water drive, the outer boundary is at constant pressure, when producing time is sufficiently long, steady-state is definitely reached. Introduction It is rare to find a reservoir being produced from only a single well. A field usually contains several wells producing from the same drainage domain, and each well will have an effect on the pressure at other wells. If we have one well producing at a constant rate, the flowing bottomhole pressure in that well is a function of its own production as well as the production from surrounding wells. For an infinite-acting multiple wells system, pressure transient analysis is already done by using superposition principle (Lee, et al., 2003).

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 16–19, 2005

Paper Number: SPE-94305-MS

... the well in for a period of time and subsequently risking potential deceleration of reserve recovery. A study of a variety of existing Morrow producers was undertaken to determine whether or not flowing

**pressure****transient****analysis**of existing properties could be utilized to "calibrate" three-dimensional...
Abstract

Abstract Sizing of hydraulic fracturing treatments in the Southeastern New Mexico (SENM) Morrow has historically relied on a trial-and error process whereby a three-dimensional fracturing model was built and run with simple gamma ray and compensated neutron density logs.Stress tables have been built utilizing over-simplified correlations involving conversions from gamma ray readings and effective porosity.The resulting simulated fracture-half lengths have been utilized in NPV (Net Present Value) optimizations to arrive at a final sizing decision. Unfortunately, this process relies on the assumption that the initial modeling generates a propped fracture geometry simulation that is realistic.Past efforts to calibrate the 3-D models in the area focused on scattered attempts to gather sonic data that could be converted to stress differentials, and the use of conventional pressure buildups before and after the treatment.While the measurement of sonic properties during open-hole logging operations assisted somewhat in calculating relative stress differentials, its application was sporadic at best, and there was no way to check the results. Pre and post-stimulation pressure buildups required shutting the well in for a period of time and subsequently risking potential deceleration of reserve recovery. A study of a variety of existing Morrow producers was undertaken to determine whether or not flowing pressure transient analysis of existing properties could be utilized to "calibrate" three-dimensional fracturing models, so that future projects would better reflect fracture geometries that were more realistic than current practice. Results of the study are presented, and a practical, user-friendly model is demonstrated whereby flowing transient analysis may be utilized to adjust three-dimensional fracturing simulations as appropriate for optimizing stimulation NPV. Introduction The literature pertaining to stimulation of southeastern New Mexico Morrow reservoirs is extensive1,2,3,4,5,6,7,8.Observations related to stimulation process are abundant, but there is a distinct shortage of guidance pertaining to maximization of NPV by optimizing treatment sizing in this formation.Literature and industry experience has made the NPV maximization process in other areas fairly routine9,10,11, but a number of factors have contributed to its lack of use in this play: The widespread absence of accurate pressure matching, caused by the prevalence of specialty fracturing fluids (primarily foam) that make it difficult to measure or estimate bottom-hole pressures during a given treatment. Industry reluctance to perform pre- and post-treatment pressure transient buildup tests; primarily due to a body of knowledge indicating that it is not uncommon to have inordinately long production recovery periods following an extended shut-in period in a typical Eddy or Lea County Morrow producer12. Wide variation in three-dimensional fracture modeling technique; probably rooted in an inability to check the results of any particular simulation.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 16–19, 2005

Paper Number: SPE-94331-MS

... line source approximation raghavan pressure transient testing drillstem testing fd 0 pressure response transient pressure behavior spe annual technical conference wellbore length dimensionless time

**pressure****transient****analysis**solid bar source drillstem/well testing transient response...
Abstract

Abstract Conventional horizontal well transient response models are generally based on the line source approximation of the partially penetrating vertical fracture solution[1].These models have three major limitations: wellbore pressure is computed at a finite radius outside the source; it is impossible to compute wellbore pressure within the source, it is difficult to conduct a realistic comparison between horizontal well and vertical fracture productivities, because wellbore pressures are not computed at the same point, and the line source approximation may not be adequate for reservoirs with thin pay zones. This work attempts to overcome these limitations by developing a more flexible analytical solution using the solid bar approximation. A technique that permits the conversion of the pressure response of any horizontal well system into a physically equivalent vertical fracture response is also presented. A new type curve solution is developed for a horizontal well producing from a solid bar source in an infinite-acting reservoir by means of Newman's product solution[2]. Analysis of computed wellbore pressures reveals that error ranging from 5 to 20% was introduced by the line source assumption depending on the value of dimensionless radius (rwD). Computations show that for rwD = 10–4 the transient response of a horizontal well is identical to that of a partially penetrating vertical fracture system, and for rwD = 0.01 the transient response of a horizontal well is indistinguishable from that of a horizontal fracture system. Type-curve plots for the ranges 0.01 = dimensionless length (LD) = 10, and 10–4 =rwD = 1.0 are presented. A dimensionless rate function (ß-function) is introduced to convert the transient-response of a horizontal well into an equivalent vertical fracture response. A step-wise algorithm for the computation ofß-function is developed using Duhamel's principle. This provides an easier way of representing horizontal wells in numerical reservoir simulation without the rigor of employing complex formulations for the computation of effective well block radius. Introduction Conventional models for horizontal well test analysis were mostly developed during the 1980s. The rapid increase in the applications of horizontal-well-technology during this period led to a sudden need for the development of analytical models capable of evaluating the performance of horizontal wells. Ramey and Clonts[3] developed one of the earliest analytical solutions for horizontal well test analysis based on the line source approximation of the partially penetrating vertical fracture solution. Conventional models [4–16] assume that a horizontal well may be viewed as a well producing from a line source in an infinite-acting reservoir system. These models have three major limitations: wellbore pressure is computed at a finite radius outside the source; it is impossible to compute wellbore pressure within the source, it is difficult to conduct a realistic comparison between horizontal well and vertical fracture productivities, because, wellbore pressures are not computed at the same point, the line source approximation may not be adequate for reservoirs with thin pay zones. The increased complexity in the configuration of horizontal well completions and applications towards the end of the 1980s made us question the validity of the horizontal well models and the well-test concepts adopted from vertical fracture analogies. In the beginning of the 1990s a new wave of developing horizontal-well solutions[17–27] under more realistic conditions emerged. As a result, some contemporary models were developed to eliminate the limitations of the earlier horizontal well models. However, the basic assumptions and methodology employed in the development of these new set of solutions have remained relatively the same as those of the earlier models. Ozkan[28] presented one of the most compelling arguments for the fact that horizontal wells deserve genuine models and concepts that are robust enough to meet the increasingly challenging task of accurately evaluating horizontal well performance. Ozkan's work presented a critique of the conventional and contemporary horizontal-well-test analysis procedures with the aim of establishing a set of conditions when the conventional models will not be adequate and the margin of error associated with these situations.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 16–19, 2005

Paper Number: SPE-93958-MS

... of a zone that may still have an unknown potential. reservoir injection testing drillstem testing permeability reservoir symposium completion strategy aca pressure transient testing pseudoradial flow halliburton pore pressure oklahoma symposium operator spe 93958

**pressure****transient**...
Abstract

Abstract In many locations, totally evaluating the quality of a reservoir based on conventional logs alone is difficult. This difficulty is especially present in lower-permeability reservoirs. Often, conventional logs can allow the operator to pass up zones that may be more productive than indicated on a conventional porosity cutoff. In such cases, a zone is perforated and allowed to flow to get a better evaluation of the zone and its production potential. However, if the zone does not flow to expectations, the operator may face a real dilemma: is it a poor-quality reservoir, or is some sort of damage prohibiting flow? This question can be very daunting and may not be easily answered, especially if the well will not flow adequately for a buildup analysis within a reasonable time frame. In this paper, the potential for using a small injection test and the subsequent pressure fall-off to analyze the reservoir pressure and permeability is evaluated. Many benefits could be derived from using an injection test for reservoir analysis. Some are obvious, such as the capability to determine permeability and reservoir pressure, but this test can also be advantageous because these properties can be determined without flowing the well (which in some circumstances may be difficult and/or costly). In this paper, a deep Atoka Wash well in Western Oklahoma is evaluated. The results of the fracture injection test are discussed, as well as how these results compare with a conventional buildup analysis. Introduction Lately, the Atoka Wash in Western Oklahoma is highly sought after for gas production; however, it can also be a difficult formation to complete because traditional porosity cutoffs do not always clearly define which zones will be productive. These difficulties probably arise in part from the changing rock composition as well as the depositional environment of this formation, and a variety of methods have been employed to determine its potential pay zones. These techniques include conventional logging, advanced logging techniques, and well testing, either through flow testing or buildup analysis. Although conventional log analysis works very well in some areas, defining a model that can adequately describe the formation with a conventional log analysis in the Atoka Wash formation is difficult. Although advanced logging tools can be employed to help describe the rock more completely, these logs may not be run for a variety of reasons and the operator may have very little information to use in choosing the overall completion strategy. Here, another tool or technique is needed during the completion so the operator can better characterize the reservoir and optimize the completion. Often at the beginning of the completion stage, the operator has felt that there were only two options. They must perforate the well and then perform a flow test or a buildup analysis to more fully determine some of the formation characteristics, or just begin completing zones with little understanding of the reservoir characteristics. In some locations, the flow tests or buildup analysis are relatively simple and inexpensive to perform after perforating because the well will flow easily and the process proceeds smoothly and at a relatively low cost. However, in many instances in this area, the ability to obtain the flow test or buildup analysis is much more complicated. Often the operator is faced with a well that will not flow on its own and they first try to break the zone down (i.e., initiate a fracture) to see if it will flow after the breakdown process. If it does not begin to flow, they may choose to bring in a coiled-tubing unit to unload some of the hydrostatic pressure off the zone until it will begin to flow. However, in this case potential complications can still arise. What if the well does not begin to flow or flows at what appears to be an unproductive rate? At this point the operator may be faced with the choice of either abandoning the zone because of apparent poor reservoir quality or hoping that the zone is actually just "damaged" and that a fracture can bypass the damage. This situation is further complicated by the fact that each additional step in this process continues to raise the completion cost of a zone that may still have an unknown potential.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations Symposium, March 23–25, 2003

Paper Number: SPE-80936-MS

... gal function plot reservoir pressure calibration test hydraulic fracturing

**pressure****transient****analysis**fracturing fluid closure analysis radial flow upstream oil & gas drillstem/well testing determination pressure transient testing Copyright 2003, Society of Petroleum Engineers Inc...
Abstract

Abstract Hydraulic fracturing design is highly dependent on the knowledge of the injection fluid efficiency. This parameter is generally derived from the interpretation of the calibration tests fall offs. Two popular methods are the square root of time and Nolte's G function 1,2,3,4 . Such interpretations are not always straightforward and can lead in some practical applications to the failure of propant placement i.e : a screen out with an impact on the post frac well's productivity. In this paper a new interpretation technique for closure pressure determination is presented. It is based on a novel utilisation of Nolte's F function 5 . Field cases on Algeria's In-Adaoui field are analysed. Proppant placement failures are explained. These examples demonstrate the usefulness of the F function for improving hydraulic fracturing design whether for a conventional permeabilty estimation or for closure pressure and hence efficiency determination. Introduction It is a conventional method to perform a calibration test before a Hydraulic fracturing job. The main objectives are an assessment of fracture as well as fluids and rock geomechanical properties. Volumes ranging from a few barrels to more than a 1000 barrels 6 are pumped at the forthcoming hydraulic fracturing job rate. Generally the same fluids are used during the calibration tests and the main treatment. The information that is commonly sought after can be as simple as the injectivity and pressure levels and as detailed as the generated fracture geometry 7,8,9 . Most often a calibration test is used as a means of optimising the main job design by better estimating fracturing fluids leak off characteristics. Fracture closure pressure and subsequent fluid efficiency are derived from fracturing pressure decline analysis using Nolte's G function or square root of time plot. Recently, Nolte et al 5 added the after closure period analysis to the fracture calibration test pressure interpretation to achieve the optimum fracture design. Such analysis consists on using the F function time to determine reservoir transmissibility and pressure. Background of After-Closure Analysis of Fracture Calibration Tests Fall off interpretations generally end after pinpointing the fracture closure. The next operation is the proppant frac itself and at this step no time is lost to proceed with designing and pumping the main job in order to save mobilisation and production time. However, The pressure transient is still in progress since closure pressure is higher than reservoir pressure. Given that the fracture is already closed then the pressure behaviour depends solely on the formation transmissibility and the fracturing fluid properties. Nolte et al 5 studied the after closure period and presented an analysis that allows the determination of two important parameters from the after closure : the transmissibility of the formation and the reservoir pressure. This effort was fully justified considering that in several instances key data for fracturing design such as permeability is not available for lack and difficulty of data collection such as a build up test in a tight formation or simply for the fact that the candidate well has not produced before the job. The after closure period of a calibration test could contain the reservoir pseudo linear flow and pseudo radial flow. The after closure pseudo-linear flow analysis is from Carslaw and Jaegar's heat transfer analysis 10 . Nolte suggested that for heat transfer and reservoir behavior temperature and pressure are analogous therefore the pressure response could be expressed by: Equation 1 For the after closure pseudo-radial flow analysis is from the impulse test test interpretation 11 . For that, Nolte et al 5,12 have developed a combined method, using numerical simulation, to apply it for the after closure period of fracture calibration tests in order to identify flow regimes and determine reservoir parameters. They developed an apparent time F function.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production and Operations
Symposium, March 24–27, 2001

Paper Number: SPE-67239-MS

... data must be critically evaluated and processed prior to the

**pressure****transient****analysis**. Once the non-reservoir effects have been identified, they can either be filtered out, corrected or ignored but must not be interpreted as reservoir effects. Mattar1-2, has discussed in detail the importance of pre...
Abstract

Abstract Pressure - Time data obtained during a pressure transient test include the effect of non-reservoir factors besides the reservoir response. Improper diagnosis to differentiate between reservoir and non-reservoir effects causes misinterpretation of well test data. Phase redistribution is one of the major non-reservoir factors. Even the best available diagnostic techniques fail to detect the phase redistribution effects when they are not obvious from the analysis plots and the data do not match the pressure derivative type curves over the complete time range. One can only suspect the phase redistribution in this case. Verification of anomalous effect due to wellbore phase redistribution is required. In the field of exploration geophysics, there have been established methods for the detection of anomalies in the gravity, magnetic or seismic data. In this paper new analysis techniques besides some of the major techniques from exploration geophysics are applied to transient well test data. And their relative success is discussed for the detection of wellbore phase redistribution effects. Introduction Pressure transient well testing is one of the major tools for formation evaluation. These days highly sophisticated electronic gauges are used for pressure measurement. A significant amount of these very accurate pressure data that are measured during a well test, do not reflect reservoir phenomena at all but are dominated by wellbore related effects or pressure gauge related effects. If not properly identified these effects could easily be misinterpreted as reservoir characteristics. In that case it will lead to erroneous answers in both the identification of the reservoir model and the calculation of parameters values. Therefore the measured data must be critically evaluated and processed prior to the pressure transient analysis. Once the non-reservoir effects have been identified, they can either be filtered out, corrected or ignored but must not be interpreted as reservoir effects. Mattar 1–2 , has discussed in detail the importance of pre-processing of well test data before its analysis or interpretation. Wellbore effects have been recognized since pressure transient testing was first established as a viable method for evaluating well and reservoir performance. In an effort to quantify and evaluate these effects the concept of wellbore storage was introduced 3–6 followed by the concept of phase redistribution phenomena 7–8 . The phenomena of wellbore phase redistribution occur in a well, which is shut in with gas and liquid flowing simultaneously in the tubing. As shown by Stegemeier and Matthews 7 , when such a well is shut in at the surface, gravity effects cause the liquid to fall and the gas to rise to the surface. Because of the relative incompressibility of the liquid and the inability of the gas to expand in a closed system, this redistribution of phases causes a net increase in the wellbore pressure. When this phenomenon occurs in a pressure build up test, the increased pressure in the wellbore is relieved through the formation, and the equilibrium between the wellbore and the adjacent formation will be attained eventually. However, at earlier times the pressure may increase above the formation pressure, causing an anomalous hump in the buildup pressure, which cannot be analyzed with the conventional techniques. In less severe cases, the wellbore pressure may not rise sufficiently to attain a maximum buildup pressure.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 9–11, 1997

Paper Number: SPE-37406-MS

... on qualitative analysis will discuss several methods of detection, ranging from core and log analysis, production history matching, and

**pressure****transient****analysis**to the use of a real-time, three-dimensional (3D) fracturing model that can possibly provide quantitative analysis. Mitigation methods with regard...
Abstract

Abstract This paper discusses multiple fracture creation, detection, and prevention. Multiple fracture creation will be discussed on the basis of rock mechanics theory, laboratory experiments, and field observations. In addition, several references from SPE papers will be outlined. The section on qualitative analysis will discuss several methods of detection, ranging from core and log analysis, production history matching, and pressure transient analysis to the use of a real-time, three-dimensional (3D) fracturing model that can possibly provide quantitative analysis. Mitigation methods with regard to perforation techniques will also be briefly discussed. Introduction Poor post-fracture well performance has long been attributed to such factors as proppant convecting out of zone or poor conductivity resulting from misapplied gel-break chemistry. Although evidence suggests that such effects could worsen poor fracturing treatment performance, many fracturing treatments that result in poor production may result primarily from the creation of multiple fractures. Many stimulation engineers have yet to accept this phenomenon fully because they believe that all multiple fractures result in screenouts. Screenouts may not always occur. This paper presents a successfully executed instance in which a 3D frac model revealed a surface treating pressure that indicated eight multiple fractures. In a recent work, Mahrer et al. cited 285 articles, reports, and other documents that provided qualified observations of multiple fractures. A vigorous research of the literature was performed to discover citings of single-wing, planar fractures. With the exception of a theoretical reference by Howard and Fast, Mahrer found no references to such fractures. At the presentation of his work, however, Mahrer was besieged by several single-wing fracture constituents who would not accept his research. Mahrer proposed that the paradigm of single planar fractures should be the exception, not the norm. This paper complements Mahrer's work by exhibiting other facets of multiple fractures. In rock mechanics theory, single-fracture planes are the given norm. This postulate is easy to address numerically and conceptually. However, many cases exist in which single planar fractures were not created during experimentation with hydrostone. Although this material is considered the most manageable rock available, it allows multiple fracture initiation in nonunique circumstances. Table 1 outlines several symptoms of multiple fractures. This paper will discuss each of these symptoms and their possible causes: sand production without the placement of more than six sand grains of proppant, cyclic production performance after the fracturing treatment, shallow mineback studies, pressure behavior during stimulation, and other lesser known illustrations. A detailed section is included that discusses how to use a 3D fracture simulator to qualify and possibly quantify multiple fractures. This section will describe the differences between single-plane tortuosity and a similar effect that occurs when multiple fractures are present. Types of Multiple Fractures and Their Environments This paper will focus on multiple fractures that coalesce, overlap, or compete for the same pore space (Fig. 1). Most experts consider noncompeting fractures (Fig. 2), such as those generated when long pay intervals are fractured with several perforated intervals, as no threat to the fracture treatment's success. An example of this type of noncompeting fracture occurs in the Hugoton wells, where several members of the Chase group are being stimulated simultaneously. Multiple fractures will most likely occur in (1) naturally fractured formations, (2) long intervals of perforations, with the perforating phase being 0 >to >180, and (3) strongly dipping planes and/or deviated wellbores to flat bedding planes. P. 163^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, April 2–4, 1995

Paper Number: SPE-29463-MS

... dimensionless layer rate corresponding curve 2 curve 3 pressure transient testing dimensionless pressure boundary effect case 3 reservoir

**pressure****transient****analysis**negative rate curve 1 upstream oil & gas layer 1 layer rate layer 3 SPE 29463 Development of a New Theoretical Model...
Abstract

Abstract In this paper we present a new theoretical model for three-layer reservoirs with unequal initial pressures. We developed a semianalytical simulator based on the developed model. The computational model proved to be much faster than a three-dimensional, finite-difference commercial simulator used to validate the analytical model. Also, the amount of information (spatial gridding) needed to run the model is much reduced. The analytical model allows each layer to have different layer properties, different boundary conditions, and different initial pressures. We used the semi-analytical simulator to perform a detailed study of the behavior of three-layered reservoirs during the "pre-production period." The pre-production period occurs early in the life of the reservoir, after perforation but before any surface production and is caused by crossflow in the wellbore. The layer information obtained is very important for scheduling production and making economic decisions concerning the future of the wells. The pre-production well test requires no production on the surface during the test; thus the impact on the environment is negligible. The main objective of this work is to develop a qualitative approach to extract more information about the reservoir from preproduction wellbore pressure, dimensionless pressure and dimensionless pressure derivative curves. More specifically, we studied the preproduction behavior of three-layered reservoirs. Effects of the ratio of flow capacity and storage in different layers were investigated. We found that the layers with highest and lowest permeabilities can be characterized with the logarithmic time derivative of pre-production pressures. A positive derivative indicates high permeability in the layer with the highest initial pressure, and a negative derivative indicates high permeability in the layer with low initial pressure. Also, the layer with the highest initial pressure will always flow into the wellbore whereas flow will always be from the wellbore into the layer with minimum initial pressure. As the sandface rates reach steady state, the three-layer system behaves like an equivalent single layer system. Thus, we can apply a single-layer model to analyze the late transient in high permeability reservoirs. Introduction Most multi-layered reservoir models reported in the literature includes only two layers with equal initial pressures. In this paper, we extend modeling first to three-layer reservoirs and provide the basis for n-layer reservoirs. This work addresses the need for a practical and easily applied method to determine the individual layer properties. The first phase in layered reservoir studies dealt with the problem of commingled reservoirs with equal initial pressures 1–11 . The second phase included the effect of unequal initial layer pressures which Papadupolos 12 studied first for layered aquifers. Larsen 13 presented a method for analyzing wellbore pressures prior to the start of production for a two-layer reservoir, provided such data are available from the infinite-acting period. The method has the disadvantage that it requires estimates of the average permeability, porosity and compressibility for each individual layer. Also, this method can yield only an estimate of the average reservoir properties and not individual layer properties. Kuchuk et a1. 14 presented generalized analytical solutions for commingled reservoirs in which each reservoir or layer can be at a different initial pressure or may have a different initial pressure distribution. Agarwal et a1. 15 presented a detailed study of preproduction time period. The study showed that much information that has bearing on production performance can be discerned by the observation of the pressure behavior during the pre-production time period. A number of approximate solutions are presented for analyzing well responses. Aly 16 and Aly et al. 17 presented a complete study of the performance of commingled reservoirs with unequal initial pressures. Aly and Lee 18 presented a comprehensive semi-analytical simulator and verified it against cases from the literature. They also introduced the pre-production well test, PPWT. They presented a detailed procedure to show how to implement this test in the field and introduced analysis methods to determine the individual layer properties from the pre-production wellbore pressure.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 21–23, 1993

Paper Number: SPE-25455-MS

... of the liquid flow pressure transient solutions for describing either the flow of real gases or multi-phase flow in the reservoir. Con"sidering the developments made in

**pressure****transient****analysis**in recent years, along with the dramatic increase in the performance of microcomputers, a need has developed...
Abstract

Abstract This paper presents a summary of the development of a semianalytic reservoir model for gas reservoirs with various reservoir complexities. The types of reservoir complexities that have been considered in this study include: multiple reservoir layers in which the reservoir layers may be infinite or finite in extent, dual or single porosity systems, and wells that have been fractured. The reservoir model that has been developed and used in this study was constructed with the appropriate Laplace domain pressure and rate-transient solutions that are available in well testing literature. This reservoir model was developed to provide a more detailed and accurate means of analyzing or predicting the performance of a gas reservoir than is possible with a simple "type curve" approach, yet would be more computationally efficient than a finite difference reservoir model. The results of the semianalytic reservoir model have been validated with the reference solutions generated with a commercial finite difference reservoir simulator. The results of the semi-analytic reservoir model are comparable to the results of the finite difference simulator, yet require substantially less computation time and computer memory. Introduction Reservoir simulation has been used for many years to predict and analyze the performance of wells completed in hydrocarbon producing reservoirs. Reservoir simulation is used to predict and analyze the performance of wells and reservoirs for many different purposes, including both primary and enhanced recovery projects. Simulation can also be a cost-effective way of predicting the future performance of a reservoir for a variety of production or injection scenarios. A numerical solution method that has found widespread acceptance in reservoir simulation is the finite difference numerical scheme. Both fully implicit and IMPES (Implicit Pressure-Explicit Saturation) formulations are commonly used in reservoir simulation. There are also any number of special grid generation techniques that can be used with finite difference numerical reservoir simulators. To analyze the production data of a reservoir with numerous complexities (such as multi-phase flow, layered systems, or fractured wells) may require weeks or months to complete using a finite difference simulation model. A significant amount of reservoir research using finite difference simulation models has been conducted. P. 453^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 21–23, 1993

Paper Number: SPE-25423-MS

... flow rate

**pressure****transient****analysis**reservoir calculation variation commingled system algorithm steady state flow rate layer flow rate transient wellbore pressure drillstem/well testing spe 25423 SPE Members Abstract This work addresses the problems of design and interpretation...
Abstract

SPE Members Abstract This work addresses the problems of design and interpretation of layered reservoir tests (LRT) in commingled wells when the layer potentials are different; the difference may be in the conditions either at the initial time or at the outer layer boundaries. The multilayer models for commingled wells are constructed from existing single-layer analytic solutions to account for different layer properties and boundary conditions. A general situation is considered in which some layers have a constant pressure condition and others have a no-flow condition at the outer boundary. The algorithms developed here will allow the reservoir engineers, for the first time, to rigorously design and interpret the multi-transient LRTs using the extensive catalog of existing single-layer analytic models, rather than relying on numerical simulation. This development will not only save a great deal of computer time, but will also enable interpretation of tests in reservoirs whose geometries and parameters place them beyond the capability of existing simulators. An LRT design consists of calculating the transient wellbore potential and the individual layer rates for a given variation of the total flow rate. Two alternative scenarios are considered for the initial state of the reservoir: Either the reservoir is in equilibrium and the well is put on production at t = 0, or the well is initially producing in a steady state. Algorithmic procedures are derived from the first principles and validated by comparison with the results of finite difference numerical simulation for three different reservoir systems. A fourth example, which is beyond the capability of simple reservoir simulators, is presented to demonstrate the power of the new procedure. The LRT interpretation requires the calculation of the total and individual layer flow rates during a multitransient test, given the measured wellbore potential over the test period and the production history of the well. The scheme presented for this problem relies on a synthesis of the new test design calculation procedures with the existing algorithms for flow rate calculation. Introduction The work of Lefkovits et al. appears to be the first among many in the petroleum technical literature that address the problem of calculating the transient response of a well producing a multilayered reservoir in which communication among the layers occurs only through the wellbore (commingled systems). However, apparently only three papers deal with reservoirs in which the layers are initially at different potential. The assumption of equal initial potential in all layers is impractical due to stratigraphic barriers and/or differential depletion. The importance of properly treating unequal potential distributions in commingled systems is twofold. First, if the presence of unequal layer potentials is neglected, the individual layer properties (and thus the relative layer producibility/injectivity) obtained from well test analysis can be in gross error. This has been shown both in practice as well as in theory. Secondly, the ability to model commingled systems with unequal potential distributions allows the engineer to apply material balance concepts on a zone-by-zone basis for more reliable analysis and prediction. Papadopulos appears to have been the first to consider layers having unequal initial potential distributions. P. 115^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 21–23, 1993

Paper Number: SPE-25507-MS

... is not a "cure all" for horizontal well

**pressure****transient****analysis**. The model can lead to erroneous and even non-physical results if the input is not guided by the known physical and geological attributes of the system under study. However, if used intelligently, it can greatly enhance the interpretation...
Abstract

Abstract This paper considers the design of an algorithm for analyzing multi-rate horizontal well pressure transient data using nonlinear regression techniques. Measured data is modeled using the analytical solution for a uniform-flux horizontal well in a rectangular parallelepiped reservoir. Parameter optimization is achieved using the public-domain Levenberg-Marquardt algorithm, LMDER, from Argonne national Laboratory. We focus on efficient methods for calculation of analytical partial derivatives of the model pressure response which are required by the optimization routine. Complete expressions for all required partial derivatives are provided in Appendices, along with details on a method of evaluating these derivatives which requires minimal computational effort. We demonstrate the utility of the method by analyzing field buildup pressure data. Introduction Pressure Transient data from horizontal wells is (in many cases) difficult to interpret using conventional well test analysis techniques; e.g., semilog analysis, type curve matching and pressure derivative analysis. This is because of the number of reservoir parameters involved (i.e., three directional permeabilities for anisotropic systems) and the complex system geometry. The location of the well in the reservoir and its proximity to the reservoir boundaries can result in pressure and pressure derivative curves that appear practically unanalyzable. Difficulties in successful interpretation are further complicated by rate variations during (or before) the test, and wellbore storage effects. In this paper, we present details on a nonlinear regression analysis technique to assist the engineer in properly interpreting pressure transient data from a drawdown or buildup test on a horizontal well. Our model is based on the assumption of a "uniform flux" horizontal well in an anisotropic, bounded, rectangular box-shaped reservoirs, with the well axis parallel to one of the principal reservoir axes (see Fig. 1). The boundaries of the reservoir may be sealed or infinite-acting. Production may be at a constant rate or at a sequence of constant (step) rates. Since buildup is a production period where the rate is constant and equal to zero, it is included as a special case of multi-rate production. Figure 1 - Horizontal Well in a Rectangular Parallelepiped Reservoir. It must be emphasized that the present model is not a "cure all" for horizontal well pressure transient analysis. The model can lead to erroneous and even non-physical results if the input is not guided by the known physical and geological attributes of the system under study. However, if used intelligently, it can greatly enhance the interpretation engineer's ability to correctly analyze well test data. P. 903^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Mid-Continent Gas Symposium, April 13–14, 1992

Paper Number: SPE-24301-MS

... of the pressure and pressure derivative type curves provides a more reliable interpretation of pressure transient test data than a match of the pressure type Curve alone. Because of this advantage, recent

**pressure****transient****analysis**papers have routinely included both pressure and pressure derivative type curves...
Abstract

SPE Members Abstract This paper introduces a new family of type curves for advanced decline Curve analysis. The new type Curves are obtained by combining the dimensionless production rate and the dimensionless cumulative production on a single log-log scale. The new type curve offers two significant advantages: observed cumulative production data is much smoother than observed production rate data, making a match easier to obtain with the new type curve; and simultaneously matching both rate and cumulative production provides more confidence in the selection of the correct early- and late-time stems. Plotting functions are presented to allow the new curves to be used for both oil and gas wells produced at either constant or varying flowing bottomhole pressure. Use of tie new type curves is demonstrated for both simulated and field data. Introduction In 1973, Fetkovich proposed a dimensionless rate-time type curve for decline curve analysis of wells producing at constant bottomhole pressure. These type curves, shown in Fig. 1, were developed for slightly compressible liquids. These type curves combined analytical solutions to the flow equation in the transient region with empirical decline curve equations in the pseudo-steady state region. The analysis procedure provided estimates of formation permeability, k, and drainage radius, re, instead of the traditional decline curve analysis parameters qi and Di. This approach to decline curve analysis, now commonly referred to as "advanced decline curve analysis", has become widely used as a tool for formation evaluation and reserves estimation. Fetkovich et al. presented several case studies of the use of advanced decline curve analysis. Bourdet, et al. introduced the use of derivative type curves for transient well test analysis in 1983. By multiplying the, pressure derivative by the time, (or equivalently, by taking the derivative of pressure with respect to the natural log of time), they were able to display both the pressure and pressure derivative type curves on a single set of axes. They pointed out that a simultaneous match of the pressure and pressure derivative type curves provides a more reliable interpretation of pressure transient test data than a match of the pressure type Curve alone. Because of this advantage, recent pressure transient analysis papers have routinely included both pressure and pressure derivative type curves. The pressure derivative type curve suffers from at least one minor disadvantage in that the process of taking the derivative from measured data amplifies any noise inherent in the data. For this reason, Blasingame, Johnston, and Lee suggested using the pressure integral rather than the pressure derivative. This procedure has the advantage of reducing rather than increasing any noise in the data. Production data often contains much more noise than pressure transient test data, making application of rate derivative type curves of little value. However, rate integral, or cumulative, type curves, can reduce the effect of this noise and make analysis of production data more reliable. This paper presents cumulative type curves for wells producing a single phase fluid, from a finite, radial reservoir, at constant flowing bottomhole pressure. In addition, plotting functions are presented to allow the new type curves to be used with gas wells and with oil or gas wells producing at varying bottomhole pressures. In principle, the concept of the combination rate and cumulative type curve may be extended to hydraulically fractured wells, to wells in dual porosity systems,, or to wells in arbitrarily shaped drainage areas. Discussion Review of Fetkovich Decline Curves Fetkovich developed his type curves by combining an analytical solution to the flow equation, describing transient flow, with empirical decline curve equations describing pseudo-steady state or boundary dominated flow. The transient portion of tile Fetkovich type curve is based on an analytical solution to the radial flow equation for slightly compressible liquids with a Constant pressure inner boundary and a no flow oiler boundary. P. 91^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 13–14, 1989

Paper Number: SPE-18835-MS

...-porosity reservoir wellbore storage observation well log-log coordinate type curve semi-log derivative

**pressure****transient****analysis**interference testing pressure type curve drillstem testing reservoir drillstem/well testing double-porosity system interference pressure response constant...
Abstract

Abstract This study presents an analytical method for determining the double-porosity reservoir properties using interference pressure data in an infinite reservoir producing at constant pressure. Wellbore storage and skin effects at the production and observation wells are neglected. The effects of r D , λ, and ω, on interference pressure responses are examined. For dimensionless inter-well distances of 100 or more, the pressure responses are practically collapsed. As a result of this, a general type curve that can be used for any value of r D , is presented. Hence, for a given pressure response and r D the type curve yields unique values of λ and ω. In addition to the log-log type curve, a semi-log type curve that is more useful for p D values greater than 0.1 is presented. The semi-log derivatives of the interference pressure responses are considered. The pressure derivatives enhance small variations that occur in the pressure response during the flow period affected by the double-porosity nature of the reservoir. It is observed that using a simple correlation with λ and r D , the derivative curves for r D values greater than 100 can be collapsed. Hence, a semi-log derivative type curve is developed. This type curve has two maxima. The early-time part is influenced by λ. The time separation between the first maximum and the second maximum is a function of ω. The late time behavior is again a function of λ. Introduction Well testing has long been a very useful tool to evaluate reservoir properties such as storativity and transmissivity. In an ordinary well test, a variety of well boundary conditions can be used, such as step changes in rate or pressure, or as instantaneous slug removal. In contrast to single well testing, interference testing is limited to the collection of pressure data from an observation well. Interference testing is a multiple-well test that requires at least one active well and at least one observation well. The active well is either a producer or an injector, and the observation wells are shut-in wells in which pressure effects caused by the active well are measured. This kind of testing has the advantage of investigating reservoir properties where the characteristic length of the system is the interwell distance rather than the wellbore radius.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 8–10, 1987

Paper Number: SPE-16188-MS

... drillstem/well testing interface perforation coefficient hydraulic fracturing minifrac pressure decline analysis simulation

**pressure****transient****analysis**equivalent fracture radius curve analysis 1987. Society of Petroleum Engineers ...
Abstract

Abstract The pressure decline analysis of minifrac treatments in uniform formations, using the type curves presented by Nolte, yields information on leak-off which is necessary for fracture treatment design. A similar analysis for minifracs initiated near or at the interface of two formations of different leak-off characteristics and penetrating both formations is presented in this paper. It is concluded that the type curves given by Nolte can be used for this case with appropriate definitions of an effective (or average) leak-off coefficient and an equivalent fracture radius. The effective leak-off coefficient is the weighted average of the individual leak-off coefficients of each formation, relative to the minifrac areas in the two formations. Similarly the equivalent fracture radius is the radius of a circle of an area equal to the sum of the areas of the minifrac in the two formations. An estimate of the individual leak-off coefficients of each formation may be obtained by a trial and error comparison of simulated values of the P- pressure (as defined by Nolte), using a three dimensional fracturing simulator, with the one obtained directly by minifrac pressure decline type curve analysis. Four examples of application of the new theory to North Sea oil wells are presented. Introduction The pressure decline analysis of minifrac treatments was first described by Nolte who applied it for minifrac treatments confined in one formation. Smith, Miller, and Haga have applied Nolte's method for unconfined minifrac treatments contained in one formation and being essentially penny shaped. The success of the method depends on the ability to derive a closed form solution based on the assumption that the fracture area is proportional to pumping time for high efficiency (storage dominated) minifracs, and proportional to the square root of pumping time for low efficiency (leak-off dominated) ones. These two cases provide the bounds for actual minifrac pressure behavior. A similar type of analysis is described in this paper, where the fracture during the minifrac treatment is assumed to have propagated into two zones of different leak-off coefficients. Fracturing treatments initiated near or at the interface of two formations have been applied in the oil fields of the North Sea to obtain relatively stable well completions. The minifrac and main fracture treatments propagate in two formations of different leak-off characteristics and mechanical properties. The usual minifrac pressure decline analyses yield leak-off coefficients that vary significantly from well to well, although the wells are located in the same region of the field and the minifracs are performed from perforations at the interface of the same formations. The calculated leak-off coefficients are often different from the leak-off coefficients obtained from minifracs contained entirely in either of the two formations. In many instances the analysis results from minifracs near formation interfaces are completely discarded as "unbelievable" and leak-off coefficients from general field experience are used to design the fracturing treatments. These discrepancies in minifrac interpretations are attributed to the complex fracture geometry and the different leak-off characteristics of the two formations. The need of a more detailed leak-off theory is apparent for such complex cases.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 8–10, 1987

Paper Number: SPE-16225-MS

... SPE Member Abstract A theoretical basis for

**pressure****transient****analysis**of gas wells with emphasis on the real gas pseudo pressure approach is outlined. An analysis procedure is developed to analyze wells either injection or producing predominantly C02 or enriched gas. This procedure 's used...
Abstract

SPE Member Abstract A theoretical basis for pressure transient analysis of gas wells with emphasis on the real gas pseudo pressure approach is outlined. An analysis procedure is developed to analyze wells either injection or producing predominantly C02 or enriched gas. This procedure 's used to calculate flow capacities and skin factors from pressure transient tests in injection and production wells from two C02 projects. A computer program is documented which aids in the analysis of gas wells with the real gas pseudo pressure. Finally, example calculations are shown for a C02 well, an enriched gas well, and an enriched gas well contaminated with C02 / H2S. Introduction Pressure transient analysis is one of the most widely used methods in reservoir engineering to obtain in-situ reservoir data. A variety of transient testing techniques have been developed including pressure buildup, pressure drawdown, injectivity, pressure falloff, and interference testing. Reservoir data calculated from these techniques includes wellbore volume, wellbore damage or stimulation, reservoir pressure, flow capacity (permeability), reserves, fracturing, reservoir discontinuities, fluid discontinuities and swept volume. Pressure transient analysis was developed for liquid filled reservoirs with a small total compressibility. The solution of the diffusivity equation for a liquid filled reservoir results in a derivative of pressure with respect to time. This is the basis of the pressure vs time plot used to determine reservoir properties. The classical liquid filled reservoir analysis has been extended to gas wells by three different approaches. The first is by analogy to the classical liquid filled reservoir analysis. This is possible through the use of average gas viscosity (jig), gas z factor (z), and gas compressibility (Cg) at the reservoir temperature, T, and average reservoir pressure, p. These assumptions are good in most was reservoirs below 2000 PSI as long as pressure gradients in the reservoir are small, since for most natural gas wells, ug z at these conditions is approximately constant, Figure 1. Above this pressure, (ug - z) / p is approximately constant. This gives rise to the second approach, where p2 instead of p is analyzed as a function of time. The p2 vs time relationship is used because the solution of the diffusivity equation for a gas filled reservoir yields a derivative of p2 with respect to time. In many cases the assumptions of constant ug, z, Cg, and small pressure gradients are not met and both the p and p2 methods are invalid. As a result, a third approach was formulated which accounts for variations in jig and z as a function of p and allows large pressure gadients making the approach much more accurate. This is achieved through the use of a real gas pseudo-pressure function, m(p), which is a function of p, ug, and z and which matches Figure 1 exactly. With this function, the solution of the diffusivity equation for a gas filled reservoir results in a derivative of m(p) with respect to time; therefore m(p) instead of p or p2 is analyzed as a function of time. The m(p) function has been applied extensively in natural gas reservoirs and many sources of natural gas m(p) data are available. The use of the real gas pseudo-pressure is not limited to gas wells, but can be applied to any flowing fluids as long as effective viscosities and compressibilities can be calculated. The wide application of miscible gas processes in the field has given rise to another set of pressure transient tests which can be analyzed with the real gas pseudo-pressure; those injecting or producing predominantly miscible gas, either C02 or enriched natural gas. This report documents application of the m(p) approach to such wells. THEORETICAL BASIS Pressure transient analysis is based on the radial diffusivity equation. This equation may be solved for slightly compressible liquids (the classical pressure transient analysis) yielding the derivative of p with respect to time, for an ideal gas yielding the derivative of p2 with respect to time, and with the real gas pseudo-pressure yielding the derivative of m(p) with respect to time. P. 517^

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the SPE Production Operations Symposium, March 10–12, 1985

Paper Number: SPE-13798-MS

... fracture geometry computer upstream oil & gas bottomhole pressure pressure transient testing leakoff coefficient fracture hydraulic fracture hydraulic fracturing fluid viscosity

**pressure****transient****analysis**viscosity fracture height sensitivity analysis SPE Society of Petroleum Engineers...
Abstract

Abstract This paper shows how an understanding of the relative influence of fracture design parameters, and treatment procedures enable the engineer to improve hydraulic fracture results. The measurement of a few critical parameters provides a better understanding of fracturing in a particular formation. provides a better understanding of fracturing in a particular formation. Results are presented from a joint program of research carried out between Gulf Research and Development Company and Gulf Oil Exploration and Production Company during 1984. The principal objectives of this program Production Company during 1984. The principal objectives of this program were to obtain improved field data for the verification of fracture simulators, and to investigate the field measurements and analysis of parameters found to significantly affect design. Emphasis is placed on parameters found to significantly affect design. Emphasis is placed on understanding the effect of reservoir properties on the created fracture and the required fracturing pressure. This information was then used in the field to optimize limited size treatments in particular formations. Introduction The technique of hydraulically fracturing formations to increase production rates and available reserves is common practice within the petroleum industry. The placement of an optimal fracture to act as a high conductivity flow channel requires both correct design and correct field procedures. The measurement, interpretation and understanding of previous procedures. The measurement, interpretation and understanding of previous treatments together with on-the-job analysis and redesign play an important role in improving treatment performance. This paper presents a sensitivity analysis of input parameters on fracture design, and results of using this information to improve hydraulic fracture treatments. Similar analysis has been used in past studies to understand the effect of particular parameters. In the present work results are included from a field research program set up similar to the program described by other engineers studying the application of massive hydraulic fracture treatments. Three West Texas formations were chosen for study during the first phase of this project. The criteria used in field/formation selection are listed in Table 1. Formation A is a shallow (2500-3000 ft deep) oil reservoir with typical net and gross pay zones of 150 and 300 ft respectively. It is characterized by gradual structural changes and no well defined cap and base rocks. Formation B is a moderately deep (6500 ft) predominantly gas reservoir with defined shale barriers. Formation C is a deep (11,000 - 15,000 ft), tight oil and gas formation characterized by a high degree of secondary permeability and poorly defined barriers. A number of different tests and measurements were selectively carried out in conjunction with the 35 hydraulic fracture treatments considered part of this project. It is not the purpose of this paper to present all of the data from each test conducted in this study. Material will be limited to showing how an analysis of input parameters affecting fracture design identified certain critical parameters, and how field measurements of these values were attempted. FRACTURE DESIGN Two fracture simulators were used for design and post-fracture analysis reported in this paper. They are referred to as the GULF-1 and GULF-2 simulators. The GULF-1 hydraulic fracture simulator is an analytical model for the design and evaluation of treatments. It is a two-dimensional model for the case of constant height vertical fractures. It consists of a fracture propagation model, a proppant transport model, and a reservoir production propagation model, a proppant transport model, and a reservoir production model. p. 77