Rate-dependent Skin Research Articles

Integrated approach for non-Darcy flow in hydraulic fractures considering different fracture geometries and reservoir characteristics

Abstract The motivation is eliminating the uncertainties in predicting reservoir performance, and reducing the errors in the reservoir characterization resulted by neglecting the impact of non-Darcy flow. In this study, an analytical multi-linear flow regimes model has been developed for pressure distribution in hydraulically fractured reservoirs and modified for the existence of non-Darcy flow by introducing the rate-dependent skin factor to the flow equations. This model is solved for different impacts of non-Darcy flow by assuming a constant flow rate and different non-Darcy flow coefficients. The effects of different cross-section areas of flow inside hydraulic fractures on the non-Darcy flow coefficient are considered in this study as well as different fracture conductivities. Reservoir configurations and petrophysical properties are also considered in calculating pressure distributions. Analytical models for hydraulic fracture linear flow regime, bi-linear flow regime, and boundary-dominated flow regime are developed based on pressure responses for different non-Darcy flow impact. Analytical models for transient and pseudo-steady state productivity indices are presented in this paper to demonstrate the impact of non-Darcy flow on these indices. The results of this study showed there are considerable effects of non-Darcy flow on reservoir performance and developed analytical mathematical models for recognized flow regimes which observed during reservoir production period. Additionally, results illustrated the reservoir configurations and petrophysical properties may not have significant contribution in developing non-Darcy flow. Finally, the productivity index has been sharply declined for later production time. Meanwhile, it is constant for high rate-dependent skin factors at the early time of production.

Analysing and characterising horizontal well performance in rectangular closed gas reservoirs considering non-Darcy flow conditions

This paper investigates the impact of non-Darcy flow, represented by rate-dependent skin factor (DQSC), on pressure profiles, flow regimes, and productivity indices of horizontal wells extending in conventional and unconventional gas reservoirs. It introduces a new simplified technique for characterising reservoir performance under different non-Darcy flow impacts. The outcomes of this study are summarised as: 1) understanding the conditions at which non-Darcy flow could have considerable effects on reservoir performance; 2) estimating the deviation in productivity index caused by non-Darcy flow. The most interesting points in this study are: 1) the ability to estimate rate-dependent skin factor from well test analysis by observing early time radial flow regime; 2) all flow regimes, unlike pressure behaviors and productivity index, are not affected by non-Darcy flow; 3) productivity index declines sharply for high rate-dependent skin factor at early production time while pseudo-steady state productivity index is not affected by non-Darcy flow. [Received: April 12, 2018; Accepted: May 9, 2018]

Analysing and characterising horizontal well performance in rectangular closed gas reservoirs considering non-Darcy flow conditions

This paper investigates the impact of non-Darcy flow, represented by rate-dependent skin factor (DQSC), on pressure profiles, flow regimes, and productivity indices of horizontal wells extending in conventional and unconventional gas reservoirs. It introduces a new simplified technique for characterising reservoir performance under different non-Darcy flow impacts. The outcomes of this study are summarised as: 1) understanding the conditions at which non-Darcy flow could have considerable effects on reservoir performance; 2) estimating the deviation in productivity index caused by non-Darcy flow. The most interesting points in this study are: 1) the ability to estimate rate-dependent skin factor from well test analysis by observing early time radial flow regime; 2) all flow regimes, unlike pressure behaviors and productivity index, are not affected by non-Darcy flow; 3) productivity index declines sharply for high rate-dependent skin factor at early production time while pseudo-steady state productivity index is not affected by non-Darcy flow. [Received: April 12, 2018; Accepted: May 9, 2018]

Predicting Performance of High Deliverability Horizontal Gas Wells and Control of Water Cresting in Tertiary Sands East Africa

The field-A1 is an offshore gas field located about 56 km from the coast of East Africa with the water depth of 1153 m. The permeability distribution varies across different layers with an overall permeability of 680 m and porosity distribution for the reservoir field-A1 varies 0.21-023. The reservoir thickness also varies up to 50 m thick. This research work identifies parameters that will contribute to the impact of water coning. Simulation sensitivities are run to observe the effect of water coning/cresting in horizontal gas wells and predicting the performance of these wells using Petrel simulator. Results have shown that put horizontal well in East-west will have early water breakthrough and not recommended due to the impact of edge aquifer due to less recovery compared to north-south and original wells orientation (northwest-southeast). The varying height of perforation and standoff as identified is at the standoff between 30-40 m in the field-A2 will delay water coning high recovery with more extended plateau length period. The gas recovery may happen to be low, due to the distribution of permeability layer for the horizontal wells and low productivity index that is the performance of the well. Rate-dependent skin and mechanical skin evolution in time show that increasing non-Darcy /turbulence factor reduces the performance of the well and decreases gas recovery the high drawdown tendency is observed before water breakthrough time however there is early water breakthrough, thus use of deep penetration. Horizontal gas wells have a constant horizontal length for all cases of 300 m increasing tubing head pressure from 40-100 bars result to decrease plateau length period of the gas production, low water production rate, and low gas recovery. Varying the kv/kh ratio from 0.1, 0.6 to 1 shows early water breakthrough by 6 months earlier from the base case with 0.1 hence will not delay water coning. The gas recovery is reduced by 5%. Gas recovery is increased with an increase in gas rates constrain, and early water breakthrough is observed when producing at high rates. Producing at low rates may delay water coning. However, it is not economical since there is less gas recovery and may take a more extended period for production to reach to its total maximum gas production of which is less compared when producing at high gas rates. There is a stronger of the aquifer from the west side, which is predictable to cause water coning than on the east side. This aquifer impacts the gas recovery reduction by 19%, with water coning radial extension of 1.7 km and peak water production rate for 16 years. The aquifer influx rate is seen to be increased by 69% when the aquifer volume is double. Therefore, from the results producing at a high rate that has high recovery before the impact of aquifer or water has occurred to the wells, known as outrunning of the aquifer. To avoid water coning, using advance completion technique such as inflow control devices (ICD), installing a down hole gauge. Also, it is essential not to perforate if well is near to gas water contact the horizontal wells should be located at maximum distance from gas water contact to maximize gas recovery. Not only that but also use of fully open choke allows much water production rate increase, which leads to water coning.

Predicting Performance Of High Deliverability Horizontal Gas Wells And Control Of Water Cresting In Tertiary Sands East Africa

The field-A1 is an offshore gas field located about 56 km from the coast of East Africa with the water depth of 1153 m. The permeability distribution varies across different layers with an overall permeability of 680 m and porosity distribution for the reservoir field-A1 varies 0.21-023. The reservoir thickness also varies up to 50 m thick. This research work identifies parameters that will contribute to the impact of water coning. Simulation sensitivities are run to observe the effect of water coning/cresting in horizontal gas wells and predicting the performance of these wells using Petrel simulator. Results have shown that put horizontal well in East-west will have early water breakthrough and not recommended due to the impact of edge aquifer due to less recovery compared to north-south and original wells orientation (northwest-southeast). The varying height of perforation and standoff as identified is at the standoff between 30-40 m in the field-A2 will delay water coning high recovery with more extended plateau length period. The gas recovery may happen to be low, due to the distribution of permeability layer for the horizontal wells and low productivity index that is the performance of the well. Rate-dependent skin and mechanical skin evolution in time show that increasing non-Darcy /turbulence factor reduces the performance of the well and decreases gas recovery the high drawdown tendency is observed before water breakthrough time however there is early water breakthrough, thus use of deep penetration. Horizontal gas wells have a constant horizontal length for all cases of 300 m increasing tubing head pressure from 40-100 bars result to decrease plateau length period of the gas production, low water production rate, and low gas recovery. Varying the kv/kh ratio from 0.1, 0.6 to 1 shows early water breakthrough by 6 months earlier from the base case with 0.1 hence will not delay water coning. The gas recovery is reduced by 5%. Gas recovery is increased with an increase in gas rates constrain, and early water breakthrough is observed when producing at high rates. Producing at low rates may delay water coning. However, it is not economical since there is less gas recovery and may take a more extended period for production to reach to its total maximum gas production of which is less compared when producing at high gas rates. There is a stronger of the aquifer from the west side, which is predictable to cause water coning than on the east side. This aquifer impacts the gas recovery reduction by 19%, with water coning radial extension of 1.7 km and peak water production rate for 16 years. The aquifer influx rate is seen to be increased by 69% when the aquifer volume is double. Therefore, from the results producing at a high rate that has high recovery before the impact of aquifer or water has occurred to the wells, known as outrunning of the aquifer. To avoid water coning, using advance completion technique such as inflow control devices (ICD), installing a down hole gauge. Also, it is essential not to perforate if well is near to gas water contact the horizontal wells should be located at maximum distance from gas water contact to maximize gas recovery. Not only that but also use of fully open choke allows much water production rate increase, which leads to water coning.

Performance-Based Comparison for Hydraulically Fractured Tight and Shale-Gas Reservoirs With and Without Non-Darcy-Flow Effect

Summary Reservoir performance of hydraulically fractured tight and shale-gas formations is affected by an extensive range of parameters. Non-Darcy flow is one of these parameters, characterized by a significant effect on near-wellbore pressure drop for horizontal wells and near-fracture tips for hydraulic fractures (HFs). Non-Darcy flow develops in porous media when the velocity of reservoir fluid becomes extremely high because of continuous narrowing in the cross-sectional area of flow and the convergence of flow streamlines. As a result, the inertial forces could be considered the major contributor to the total pressure drop required by fluids to move from the outer drainage area toward the wellbore. Pressure drop, caused by non-Darcy flow, is described by the Forchheimer (1901) equation, wherein the deviation from Darcy's law is proportional to the inertial factor (β), which in turn is a function of porous-media characteristics such as permeability and porosity. This paper investigates the effect of non-Darcy flow, represented by the non-Darcy-flow coefficient (D) and/or the rate-dependent skin factor (DQsc), on pressure profiles, flow regimes, and productivity indices (PIs) of multiple HFs that propagate in tight and shale-gas reservoirs. This paper also introduces a new simplified technique for estimating both DQsc and D by knowing bottomhole flowing pressure and cumulative production at any time. For this purpose, a multilinear-flow-regime model was generated and modified for the existence of non-Darcy flow. A comparison for reservoir performance with and without non-Darcy flow was conducted for different reservoir configurations, including the reservoir-drainage area (2xe and 2ye), fracture conductivities, fracture dimensions, and fracture-propagation ratios. A set of plots has been developed for estimating the rate-dependent skin factor depending on production time with respect to cumulative PI. The outcomes of this study can be summarized as understanding the conditions at which non-Darcy flow could have considerable effects on reservoir performance; estimating the deviation in PI caused by the existence of non-Darcy flow from the cases where Darcy flow is the dominant; and introducing a new technique to estimate DQsc and D. The most interesting points in this study are the ability to estimate these two parameters without the need for experimental studies or use of an empirical model; that all flow regimes expected to develop in the entire life of reservoirs are not affected by non-Darcy flow, unlike pressure behaviors and PI; and that the PI is constant for high values of DQsc at early-time production and sharply declines at later production time.

New technique for determining rate dependent skin factor & non-Darcy coefficient

A non-Darcy flow develops in porous media when the velocity of reservoir fluids becomes extremely high because of the continuous narrowing of the cross section area of the flow and the convergence of flow streamlines. Therefore, the inertial effect increases significantly and the total pressure drop, required by fluids to move from the outer drainage area towards the wellbore increases significantly due to the extra pressure drop caused by the non-Darcy flow. The extra pressure drop is described by the Forchheimer equation in which the deviation from Darcy's law is proportional to the inertial factor which in turn is a function of porous media characteristics such as permeability and porosity.This paper introduces a new technique for estimating rate dependent skin factors (DQsc) and non-Darcy flow coefficients (D). The new technique uses dimensionless pressure for steady state flow to determine these two parameters. A set of plots has been developed for the term (DQsc) based on reservoir configurations i.e. reservoir boundaries (2xe & 2ye), wellbore length, and anisotropy. All the plots have been developed based on the fact that the rate dependent skin factor represents the difference between the total pressure drop and the pressure drop caused by Darcy flow only when non-Darcy coefficient equals to zero. Dimensionless pressure drops for horizontal wells producing from finite acting reservoirs have been calculated for steady state flow when the impact of dimensionless time can be eliminated. The calculated pressure drops have been used in reservoir performance models to estimate rate dependent skin factors and non-Darcy coefficients.A point of special interest in this study is the ability to estimate these two parameters without the need for experimental work or the need to use currently proposed empirical models for calculating them. This new technique requires knowing reservoir configurations (reservoir width and length), the length of the wellbore, and the height of the formation in addition to the anisotropy. The study indicates that rate dependent skin factors and non-Darcy coefficients have the minimum values when the reservoirs having square-shape drainage area. It has also been found that both parameters have great impact on wells with short wellbore length. Additionally, isotropic formations and symmetrical wells perform better than anisotropic formations and asymmetrical wells in terms of extra pressure drop caused by non-Darcy flow.

Flow Rate-Dependent Skin in Water Disposal Injection Well

Reinjection is one of the most important methods to dispose fluid associated with oil and natural gas production. Disposed fluids include produced water, hydraulic fracture flow back fluids, and drilling mud fluids. Several formation damage mechanisms are associated with the injection including damage due to filter cake formed at the formation face, bacteria activity, fluid incompatibility, free gas content, and clay activation. Fractured injection is typically preferred over matrix injection because a hydraulic fracture will enhance the well injectivity and extend the well life. In a given formation, the fracture dimensions change with different injection flow rates due to the change in injection pressures. Also, for a given flow rate, the skin factor varies with time due to the fracture propagation. In this study, well test and injection history data of a class II disposal well in south Texas were used to develop an equation that correlates the skin factor to the injection flow rate and injection time. The results show that the skin factor decreases with time logarithmically as the fracture propagates. At higher injection flow rates, the skin factor achieved is lower due to the larger fracture dimensions that are developed at higher injection flow rates. The equations developed in this study can be applied for any water injector after calibrating the required coefficients using injection step rate test (SRT) data.

The Precise Prediction of the Turbulence Coefficient Based on Neural Network Modeling

Skin is the most challenging problem in oil and gas production resulting from near wellbore mechanical damage or non-Darcy effect due to gas turbulence. Mechanical skin is introduced to the pay zone during drilling and completion phase while rate-dependent skin (non-Darcy effect) comes into play as gas production commences. Also turbulence effect may cause a huge pressure drop for oil wells but it is more sensitive in gas production. Rate-dependent skin is caused by contravening basic Darcy's assumptions in gas reservoir and would be sensible as gas starts rushing to the wellbore. It can be used to have an idea about fluid compressibility and flow path tortuosity near wellbore caused by high gas flow rate. Lots of attempts have been directed for computation of rate-dependent skin. Most of them proposed a power mode equation for estimation of non-mechanical skin in gas reservoirs. This includes turbulence coefficient, squared drawdown pressure, flow rate, and deviation coefficient. The turbulence coefficient (D) to be determined needs running a gas well test or at least two pressure flow rate data points. Other conventional methods also can be used for prediction of this parameter. But as a matter of fact, every predictor model may ignore some effective parameters for simplicity, which might deviate the result from reality. Thus, using a better approach including as much as possible effective parameters such as artificial intelligence can result in more accurate results. The authors propose a new technique to estimate value of the turbulence coefficient (D) by using neural networks based on skin factor, reservoir rock, and fluid properties. It is easy to apply and evaluate. The proposed method is validated using field data under variety of conditions. A computed value of D from neural network matches real data pretty well in comparison with conventional correlations.

Technology Focus: Well Testing (February 2012)

Technology Focus The value of information has a ubiquitous and sometimes pervasive role in modern well testing. From exploration to field management to surveillance, well-test practitioners deal with a wide array of measurements (e.g., pressure, flow rates, temperature, and fluid analysis) that, more often than not, encompass large amounts of data. This is particularly true for long-term-production-data analysis of established fields, and one can argue the same for any current pressure-transient analysis that also has benefited from improved and more-robust data-acquisition available today. Likewise, dynamic information through downhole testing equipment can be acquired in real time—wirelessly and at sampling frequencies that were not possible only a decade ago. Yet what seems to be a relative abundance of data often is challenged by the complex environments in which we operate and by our need to assess its value against associated costs and business risks. One way to look at this is under the premise that, while “perfect” information is beneficial to have, it also is costly to acquire and economically inefficient. Is there a unique answer in our choice of type curves, material balance, or specialized graphs? Should we account for multiphase flow or rock compaction? More importantly, what is the value of the next-best substitute for the information we require? And can this substitute information still allow us to meet our testing objectives? Herein lies the delicate balance between our choices of risk and uncertainty, which brings us to the message of this feature: We should not look for data-rich, but information-rich, content that meets our testing needs. The papers selected for this feature describe exciting advances and opportunities in well testing. They also show that the proper use of advanced techniques can lead to maximizing the value of the information at hand, even in hostile and unconventional situations. Recommended additional reading at OnePetro: www.onepetro.org. SPE 143592 Assessment of Rate-Dependent Skin Factors in Gas-Condensate and Volatile-Oil Wells by A.C. Gringarten, SPE, Imperial College London, et al. SPE 146450 3D Multiphase Streamline-Based Method for Interpretation of Formation-Tester Measurements Acquired in Vertical and Deviated Wells by Hamid Hadibeik, SPE, University of Texas at Austin, et al. SPE 142818 Application of IFOT in Tight Gas as a Reservoir-Surveillance Technique by E. Pinto, BP plc, et al.

Dealing With the Challenges of the Rate-Dependent Skin Phenomenon in a Gas Condensate Reservoir: A Simulation Approach

Skin is one of the most challenging problems in oil and gas production, resulting in a reduction in reservoir deliverability. Mechanical skin is introduced to the pay zone during the drilling and completion phase, while rate-dependent skin comes into play as production starts, and is caused by infracting basic Darcy assumptions in a gas reservoir. Dissimilar to conventional gas reservoirs, the formation of condensate jots in a gas condensate reservoir when the bottomhole pressure drops below the dew point causes higher skin, which imposes a greater pressure drop. The authors investigated dependency of skin to flow rate in gas condensate reservoirs through a simulation approach. A radial synthetic reservoir compositional model was developed by using rock and fluid properties and well data based on information from a real gas condensate field in south Iran. A well test analysis was utilized to verify the validity and accuracy of the model. Due to heterogeneity existence in particular field, the authors tried to consider different reservoir and wellbore characteristics in reservoir simulation models. A wide range of rock permeabilities and mechanical skins were examined in different irreducible water saturations. Moreover, all the scenarios were run in two different initial reservoir pressures individually. The result of numerous simulations showed a similarity between the trends of rate-dependent skin versus flow rate for the entire tested model. It was also illustrated that in low-permeable gas condensate reservoirs, the existence of mechanical skin leads to inefficient production. Because mitigation of some kind of mechanical skin types are not efficient, the same simulation study should be performed before starting the drilling operation in a gas condensate reservoir to assess the effect of mechanical skin.

Near‐Well Nonlinear Flow Identified by Various Displacement Well Response Testing

The impact of nonlinear flow phenomena on well response tests is still not completely understood today. With the present paper, a set of 10 well response tests is investigated. The tests were conducted in a fractured Devonian limestone formation close to the western national border of Germany. The test design incorporates a packer as well as different solid cylinders to initiate a series of slug-injection and slug-withdrawal tests by various initial displacements. Nonlinear response characteristics were observed in the course of the tests, which cannot be explained by tubing-controlled flow inside the cased well. The analysis shows that the nonlinear response characteristics are likely to be either formation controlled according to non-Darcian flow developing in a high-conductivity fracture compartment of the tested limestone formation or a consequence of a severe well inefficiency caused by some sort of screen clogging. This inference is obtained from analyzing the data by a nonlinear well response test model, which differentiates between wellbore internal hydraulic head losses and a generalized rate-dependent skin effect accounting for nonlinear flow processes in the vicinity of the well. The potential of identifying near-well nonlinear flow by various displacement well response testing may indicate this methodology to be a valuable complement to modern high-resolution borehole imaging techniques used when characterizing fractured reservoirs and the tightness of fractured reservoir cap rocks.

Fractured-Well-Test Design and Analysis in the Presence of Non-Darcy Flow

Summary The objective of this paper is to discuss the design and analysis of fractured-gas-well tests to account for non-Darcy flow within the fracture. The results and discussions are based on a semianalytical model. Guidelines and correlations are presented to enable engineers to design fractured-well tests whereby the magnitude of non-Darcy flow may be estimated and its effect minimized, if necessary. The effect of non-Darcy flow skin (or rate-dependent skin) is discussed in detail. A method is also presented to analyze fractured-well tests under non-Darcy flow conditions to estimate the non-Darcy flow coefficient, fracture conductivity, and reservoir properties. Unlike the conventional methods, this method does not require two tests at different production rates.

Analysis of Hydraulic Fracturing of High Permeability Gas Wells to Reduce Non-Darcy Skin Effects

Abstract Hydraulic fracturing has become increasingly popular in high permeability gas reservoirs in order to reduce apparent skin and thus improve well productivity. The remaining post fracture rate dependent skin effect varies from case to case and it is unclear whether this is a result of non-Darcy flow in the fracture, the reservoir or both. This paper presents a study of the effects of reservoir and fracture turbulence in fractured gas wells. A quantification of the fracture length required to eliminate the effects of reservoir turbulence is obtained by means of a numerical study. A similar study with non-Darcy flow in both the reservoir and the fracture results in a correlation of fracture length required to get zero apparent skin at 75﹪ of AOF as a function of reservoir permeability, pressure, fracture conductivity and β factor. Introduction As shown first by Forschheimer(1) flow through porous media deviates from the linear Darcy's law and can be described by a quadratic equation with a non-Darcy flow coefficient β in the nonlinear term. The coefficient β has been correlated to reservoir permeability by numerous authors; in general β decreases with increasing reservoir permeability. Experience has shown that the non-Darcy term becomes more significant in higher permeability gas reservoirs. Generally for reservoir permeabilities below 1 mD there is little effect from non-Darcy flow. In higher permeability reservoirs non-Darcy flow can significantly restrict well production rates and may also affect the pressure transient response. Hydraulic fracturing has become increasingly popular in high permeability gas reservoirs. Normally the goal for hydraulic fracturing high permeability gas wells is to bypass skin damage and thus increase initial flow rates. These 'skin' fractures are generally small in nature and may or may not include high-grade proppants. Prior to performing such a treatment there is often evidence to support a high permeability reservoir and a high apparent positive skin. Unfortunately there is rarely enough data to distinguish if this skin is a true mechanical skin or rate dependent (non-Darcy) skin. Post fracture analysis may show apparent skins ranging from slightly negative to neutral to positive. If a multi-rate post fracture test was performed it is sometimes possible to separate mechanical skin from rate dependent skin. The basic problem with applying the rate dependent skin analysis to a fractured well is that the rate dependent skin was developed based on the assumption of radial homogeneous flow into the wellbore. By adding a hydraulic fracture the flow regime has been altered and the theory breaks down. It is unclear whether the rate dependent skin is occurring in the linear fracture flow or in the reservoir or in both. The primary purpose of this study is to quantify when reservoir turbulence is insignificant for a fractured well. The second purpose is to provide a simple method for predicting post fracture rates in high permeability reservoirs taking into account fracture turbulence. Literature Review The previous work on non-Darcy flow can be divided into two main categories:what is the exact nature of non-Darcy flow andhow to predict when non-Darcy flow will have a significant effect on production.

IMPROVED CONVOLUTION ANALYSIS OF LATE WELLBORE STORAGE BUILDUP DATA OF GAS WELLS

ABSTRACT Conventional pressure buildup tests of gas wells with wellbore storage have long been recognized as providing somewhat inaccurate estimates of the reservoir parameters. Also, the application of these tests to low permeability reservoirs is time consuming and impractical in some field practice. Moreover, these tests do not offer a straight forward method to determine of the rate-dependent skin factor of high-flow-rate wells. This paper presents an extension of the convolution methods to analyze late wellbore storage buildup data of high-flow-rate gas wells. In addition of possessing all the advantages of the convolution techniques, the proposed extension offers a simple method that permits a direct estimation of the formation permeability, the mechanical and the rate-dependent skin factors, and the extrapolated reservoir pressure from three different analysis plots.

Pressure buildup analysis of gas wells with damage and non-Darcy flow effect

This paper presents a technique to analyze pressure buildup test data of gas wells with damage and non-Darcy skin effect. This technique allows the analyst to estimate reservoir permeability and mechanical and rate-dependent skin factors directly by using 2 analysis plots. Formation permeability and rate-dependent skin are obtained from the slope and the intercept of the first plot, respectively, whereas the mechanical skin factor is determined from the intercept of the second plot. In addition, a graphical method to determine the reservoir pressure at infinite shut-in time is proposed. Field and simulated tests are presented to demonstrate the applicability of the technique. The results obtained are compared with new, conventional, and pressure derivative type curve matching techniques.

Pressure Transient Analysis of Fracture Calibration Tests

Summary Fracture-calibration pressure decline has been used for determination of the leakoff coefficient, a bulk variable describing the process of fluid influx into the reservoir, normal to the created fracture face. In this work, the fluid loss is modeled in terms of the controlling mechanisms: flow through the filter cake, the invaded zone, and the reservoir. A rigorous model describes unsteady-state fluid flow from fractures of varying area into the formation, with the filter cake considered as a time- and rate-dependent skin effect. The injection history is superposed on the pressure decline. This work provides a straight-line technique for determination of reservoir permeability and fracture-face resistance. Log-log diagnostic plots provide the means to recognize visually whether the transient response is dominated by flow in the reservoir or at the fracture face. We found that the pressure transient very frequently is dominated by the flow in the reservoir rather than through the filter cake. The reservoir permeability (an essential value for fracture design that is usually not available) can be estimated, while the model captures all trends of the falloff-pressure variation. Introduction The fracture-calibration treatment, also called an injection test or "minifracture," frequently is conducted before the main stimulation treatment. For the injection test, the fracturing fluid intended for the main treatment is pumped at a constant rate of a sufficient magnitude to achieve fracturing pressure. After several minutes (usually 20 to 30) the pumps are shut off and the bottomhole pressure declines as the fracture closes. During pumping, while the fracture volume grows, some of the fracturing fluid leaks off into the formation. After pumping ends, the fluid leakoff into the formation continues until the fracture is closed. Material balance, coupled with a model of propagation, permits estimation of the rate of fluid loss during pumping. The behavior of the pressure decline after the end of pumping has been used to estimate the leakoff (fluid-loss) coefficient, with techniques pioneered by Nolte. Castillo, using Nolte's G-function for modeling the pressure-decline behavior, developed the straight-line plot of the G-function vs. pressure. The slope of this curve is used for the computation of the leakoff coefficient that is independent of pressure.

Use of Simultaneous Flow-Rate and Pressure Measurements to Replace Isochronal Gas Well Tests

Summary The interpretation of gas well pressure-transient tests differs from that of oilwell tests in two important respects: the nonlinearity of the governing equations and the presence of a rate-dependent (non-Darcy) skin. The nonlinearities are commonly avoided by use of pseudofunctions, and the non-Darcy skin effect is handled by use of flow-after-flow, isochronal, or modified isochronal tests. Recent investigations have shown that the simultaneous measurement of well flow rate with well pressure can significantly shorten the test duration required for accurate interpretation. These methods rely on use of the straight-line approach, however, and in some cases on trial and error. This paper describes a computer-automated interpretation approach that can be applied generally for any type curve without trial and error. The use of this interpretation technique can reduce the test duration to only that required for a standard drawdown or buildup test, and will allow the estimation of the stabilized deliverability potential without flowing the well until stabilization is reached. Examples of use of the method on both simulated and real data demonstrate its effectiveness.

Gas Well Test Analysis: Use of Normalized Pseudovariables

Summary Pressure data from gas wells are normally analyzed by use of pseudopressure, which is a transformation of measured pressure. When tests are associated with large pressure changes accompanied by a severe wellbore storage effect, such as in tight reservoirs, use is made of pseudopressure and pseudotime transforms. The purpose of the pseudovariables is to linearize "effectively" the governing diffusivity equation so that proper test interpretation can be made. In this study, normalized pseudovariables or transforms are introduced. Use of these new pseudovariables produces results identical to those obtained with the conventional pseudovariables. However, the proposed pseudovariables offer some distinct practical advantages. For example, units of pressure and time are retained, thus giving a physical "feel" for the pseudovariable definitions. Other features include use of liquid equations for solving the gas flow problems—i.e., constants of the working equations remain unchanged. This study also proposes two methods for estimating the rate-dependent skin, together with permeability, mechanical skin, and well deliverability. The first method involves logarithmic convolution of pressure with flow rate, both measured downhole, by use of a radial model. A trial-and-error approach is used to obtain the rate-dependent skin on a convolution plot. The second method requires a transient flow-after-flow test of short duration; a standard graphic technique allows the estimation of the desired reservoir parameters. Once the reservoir parameters are estimated with either method, the absolute open-flow potential (AOFP) of a well can be established by assuming a reservoir radius because the AOFP is relatively insensitive to this assumption.