Type-curve Method Research Articles

A Two-Phase Flowback Type Curve with Fracture Damage Effects for Hydraulically Fractured Reservoirs

Summary Type curves are a powerful tool in characterizing hydraulic fracture (HF) and reservoir properties based on flowback and production data. We propose a type-curve method to evaluate HF characteristics and their dynamics for multifractured horizontal wells (MFHWs) in hydrocarbon reservoirs using flowback production data. The type curve incorporates the HF damage effect of choked-fracture skin factor in the two-phase flow in HF and matrix domains. The type-curve method can be applied to inversely estimate choked-fracture skin factor, s, HF pore volume (PV), Vfi, and HF initial permeability, kfi, by analyzing two-phase flowback production data. By introducing the new dimensionless parameters, the nonuniqueness problem of the type-curve analysis for two-phase flow is significantly reduced by incorporating the complexity of fracture dynamics into one set of curves. The accuracy of the type curve is examined against the results obtained from numerical simulations of shale gas and oil reservoirs. The validation results demonstrate a good match of analytical type curves and numerical data plots and confirm the accuracy of the proposed method in estimating the static and dynamic fracture properties. The results show that the relative errors in Vfi, kfi, and s estimations are all <10% for the simulated cases that are presented in this work. The flexibility and robustness of the proposed method are illustrated using the field example from a shale oil MFHW. The accuracy and applicability of the proposed type curve are also validated by comparing the calculated fracture properties from the field example using straightline analysis with Vfi and kfi of 705.3 Mcf and 245.2 md, type-curve analysis method (without skin effect) with Vfi and kfi of 751.9 Mcf and 249.8 md, and the type-curve method (with the choked fracture skin considered) with Vfi and kfi of 708.7 Mcf and 252.9 md, which showed that the results of each case are very close to one another. The interpreted results from the flowback analysis of the field example offer quantitative insight into HF properties and dynamics.

Rate transient analysis methods for water-producing gas wells in tight reservoirs with mobile water

Tight gas reservoirs with mobile water exhibit multi-phase flow and high stress sensitivity. Accurately analyzing the reservoir and well parameters using conventional single-phase rate transient analysis methods proves challenging. This study introduces novel rate transient analysis methods incorporating evaluation processes based on the conventional flowing material balance method and the Blasingame type-curve method to examine fractured gas wells producing water. By positing a gas-water two-phase equivalent homogenous phase that considers characteristics of mobile water, gas, and high stress sensitivity, the conventional single-phase rate transient analysis methods can be applied by integrating the phase's characteristics and defining the phase's normalized parameters and material balance pseudo-time. The rate transient analysis methods based on the equivalent homogenous phase can be used to quantitatively assess the parameters of wells and gas reservoirs, such as original gas-in-place, fracture half-length, reservoir permeability, and well drainage radius. This facilitates the analysis of production dynamics of fractured wells and well-controlled areas, subsequently aiding in locating residual gas and guiding the configuration of well patterns. The specific evaluation processes are detailed. Additionally, a numerical simulation mechanism model was constructed to verify the reliability of the developed methods. The methods introduced have been successfully implemented in field water-producing gas wells within tight gas reservoirs containing mobile water.

Estimating Hydraulic Parameters of Aquifers Using Type Curve Analysis of Pumping Tests with Piecewise-Constant Rates

Aquifer hydraulic parameters play a critical role in investigating various groundwater hydrology problems (e.g., groundwater depletion and groundwater transport), and the Theis formula for constant-rate pumping tests is commonly used to estimate them. However, the pumping rate in the field usually varies with time due to some factors, making the classical constant-rate model unsuitable for accurate parameter estimation. To address this issue, we developed a novel dimensionless-form analytical solution for variable-rate pumping tests involving piecewise-constant approximations for variable pumping rates. Analysis of the time–drawdown curves revealed that the first-step type curve was consistent with the Theis curve. However, the curves of subsequent steps deviated from the Theis curve and were associated with the first dimensionless inflection time (t1,D), which depended on the hydraulic conductivity (K) and specific storage (Ss) of the confined aquifers. On this basis, a new type curve method for estimating the aquifer K and Ss was proposed by matching the observed drawdown data with a series of type curves dependent on t1,D. Furthermore, this method can handle recovery drawdown data. We applied this method to a field site in Wuxi City, Jiangsu Province, China, by analyzing the drawdown data from four pumping tests. The hydraulic parameters estimated using this method were in close agreement with those calibrated via PEST. The calibrated K values were further validated by comparing them with lithology-based results. In summary, the geometric means of K and Ss were 6.62 m/d and 3.16 × 10−5 m−1 for the first confined aquifer and 0.92 m/d and 2.34 × 10−4 m−1 for the second confined aquifer.

Determination of hydraulic parameters of non-linear consolidation clay layers by type curve method

The consolidation of clay layers is of great significance for groundwater environmental protection, groundwater storage utilization, and land subsidence. In this study, the governing equation for the excess pore water pressure during the non-linear consolidation process of clay layers under load conditions is obtained based on the one-dimensional non-linear consolidation theory. Analytical solutions are then derived for clay layers with single or double drainage caused by the dissipation of the excess pore water pressure. With these analytical solutions, the groundwater dynamics and deformation of the clay layer are analyzed. Correspondingly, a type curve method is proposed to calculate the hydraulic parameters of the clay layer through laboratory experiments, which verifies the reliability of the analytical solutions. The study results show that the deformation of the clay layer predicted by the non-linear consolidation theory is smaller than that predicted by the linear consolidation theory. The deformation of the clay layer increases with the increase in the thickness of the clay layer, the compressive index, and the overburden load, while it decreases with the increase in the initial void ratio and the initial effective stress. The stable time, at which the consolidation of the clay layer is completed, increases with the increase in the compression index and the thickness of the clay layer, while it decreases with the increase in the initial void ratio, the initial effective stress, and the initial hydraulic conductivity. It does not vary with the load pressure. Conclusively, the deformation prediction based on the non-linear consolidation theory is more accurate and applicable to further load pressures.

A two-phase type-curve method with multiscale fluid transport mechanisms in hydraulically fractured shale reservoirs

The quantitative understanding of hydraulic fracture (HF) properties guides accurate production forecasts and reserve estimation. Type curve is a powerful technique to characterize HF and reservoir properties from flowback and long-term production data. However, two-phase flow of water and hydrocarbon after an HF stimulation together with the complex transport mechanisms in shale nanopores exacerbate the nonlinearity of the transport equation, causing errors in type-curve analysis. Accordingly, we propose a new two-phase type-curve method to estimate HF properties, such as HF volume and permeability of fracture, through the analysis of flowback data of multi-fractured shale wells. The proposed type curve is based on a semianalytical solution that couples the two-phase flow from the matrix with the flow in HF by incorporating matrix influx, slippage effect, stress dependence, and the spatial variation of fluid properties in inorganic and organic pores. For the first time, multiple fluid transport mechanisms are considered into two-phase type-curve analysis for shale reservoirs. We analyze the flowback data from a multi-fractured horizontal well in a shale gas reservoir to verify the field application of the proposed method. The results show that the fracture properties calculated by the type-curve method are in good agreement with the long-time production data.

A type-curve method for two-phase flowback analysis in hydraulically fractured hydrocarbon reservoirs

As a powerful technique for quantitative production data analysis, type curves play an essential role in estimating reservoir and fracture properties. However, two-phase flow after hydraulic fracturing furthers the governing equation's nonlinearity and introduces substantial errors in type-curve analysis, which must be extended to two-phase systems. This study presents a new type-curve method to characterize hydraulic fracture (HF) attributes and dynamics by analyzing two-phase flowback data from multi-fractured horizontal wells (MFHWs) in hydrocarbon reservoirs. The proposed method is, to the best of our knowledge, the first semi-analytical type-curve approach that not only considers the two-phase flow in both fracture and matrix, but also takes variable BHP and rate conditions. Meanwhile, a new set of dimensionless groups are proposed to incorporate the complexity of the coupled two-phase flow in fracture and matrix into one unique curve, rather than families of curves, which significantly reduces the non-uniqueness issue of type-curve matching for MFHWs. Unlike other two-phase type curves, the pressure and saturation dependent parameters in the dimensionless groups are rigorously evaluated at the average properties within the HF based on the material balance equations. The accuracy of the proposed method is tested using the synthetic data generated from six numerical simulation cases for shale gas and oil reservoirs. The numerical validation confirms the unique behavior of type curves during fracture boundary dominated flow and verifies the accuracy of the type-curve analysis in the characterization of fracture properties. For field application, the proposed method is applied to two MFHWs in Marcellus shale gas and Eagle Ford shale oil. The agreement of interpreted results between the proposed method and straight-line analysis not only demonstrates the practicality in field application but also illustrates the superiority of the type-curve method as an easy-to-use technique to analyze two-phase flowback data.

Estimation of aquitard hydraulic conductivity and skeletal specific storage considering non-Darcy flow

Darcy's law has been widely used to study the groundwater drainage process within an aquitard. However, non-Darcy flow is frequently encountered in laboratory and in situ investigations. With consideration of a sudden drop in boundary hydraulic heads, aquitard compaction characteristics and their sensitivities to the non-Darcy flow control variables were analyzed. The non-Darcy flow was found to retard groundwater drainage, and the retardation effects were much more significant at early-to-intermediate time points. Under this specific boundary condition, the time–compaction curve in a log–log graph at early time points was found to be close to a straight line, whose slope can be used to indirectly evaluate the extent of the non-Darcy effect. A non-Darcy flow-based type curve method was developed for estimating aquitard hydraulic conductivity (K) and skeletal specific storage (Ss), and this method was used to interpret the time–compaction data recorded in a laboratory experiment. The tested aquitard was determined to be associated with non-Darcy flow due to the fact that the time–compaction curve deviated from the Darcy's law-based theoretical curve. Darcy's law resulted in an underestimated K. In contrast, the estimated Ss was almost unaffected by the flow state, if the observation lasted long enough to reach final steady compaction.

Non-Darcian effect on a variable-rate pumping test in a confined aquifer

Groundwater flow in an aquifer has frequently been found to be non-Darcian. In this study, a transient model of a variable-rate pumping test in a confined aquifer was established considering non-Darcian flow in the aquifer. A piecewise-linear function was adopted to reproduce the variability in pumping rate, and the classical Izbash equation was employed to describe the non-Darcian flow. The type-curve analysis suggested that a smaller quasi-conductivity will result in an earlier deviation and a smaller extent of the decreasing features in the drawdown under the condition of a linearly decreasing pumping rate compared to that under the condition of a constant pumping rate. The sensitivity analysis indicated that the variability in pumping rates under non-Darcian flow can increase the sensitivity of drawdown to the radius of the well casing at inflection times of the discrete linear stages, and drawdown closer to the pumping well is more sensitive to the change in the well casing. A type-curve method was proposed and employed to interpret the pumping test data, which were collected at a field site located in Wuxi city, Jiangsu Province, China. The parameter estimates indicate a high possibility of the occurrence of prelinear flow in the aquifer of interest.

A Type-Curve Method for the Analysis of Pumping Tests with Piecewise-Linear Pumping Rates.

Aquifer hydraulic parameters are commonly inferred from constant-rate pumping tests, while variable pumping rates are frequently encountered in actual field conditions. In this study, we propose a generally applicable dimensionless form of the analytical solution for variable-rate pumping tests in confined aquifers. In particular, we adopt a piecewise-linear fitting of variable pumping rates and propose a new type-curve method for estimating the hydraulic conductivity (K) and specific storage (Ss ) of the investigated confined aquifer. For each test, a series of type curves, which depend on the variable pumping rates, the location of observation wells and the introduced first dimensionless inflection time, need to be provided for matching the observed drawdown data on a log-log graph. We first demonstrate the applicability and robustness of this method through a synthetic pumping test. Subsequently, we apply this method to analyze drawdown data from four pumping tests conducted within a multilayered aquifer/aquitard system in Wuxi city, Jiangsu Province, China. The parameter estimates are then compared with those reported by PEST. The K and Ss values estimated by the new type-curve method are found to be quite close to PEST-based estimates. Parameter estimation results demonstrate the difference in K and Ss values between observation wells. The difference could be attributed to the spatial heterogeneity in K and Ss . A future research topic may focus on the characterization of K and Ss heterogeneity with the currently available drawdown data from variable-rate pumping tests.

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

AbstractActual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (Ss) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and Ss of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.

A production data analysis model for gas/condensate reservoirs

Abstract Production decline analysis is a technique where actual production history is modeled with a theoretical relation. The production model could then be used to estimate hydrocarbon in place and reservoir properties just like expensive pressure transient tests. Gas/condensate reservoirs exhibit different thermodynamic and flow behavior and the multi-phase production data of such reservoirs cannot be accurately analyzed using available production models. This study presents a novel analytical model to analyze multi-phase gas/condensate production data in both transient and boundary dominated flow regions for variable bottom-hole pressure/rate conditions. Initial gas-in-place, average reservoir pressure, and drainage area size could be calculated from analysis of boundary dominated flow region data and reservoir permeability and well skin could be calculated from analysis of transient flow region data. The effects of positive coupling and negative inertia are also included in the formulation. The proposed model forms a linear plot and the desired estimates of reservoir properties could be determined simply. To use the transient flow region data in analysis, new dimensionless parameters are introduced and the proposed model is also presented in type curve analysis format. Different fine-grid compositional simulation models are used to validate the proposed method. The effects of reservoir fluid types, relative permeability data, production well survey, and production history mode on the results were evaluated. The model is also evaluated using actual field data. Small error values in all cases (below 5%) show that the proposed method estimates the reservoir properties quite well and it is applicable to field data. Moreover, the developed type curve method is a good tool to diagnose the reservoir flow regime.

Virtual special issue: Advanced numerical simulation technology enabling the analytical and semi-analytical modelling of natural gas reservoirs (2009–2015)

Production decline analysis is a technique where actual production history is modeled with a theoretical relation. The production model could then be used to estimate hydrocarbon in place and reservoir properties just like expensive pressure transient tests. Gas/condensate reservoirs exhibit different thermodynamic and flow behavior and the multi-phase production data of such reservoirs cannot be accurately analyzed using available production models.This study presents a novel analytical model to analyze multi-phase gas/condensate production data in both transient and boundary dominated flow regions for variable bottom-hole pressure/rate conditions. Initial gas-in-place, average reservoir pressure, and drainage area size could be calculated from analysis of boundary dominated flow region data and reservoir permeability and well skin could be calculated from analysis of transient flow region data. The effects of positive coupling and negative inertia are also included in the formulation. The proposed model forms a linear plot and the desired estimates of reservoir properties could be determined simply. To use the transient flow region data in analysis, new dimensionless parameters are introduced and the proposed model is also presented in type curve analysis format.Different fine-grid compositional simulation models are used to validate the proposed method. The effects of reservoir fluid types, relative permeability data, production well survey, and production history mode on the results were evaluated. The model is also evaluated using actual field data. Small error values in all cases (below 5%) show that the proposed method estimates the reservoir properties quite well and it is applicable to field data. Moreover, the developed type curve method is a good tool to diagnose the reservoir flow regime.

A new type curve method for estimating aquitard hydraulic parameters in a multi-layered aquifer system

Summary We propose a new type curve method for estimating the hydraulic conductivity ( K ) and the specific storage ( S s ) of an aquitard in a multi-layered aquifer system. Theoretical type curves of rate of aquitard compaction versus time are obtained through drawdown-time series in the aquitard, under a condition that the drawdown history of the underlying aquifer can be approximated as piecewise linear segments (PLS), in each of which the drawdown shows a linear increase trend with time. Comparing with previous analytical solutions, which are limited by the assumption of a constant head in the overlying unconfined aquifer, the superposition principle can be called when water levels fluctuate with time in both upper and lower aquifers adjacent to the aquitard. When applying the new PLS method to estimate K and S s values of an aquitard, the starting point of drawdown history at adjacent aquifers should be determined at first. After that the drawdown history is approximated as PLS to obtain drawdown rate of change for each linear stage and turning points of drawdown history. The new PLS method is demonstrated at a field site in Changzhou City, Jiangsu Province of China. Estimated results show that K and S s are, respectively, 9.80 × 10 −10 m/s and 4.46 × 10 −4 m −1 for a thick aquitard, and 2.34–3.50 × 10 −10 m/s and 2.28 × 10 −4 m −1 for a thin aquitard. Estimated field K values, as well as S s values, through the new PLS method, are generally in accordance with the results obtained from the geologic method by Konikow and Neuzil (2007). They are also in agreements with the numerically calibrated results of Shi et al. (2008a) at the regional scale and the laboratory experimental values of in-situ soil samples collected by Geological Survey of Jiangsu Province of China.

Effect of Real Bentonite Cake on Slug Test Analysis for Slurry Trench Wall

The slug test is a viable method in estimating the hydraulic conductivity of the slurry trench wall backfill because of its ability to consider a more representative volume of the backfill and to reflect the in situ performance of the construction. A three-dimensional numerical model is developed to simulate the slug test in a slurry trench wall with the presence of bentonite cake on the interface boundary between the wall and the surrounding soil formation. Influential factors such as wall width (i.e., proximity of wall boundary), well deviation, vertical position of the well intake section, and compressibility of the wall backfill are taken into account in the model. The experimentally obtained hydraulic properties of the bentonite cake are also incorporated in a series of slug test simulations. The simulation results are then examined to evaluate the bentonite cake effect in analyzing practical slug test results in the slurry trench wall. The simulation results show that the modified line-fitting method can be used without any reduction factor for the slug test in the slurry trench wall with the presence of bentonite cake. A case study is reanalyzed with the assumption of existing bentonite cake. The results are compared with the previously reported results by the approaches used for the case of no bentonite cake (constant-head boundary) and upper-bound solution (no-flux boundary). The modified line-fitting method and the type curve method produce similar results for slurry walls with bentonite cakes. The case study results demonstrate the importance of the bentonite cake effect in estimating the hydraulic conductivity of the slurry wall backfill.

Classification of carbonate gas condensate reservoirs using well test and production data analyses

Carbonate reservoir patterns play an important role in the production performance of oil and gas wells, and it is usually classified through static data analysis which cannot reflect the actual well performance. This paper takes the Tazhong No. 1 gas field in the Tarim Basin, China as an example to investigate the classification of carbonate reservoirs. The classification method mainly combines well test analysis with production analysis — especially the Blasingame type curve method. Based on the characteristics of type curves for well test analysis and the Blasingame method, the relationship between the type curves and reservoir pattern was established. More than 20 wells were analyzed and the reservoirs were classified into 3 major patterns with 7 sub-classes. Furthermore, the classification results were validated by dynamic performance analysis of wells in the Tazhong No.1 gas field. On the basis of the classification results, well stimulation (i.e. water flooding in a single well) was carried out in three volatile-oil wells, and the oil recovery increased by up to 20%.

Slug Test Analysis in Vertical Cutoff Walls with Consideration of Filter Cake

In constructing a vertical cutoff wall, bentonite-water slurry is frequently used to maintain the stability of sidewalls during excavation before backfilling the trench with less permeable materials to complete the cutoff wall construction. This procedure leads to a thin but relatively impermeable layer, called a filter cake, on the excavation surface. The aim of this paper is to examine the effect of a filter cake on evaluating hydraulic conductivity of the cutoff wall backfill through a slug test analysis with the aid of the verified numerical program, Slug_3D. As an upper bound solution for evaluation of the hydraulic conductivity of the cutoff wall backfill, no-flux boundary conditions for the boundaries of cutoff walls are imposed to consider the effect of filter cakes. The type-curve method and modified line-fitting method are employed to reanalyze the case of EMCON/OWT, Inc., as an example. The previous analysis, without consideration of a filter cake, is compared with the current results that cons...

Estimation of effective hydrogeological parameters in heterogeneous and anisotropic aquifers

Summary Obtaining reasonable hydrological input parameters is a key challenge in groundwater modeling. Analysis of temporal evolution during pump-induced drawdown is one common approach used to estimate the effective transmissivity and storage coefficients in a heterogeneous aquifer. In this study, we propose a Modified Tabu search Method (MTM), an improvement drawn from an alliance between the Tabu Search (TS) and the Adjoint State Method (ASM) developed by Tan et al. (2008) . The latter is employed to estimate effective parameters for anisotropic, heterogeneous aquifers. MTM is validated by several numerical pumping tests. Comparisons are made to other well-known techniques, such as the type-curve method (TCM) and the straight-line method (SLM), to provide insight into the challenge of determining the most effective parameter for an anisotropic, heterogeneous aquifer. The results reveal that MTM can efficiently obtain the best representative and effective aquifer parameters in terms of the least mean square errors of the drawdown estimations. The use of MTM may involve less artificial errors than occur with TCM and SLM, and lead to better solutions. Therefore, effective transmissivity is more likely to be comprised of the geometric mean of all transmissivities within the cone of depression based on a precise estimation of MTM. Further investigation into the applicability of MTM shows that a higher level of heterogeneity in an aquifer can induce an uncertainty in estimations, while the changes in correlation length will affect the accuracy of MTM only once the degree of heterogeneity has also risen.

Slug Test Analysis to Evaluate Permeability of Compressible Materials

The line-fitting methods such as the Hvorslev method and the Bouwer and Rice method provide a rapid and simple means to analyze slug test data for estimating in situ hydraulic conductivity (k) of geologic materials. However, when analyzing a slug test in a relatively compressible geologic formation, these conventional methods may have difficulties fitting a straight line to the semilogarithmic plot of the test data. Data from relatively compressible geologic formations frequently show a concave-upward curvature because of the effect of the compressibility or specific storage (S(s)). To take into account the compressibility of geologic formations, a modified line-fitting method is introduced, which expands on Chirlin's (1989) approach to the case of a partially penetrating well with the basic-time-lag fitting method. A case study for a compressible till is made to verify the proposed method by comparing the results from the proposed methods with those obtained using a type-curve method (Kansas Geological Survey method [Hyder et al. 1994]).

An Assessment of the Way and McKee (1982) Type‐Curve Method

An Assessment of the Way and McKee (1982) Type‐Curve Method

Type curve interpretation of late‐time pumping test data in randomly heterogeneous aquifers

The properties of heterogeneous media vary spatially in a manner that can seldom be described with certainty. It may, however, be possible to describe the spatial variability of these properties in terms of geostatistical parameters such as mean, integral (spatial correlation) scale, and variance. Neuman et al. (2004) proposed a graphical method to estimate the geostatistical parameters of (natural) log transmissivity on the basis of quasi–steady state head data when a randomly heterogeneous confined aquifer is pumped at a constant rate from a fully penetrating well. They conjectured that a quasi–steady state, during which heads vary in space‐time while gradients vary only in space, develops in a statistically homogeneous and horizontally isotropic aquifer as it does in a uniform aquifer. We confirm their conjecture numerically for Gaussian log transmissivities, show that time‐drawdown data from randomly heterogeneous aquifers are difficult to interpret graphically, and demonstrate that quasi–steady state distance‐drawdown data are amenable to such interpretation by the type curve method of Neuman et al. The method yields acceptable estimates of statistical log transmissivity parameters for fields having either an exponential or a Gaussian spatial correlation function. These estimates are more robust than those obtained using the graphical time‐drawdown method of Copty and Findikakis (2003, 2004a). We apply the method of Neuman et al. (2004) simultaneously to data from a sequence of pumping tests conducted in four wells in an aquifer near Tübingen, Germany, and compare our transmissivity estimate with estimates obtained from 312 flowmeter measurements of hydraulic conductivity in these and eight additional wells at the site. We find that (1) four wells are enough to provide reasonable estimates of lead log transmissivity statistics for the Tübingen site using this method, and (2) the time‐drawdown method of Cooper and Jacob (1946) underestimates the geometric mean transmissivity at the site by 30–40%.