Fracture Half-length Research Articles

A semi-analytical model for investigating the productivity of fractured horizontal wells in tight oil reservoirs with micro-fractures

Combining horizontal drilling with hydraulic fracturing has become a well-established technique to improve well productivity in tight oil reservoirs. The existence of micro-fractures in these reservoirs affects the fluid flow process as well as the productivity. However, current models for evaluating the well performance of fractured horizontal wells containing micro-fractures lack accuracy. Hence, the objective of this study is to build an efficient model to analyze well productivity, considering the effects of micro-fractures. A novel flow model for multi-fractured horizontal wells was established, considering the effect of micro-fractures on the fluid flow. Subsequently, we built a reservoir model based on the typical fracture and fluid properties of a tight oil block in the Daqing oil field, China. Good agreement between the prediction results and field data was obtained, indicating that the effect of micro-fractures on well productivity cannot be neglected. Further study reveals that micro-fractures essentially function as a joint connecting reservoir matrix and have a persistent impact on well productivity. Micro-fractures can promote well productivity; however, if the value of micro-fracture permeability increases, this promotional effect will slow down. Well productivity can be considerably improved as an increase in micro-fracture percentage. Finally, a series of sensitivity studies were conducted to identify the effects of critical parameters on well productivity. Results show that reservoir permeability significantly influences well productivity, followed by reservoir effective thickness, micro-fracture percentage, fracture number, hydraulic fracture half-length. Pressure sensitivity coefficient, threshold pressure gradient and micro-fracture permeability have the least effect on well productivity. This work provides a sophisticated and efficient tool to evaluate the productivity of multi-fractured horizontal wells in tight oil reservoirs with micro-fractures.

Flowback fracture closure of multi-fractured horizontal wells in shale gas reservoirs

In multi-fractured horizontal wells (MFHW), fracture properties such as permeability and fracture half-length significantly deteriorate during production, which negatively affects gas production from shale reservoirs. Therefore, it is crucial to evaluate the temporal changes in fracture properties using production data. This paper presents two multiphase flowback models for gas and water phase under boundary dominated flow (BDF) condition by considering gas influx from matrix. In addition, a workflow is proposed to quantitatively evaluate hydraulic fracture closure and fracture properties using both water-phase and gas-phase flowback data. A material balance equation (MBE) is derived to obtain average pressure in the fracture by calculating gas influx from matrix under variable bottomhole pressure (BHP) condition based on Duhamel's principle. The flowback models, average pressure calculation method, and workflow are validated against numerical simulations and applied to an MFHW drilled in Marcellus Shale. The results show that the developed models are capable of predicting fracture properties, and MBE could accurately calculate average pressure in the fracture. Furthermore, the proposed workflow provides quantitative insights into the performance of stimulation jobs by accurately predicting fracture half-length, fracture permeability, and permeability modulus using flowback data. By reconciling flowback analysis with long-term production data analysis, a significant decrease in fracture properties due to fracture closure is observed in the Marcellus MFHW.

Multiphase flowback rate-transient analysis of shale gas reservoirs

Multi-fractured horizontal well (MFHW) is commonly used in the development of unconventional reservoirs. Flowback data after hydraulic fracturing is of critical importance in the characterization of hydraulic fracture, stimulation evaluation, and reservoir simulation. This study presents a two-phase diagnostic plot and a semi-analytical flowback model for the early-time flowback period when fluid influx from matrix remains insignificant and production is mainly from the fracture network. The developed model considers the changes of water saturation in hydraulic fracture (HF) under fracture depletion mechanism and pressure-dependent permeability and porosity, and is able to predict HF attributes, such as fracture half-length, initial fracture permeability, and initial pore volume of fracture network. A new method of calculating average pressure in the fracture is developed based on the solution of water-phase diffusivity equation and is compared with the traditional material balance approach based on the tank model. Three iterative workflows are proposed using the successive substitution method to calculate fracture attributes under different production conditions. Validation of the developed flowback model, average pressure calculation method, and the analysis workflow, as well as their application in an MFHW drilled in Horn River Shale show the applicability of this study to interpret flowback data quickly and estimate HF properties accurately.

Effectiveness and sensitivity analysis of solution gas re-injection in Baikouquan tight formation, Mahu sag for enhanced oil recovery

To address the fast productivity decline of the horizontal wells and low oil recovery during natural depletion in Baikouquan formation, the approach of solution gas re-injection was proposed with the primary objective of further developing this formation. Herein, a field-scale numerical compositional reservoir model was built up based on the formation properties and then the effects of permeability, fractures and formation stress on the production dynamics were thoroughly investigated. A sensitivity analysis, which can correlate the oil recovery with these parameters, was also performed. The results showed that the re-injection of solution gas could remarkably retard the production depletion of the horizontal wells thereby improving the oil production. The oil recovery rate increased with permeability, fracture half-length, fracture conductivity, and formation dip. With regard to the fracture distribution, it was found that the interlaced fracture outperformed the aligned fracture for the solution gas re-injection. The influence of the formation stress should be carefully considered in the production process. Sensitivity analysis indicated that the formation dip was the paramount parameter, and the permeability, fracture half-length, and fracture conductivity also played central roles. The results of this study supplement earlier observations and provide constructive envision for enhanced oil recovery of tight reservoirs.

Simulation Study of Allied In-Situ Injection and Production for Enhancing Shale Oil Recovery and CO2 Emission Control

The global greenhouse effect makes carbon dioxide (CO2) emission reduction an important task for the world, however, CO2 can be used as injected fluid to develop shale oil reservoirs. Conventional water injection and gas injection methods cannot achieve desired development results for shale oil reservoirs. Poor injection capacity exists in water injection development, while the time of gas breakthrough is early and gas channeling is serious for gas injection development. These problems will lead to insufficient formation energy supplement, rapid energy depletion, and low ultimate recovery. Gas injection huff and puff (huff-n-puff), as another improved method, is applied to develop shale oil reservoirs. However, the shortcomings of huff-n-puff are the low sweep efficiency and poor performance for the late development of oilfields. Therefore, this paper adopts firstly the method of Allied In-Situ Injection and Production (AIIP) combined with CO2 huff-n-puff to develop shale oil reservoirs. Based on the data of Shengli Oilfield, a dual-porosity and dual-permeability model in reservoir-scale is established. Compared with traditional CO2 huff-n-puff and depletion method, the cumulative oil production of AIIP combined with CO2 huff-n-puff increases by 13,077 and 17,450 m3 respectively, indicating that this method has a good application prospect. Sensitivity analyses are further conducted, including injection volume, injection rate, soaking time, fracture half-length, and fracture spacing. The results indicate that injection volume, not injection rate, is the important factor affecting the performance. With the increment of fracture half-length and the decrement of fracture spacing, the cumulative oil production of the single well increases, but the incremental rate slows down gradually. With the increment of soaking time, cumulative oil production increases first and then decreases. These parameters have a relatively suitable value, which makes the performance better. This new method can not only enhance shale oil recovery, but also can be used for CO2 emission control.

Study of the effects of hydraulic fractures on gas and water flow in shale gas reservoirs

ABSTRACT Horizontal drilling and multi-stage hydraulic fracturing are the two key technologies for the successful development of shale gas reservoirs. However, there exist large uncertainties in optimizing hydraulic fracturing which affects water retention into shale matrix and gas productivity. In this work, a basic reservoir model with six-stage hydraulic-fracturing treatment was constructed to understand water retention and gas production in shale gas reservoirs. Gas diffusion, gas desorption, Darcy flow as well as non-Darcy flow were considered in this model. Then, a sensitivity study was performed to investigate the effects of hydraulic fractures on water retention and gas conductivity. The results indicate that only 34% of the fracturing water could be recovered back to the surface, and most of them remain in shale formations to interfere with gas production. The increase of fracture half-length, fracture width, fracture permeability, and fracture conductivity will reduce water retention while water retention in shale matrix will increase with the increasing of fracture spacing and fracture number. This work can provide a better understanding of the effects of hydraulic fractures on gas and water flow so as to optimize the hydraulic-fracturing treatment in shale gas reservoirs.

To Spark Real-Time Revolution, Fracture Diagnostic Firms Partner Up and Innovate

While waiting to give a presentation at an industry conference last year, Dale Logan was sitting in his chair listening to one of the speakers lined up ahead of him. The man at the podium was describing an emerging fracture diagnostics system that analyzes the “noise” coming out of a hydraulically stimulated well to measure the size of its fractures. “I’m just as skeptical as the next guy,” said Logan, a 31-year field operations veteran turned senior vice president of marketing for C&J Energy Services in Houston. “So I said to him, ‘Look, if this stuff is really as good as you guys say it is, then I’m interested.’” The technology that caught his eye that day comes from an Austin-based startup called Seismos. The chance meeting led to more. Then late last year, the Houston-based pressure pumping company (which will soon become the third largest in the US after its merger with Keane Energy Services) and the startup of fewer than 40 people began working together in the field. Their experiment was to see if combining C&J’s relatively new drilling data-based completions advisory tool with Seismos’ wellhead-based acoustic analysis proves out the value proposition of both technologies at the same time. Success would be convincing operators that there is a way to predict the relationship between rock properties, fracture half-lengths, and near- wellbore conductivity—opening the door for geologic-based, or “engineered completion” strategies. The project has borne fruit, but it remains a work in progress as the two companies make sure they know how best to use their data sets together. “It’s not that easy,” said Logan on the pains of the validation process. “You come up with something new, you show people the answer, and then they ask how do you know if it’s right?” To zoom out here is to see that this partnership is but a single team in the race to revolutionize how the shale sector monitors and executes multimillion-dollar hydraulic fracturing operations. Taking part are at least a dozen service companies and new technology developers that are importing advanced computing and communications technologies that have proven to work in other areas of the•business.• The objective of these firms is to shed new light on what fractures look like, where they going as they are made, and how much profit they are likely to generate—or lose. Some are aiming to serve up these answers in real time, others, a few minutes after each fracture stage is completed. Either way, the fracture analysis can be used to guide a well completion as it unfolds. In July, the exhibition floor of the Unconventional Resources Technology Conference (URTeC) became the physical manifestation of these grand ambitions. Service providers used the gathering in Denver of more than 6,000 petrotechnicals to unveil new software platforms that manage and integrate hydraulic fracture data, which does not have a formal standard across the board as in the drilling sector. Also on display were new ways to capture fracture data.

Semi-analytical modeling of productivity analysis for five-spot well pattern scheme in methane hydrocarbon reservoirs

Five-spot well pattern (FSWP) scheme has shown appealing potentialities to enhance the recovery of coal-bed methane (CBM) from methane hydrocarbon reservoirs (MHR). In this paper, a new framework aimed at systematically investigating productivity performance of FSWP scheme with inter-well pressure interference (IWPI) is presented. First, mathematical models which are used to characterize the fluid flow within MHR and hydraulic fractures (HFs) are separately derived. Second, Laplace transformation and Stehfest numerical algorithm are utilized to couple those two flow systems and obtain the pressure-transient solutions of FSWP scheme. Finally, pressure characteristics are discerned and sensitivity analysis of key parameters is implemented as well. This semi-analytical approach outperforms numerical simulation from the point of computational efficiency. Several common flow regimes, e.g., linear and bi-linear flow regimes, are essentially deformed induced by IWPI. Several significant parameters, including gas rate, fracture half-length, and well spacing on the occurrence of IWPI are systematically analyzed. This work gains some new knowledge about the productivity performance of FSWP scheme with the existence of IWPI when extracting CBM from methane hydrate reservoirs (MHR), which provides energy engineers considerable instructions on optimizing the development of methane hydrate reservoirs.

Improving acid fracture design in dolomite formations utilizing a fully integrated acid fracture model

Acid reactivity with dolomite is more sensitive to temperature as compared to calcite formations, resulting in different dissolution profile. Acid fracture fluids are heated inside the fracture, as it flows away from the wellbore, due to the reservoir heat flux. This causes a sharp increase in dolomite reactivity, resulting in a bell-shaped conductivity profile along the fracture half-length. The productivity of such conductivity distributions will be wrongly estimated if a single average conductivity value is used. In the present research, a reservoir simulator that includes variable fracture conductivity was coupled with an integrated acid fracture model. Also, design guidelines for acid fractures in dolomite formations have been proposed.Case studies are presented, showing that in conventional acid fracture designs, the maximum dissolution in dolomite usually occurs away from the wellbore. This negatively affects productivity, as maximum conductivity is desired near the wellbore. This effect is especially significant for fracturing candidate wells in higher permeability reservoirs. This study shows that in good permeability formations, productivity can be improved by acid fractures designed at a lower injection rate. In cases where the desired injection rate is not sufficient to propagate the fracture, good productivity can be obtained by using two acid stages with different injection rates. A higher injection rate is employed to create the desired fracture dimensions, and a smaller rate used to obtain good conductivity in the near-wellbore region. In low permeability reservoirs, it is desirable to alternate injections of retarded acid systems with pad fluid to create longer acid penetration distances. The results show that, in certain conditions, designs following the proposed guidelines can result in substantial productivity improvement compared to the conventional approach.

Interference well-test model for vertical well with double-segment fracture in a multi-well system

Single well pressure transient analysis ignores the impact from adjacent wells, while well interference has obvious effect on the pressure response. Additionally, fracture conductivity and half-length may decrease severely, leading to non-uniform closure along fractures. The interpreted fracture half-length could be much shorter than designed half-length if this phenomenon is ignored. Besides, well interference caused by adjacent wells in multi-well system could be mistaken as boundary effect in single-well model since type curves of these two circumstances are quite similar to each other, which could bring about unrealistic results compared with geologic characteristics. Therefore, distinguishing interference effect from boundary effect while considering non-uniform fracture closure becomes a major challenge.This work proposes a new interference well-test model of vertical well with double-segment fractures (VWDSF). Each double-segment fracture (DSF) contains two fracture segments (FS) with individual length, rate and conductivity, etc. The new model allows the observation well and adjacent wells to produce at the same time, which does not influence production. Analytical solution is verified by comparing with numerical solution from Saphir, and model comparison is proposed to elaborate the significance of the novel model. New flow regimes including fracture interference flow, multi-well interference flow, interference-radial flow regime (IRFR) and system-radial flow can be observed on type curves. Furthermore, the influence of the observation well and adjacent wells on type curves are analyzed. Case study highlights the ability of the developed model in distinguishing the interference effect and boundary effect using the novel model. The proposed model provides a useful tool for addressing erroneous interpretation of pressure transient data due to non-uniform fracture closure and/or well interference.

A semi-analytical model for multiple-fractured horizontal wells in heterogeneous gas reservoirs

Most gas reservoirs are not homogeneous in practice. Due to the influences of the nonlinearity and heterogeneity, little work has focused on the behavior of multiple-fractured horizontal wells (MFHWs) in heterogeneous gas reservoirs. In this study, a semi-analytical model based on a detailed analytical method for MFHWs in heterogeneous gas reservoirs is established. The source functions, boundary element method and Green's solution are used to build the model in Laplace space. To solve the problem that the combination of the pseudo-function approach with the material balance equation describing homogeneous gas reservoirs cannot be effectively linearize the nonlinearity in heterogeneous gas reservoirs, a multi-region material balance equation for heterogeneous gas reservoirs is derived. Then, the performance of an MFHW in a two-block gas reservoir is calculated. The pressure behavior and the flux distribution are influenced by the crossflow coefficient, fracture conductivity, size of the gas reservoir, fracture half-length and storage ratio. A high crossflow coefficient increases the flux of the interface and the difference in flux between fractures in different blocks. The effects of the crossflow can be weakened by a high fracture conductivity and large fracture half-length. This study provides a theoretical basis for MFHWs in heterogeneous gas reservoirs.

The Influence of Stimulated Reservoir Volume in Dense Reservoir on the Fracturing Effect

Based on the finite element theory, the mathematical model of oil-water two-phase flow is established. Applying the mixed element finite element method to numerical simulation studies for complex artificial fracture which after volume fracturing of horizontal well in dense reservoir, using arbitrary triangle elements to describe the formation, line elements to describe the artificial fracture. For the convenience of simulation calculation, the fracture network is processed into two parts of the main fracture and the high permeability stimulated region. The bandwidth of stimulated region is determined by results of the micro seismic monitoring; the permeability is determined by single well history matching. Aiming at the problem of volume fracturing of horizontal well in dense reservoir, in the way of natural energy exploitation, with the single well as the research object, according to different calculation schemes to carry out stimulated reservoir volume(SRV) calculation, to study the influence of the SRV on fracturing effect. Research results show that under the condition of natural energy, when the fracture half-length is unchanged, with the increasing of the transformation segment number, the SRV increases, the cumulative oil production increased. However, the increasing of oil production is smaller gradually, so there is an optimal SRV. Under the given conditions, when the fracture half-length is 240m, horizontal well length is 600m, 800m and 1000m, 1200m, the optimal SRV respectively are 350×104m3、 500×104m3、 600×104m3、 750×104m3。

Reducing uncertainty in unconventional reservoir hydraulic fracture modeling: A case study in Saudi Arabia

Saudi Aramco is exploring and appraising liquid rich and dry gas unconventional reservoirs. Part of this effort has focused on understanding the effective fracture geometry and its role in optimal well spacing and reservoir drainage. A review of collected data and existing hypotheses indicated that there are multiple models for optimal production yet each calls for a dramatically different approach. Long term flow data is recommended in such cases but this is often complicated by the fact that decisions in a fast paced environment might rely on short production history.A field pilot in a carbonate-rich ultra-low permeability source rock in Saudi Arabia incorporated multiple hydraulic fracture monitoring techniques to validate outputs from a classical linear elastic fracture model. All employed monitoring techniques had their results assessed in conjunction with their strengths and weaknesses for more inclusive interpretations. From the reservoir flow regimes and the various hypotheses on effective fracture geometries, the extent to which non-uniqueness impacts determination of the most probable fracture geometry and matrix permeability was investigated. Long and short hydraulic fractures were used to match the short production history with reservoir simulation models under different sets of assumptions. The contradictions in the assumptions and difficulty in transferring fracture geometries, calibrated by the monitoring results, to production data modeling, were used to gauge the validity of associated effective fracture geometry hypotheses.From the pilot, microseismic monitoring indicated that more stimulation volumes yielded longer microseismic geometries. Offset well stimulation induced pressure interference in adjacent wells. Cross-well hydraulic communication illustrated by chemical and oil tracers corroborated the longer fractures mapped by microseismic events and also predicted by linear elastic fracture models. In addition, the sequential opening of the pilot pad wells induced subtle production-induced pressure interference in the early flow period. While the subtle production-induced pressure interference was initially thought to be the ground truth for adequate well spacing, it was shown that it was not unique due to the fact that ultra-low matrix permeability can prolong onset of fracture interference. The hydraulic fracture monitoring methods showed identical results for the estimated hydraulic fracture half-length which allowed the constraining of the parameter. Reservoir simulation was used to match the short production history with both short and long planar fractures even though the former had not been validated by most of the observed data. Consideration of all observed data, dimensionless fracture conductivity for stimulation design criteria and the reservoir simulation assumptions provided validation for long effective fractures.This study shows the contribution of a diverse surveillance data acquisition in reducing uncertainty in unconventional reservoir fracture modeling for realistic reservoir simulation and development solutions. In addition, insights derived from this work provided important clues for testing the validity of hypotheses in unconventional reservoir studies.

New correlations for etched fracture width and half-length of acid-fractured wells

Acid fracturing is one of the most efficient well stimulation techniques in carbonate reservoirs. Estimation of well productivity after fracturing is an important issue in acid fracturing design and production engineering analysis. There are some correlations, available in the literature, for estimation of effective wellbore radius of hydraulically fractured wells. However, fracture etched width and its half-length must be known to use these correlations and, to our best knowledge, a simple and correct method for prediction of these parameters has not been reported yet.This paper presents a couple of correlations for estimation of etched fracture width and fracture half-length considering acid-rock interactions, reservoir and operational parameters. To develop and verify the proposed correlations, we used a large data bank produced by our in-house simulator, which models one-dimensional acid flow through a single hydraulic fracture considering acid-rock reaction and also fluid leakoff to the matrix. The governing equations are solved numerically using finite difference approach and the results were compared with a commercial simulator for verification. It is also explained how the values of etched fracture width and fracture half length, estimated by our new correlations, can be used in the available correlations for prediction of effective wellbore radius.

Generalized analytical model of Transient linear flow in heterogeneous fractured liquid-rich tight reservoirs with non-static properties

• New analytical transient linear flow is rigorously modeled in heterogeneous fractured liquid-rich tight reservoirs with non-static properties . • Improved rate-transient analysis workflow is proposed to estimate reservoir/fracture properties. • Three liquid-rich shale field examples in North America are analyzed to demonstrate the practical applicability of new model. The industry is increasingly reliant on rate-transient analysis (RTA) to extract valuable information about the reservoir and hydraulic fractures. However, the application of current, commercially-available RTA models can lead to incorrect estimates of reservoir/fracture properties, potentially causing costly mistakes to be made in capital planning and reserve estimation. The root cause of these errors is that currently-available analytical solutions used in RTA models largely ignore reservoir heterogeneities, and assume static reservoir properties. In this work, a new transient linear flow is rigorously modeled in unconventional reservoirs with (1) pressure-dependent rock and fluid properties and (2) both continuous and discontinuous (heterogeneous) porosity and permeability. To achieve this, new transformations of pseudo-pressure, pseudo-time and pseudo-distance are first introduced to reduce the temporal and spatial non-linear diffusivity equation to that with approximately constant coefficients. Both a Laplace-domain solution and approximate analytical solution to the diffusivity equation are verified against a series of fine-grid numerical simulations for the assumption of fractal-based reservoir heterogeneity (over a wide range of stress-dependent rock and fluid properties). The results indicate that reservoir heterogeneity can result in nonlinear square-root-of-time plots. Further, rock and fluid pressure-dependencies act to decrease the slope of the square-root-of-time plot and affect reservoir/fracture property evaluations. Three liquid-rich shale (LRS) field examples in North America are analyzed to demonstrate the practical applicability of the new RTA models. Additional value of new RTA models over the sophisticated numerical simulation is to provide us an improved backforward-analysis workflow that can be used to quantify both effective fracture half-length and non-uniform permeability distribution around the fractures. The major contribution of this work is the introduction of a new analytical model for evaluating the transient linear flow period for the cases of arbitrary reservoir heterogeneity and non-static reservoir properties. This new approach is particularly useful for evaluating the effectiveness of hydraulic fracturing operations by extracting the spatial variability of reservoir quality within the stimulated reservoir volume (SRV).

Inversing fracture parameters using early-time production data for fractured wells

ABSTRACTThe authors studied models of inversing fracture parameters using early-time production data from fractured wells. Inverse results help evaluate the performance of fracturing, improve fracturing design, and predict the long-term production dynamics of fractured wells. First, polynomials were used to match variable flows. A new analytical model describing the transient-pressure behaviour of variable flow production was developed. This model is significantly superior to existing superposition analysis models in terms of calculation speed, accuracy, and stability. Then, in order to establish the best match between the calculated bottomhole pressure and the actual measured bottomhole pressure, the wellbore storage coefficient, fracture conductivity, fracture half-length, and fracture skin factor were selected as inverse fracture parameters. An automatic matching model was established, and a Levenberg-Marquardt algorithm based on a stochastic initial value and maximum probability was developed. This algorithm (1) is easy to implement, (2) can search local optimal solutions as much as possible, and (3) to improves the multisolution of inverse problems. Finally, the sensitivity of fracture parameters was analysed. Some existing automatic matching methods were compared and validated. A set of accurate, high-precision data acquisition and calculation devices was identified to promote application of the results.

Estimating carbon geosequestration capacity in shales based on multiple fractured horizontal well: A case study

Nowadays, shale reservoirs have been though as good candidates for CO2 geosequestration for reduction of carbon emission. When estimating the carbon geosequestration capacity, multiple fractured horizontal well (MFHW) is a prerequisite for consideration when shale reservoirs are included in candidate geological sites, as it is one of the critical factors for the successful development of shale reservoirs. In order to perfect our previous works, a new model is proposed to calculate the carbon geosequestration capacity of depleted shale reservoirs based on MFHW. The methodology calculates carbon geosequestration capacity of shale reservoirs by considering Knudsen diffusion, molecular diffusion, supercritical Langmuir adsorption, stimulated reservoir volume (SRV), and stress-sensitivity of the permeability. Utilizing the perturbation transformation technique, finite difference method, and Laplace transform technique, our method is more in accordance with the actual situations, allowing us to accurately estimate the carbon storage capacity by capturing the transient pressure response of the MFHW. A field case from the Ordos Basin in China presents that the CO2 geosequestration capacity is proportional to the dimensionless fracture half-length and conductivity. The properties of hydraulic fractures only affect the early period of the CO2 geosequestration process. For the adsorption coefficient and flow coefficient ratio, with the change of these parameters, the middle and late periods of the CO2 geosequestration process are mainly influenced.

Investigation of imbibition areas during well shut-in based on mercury injection experiment and BP neural network

Hydraulic fracturing appears to be an important and efficient method in the development of tight oil reservoirs. Well shut-in process after hydraulic fracturing enables the capillary imbibition process in leak-off area thus improving the production in tight oil reservoirs. Therefore, leak-off area is also the imbibition area. However, the range of leak-off area has not been fully understood for production engineers due to the complexity and dynamics of fracturing. In this work, we applied fractal theory to derive the matrix permeability in tight oil reservoirs, which can better describe the microscopic characteristics of reservoirs and manage the reservoir performance. Subsequently, we developed an analytical model to calculate pressure distribution at leak-off areas during the fracturing and well shut-in processes. To avoid solving nonlinear equations, we used Newton-Raphson iterative method to calculate the correlation of time and pressure. The effects of six parameters (e.g., permeability, shut-in time, viscosity, half-length of fracture and height of fracture) on the leak-off area were examined using BP neural network, and a two-dimensional distribution grid of fracturing leak-off was developed. Moreover, we computed pressure distribution of fracturing fluid leak-off area numerically to verify the reliability of the new model. Our results show that the leak-off area of fracturing fluid increases with shut-in time. Based on the BP neural network, permeability and shut-in time play significant influences in the leak-off area of fracturing fluid. This work provides insights to examine the process of hydraulic fracturing and shut-in in tight oil reservoirs, and the proposed model is a useful tool to quantify the leak-off area of fracturing fluid after shut-in stage.

Guidelines for Economic Design of Multistage Hydraulic Fracturing, Yanchang Tight Formation, Ordos Basin

It is common practice to exploit tight oil resources with the assistance of techniques such as horizontal drilling and multistage hydraulic fracturing (MHF). Due to the high capital costs of such techniques and rapid oil decline rates of wells in tight oil reservoirs, the economic performance of a well, which is commonly evaluated by payback period and net present value, becomes crucial in the early stage of exploiting tight oil resources. A reasonable MHF design is one key factor that can benefit a well in both production and economic perspectives. Although many optimization studies have been conducted on MHF designs, hardly any focus has been given to the optimum design of total fracture length, number of stages and number of clusters per stage in the economic perspective for tight oil formations. In this work, economic performances under different MHF designs were studied through a series of numerical simulations and a statistical study for the Yanchang tight formation, Ordos Basin. Three matrix permeability levels (0.06 md, 0.10 md and 0.22 md) were considered in a single-well simulation model. In total, 264 MHF designs were investigated. The results showed that the production in the first 5 years was significant for a well to make a profit for a tight formation with a permeability less than 0.22 md. With a higher matrix permeability, the payback period became shorter under the same MHF design. This study also found that the NPV of a well with MHF can be expressed as a quadratic function of the fracture half-length. R2 values of parabolic correlations were more than 0.91 for all three permeability levels. With increasing matrix permeability, the R2 value increases. For tight formations with similar reservoir properties, this type of correlation can be used to evaluate MHF designs under the given economic parameters. It is worth noting that the optimal MHF design from the production perspective does not always lead to that from the economic perspective. Therefore, the economic optimization of MHF designs is necessary for tight oil formations. A rule of thumb for designing MHF is to have a longer fracture half-length, a smaller number of clusters and a smaller number of stages for tight oil formations with permeabilities in the range of 0.06 to 0.22 md.

Inversion of Downhole Temperature Measurements in Multistage-Fracturing Stimulation of Horizontal Wells in Unconventional Reservoirs

Summary There are still many challenges involved with the quantitative interpretation of downhole distributed-temperature measurements for diagnosing multistage-fracturing treatments in horizontal wells. These challenges include handling enormous amounts of data measured by the sensors in a continuous time and space domain, a ready-to-use fast and robust forward model to simulate temperature behavior, and an efficient algorithm to invert the parameters that are of interest. Because multistage fracturing involves many uncertain parameters (ranging from reservoir properties to treatment design, to fracture geometries and conductivity), the problem becomes extremely complicated when the measured temperature is inverted to a downhole flow profile. In this study we present an approach for combining forward and inverse models to interpret downhole temperature data. Our goal was to improve computational efficiency. Field data from a gas well in the Marcellus Shale were used to illustrate the feasibility of quantitative interpretation of temperature measurement for fracture diagnosis. The forward model used the fast-marching method (FMM). The forward simulation was an order of magnitude faster than the semianalytical model, which is the essential contribution for successfully applying the method in the field case. The improved inversion procedure increased the efficiency of the interpretation. The inversion procedure began with a sensitivity study to select the inversion parameters among various other parameters, such as fracture half-length and the fracture conductivity, and to determine the impact of their uncertainty on inversion. The inversion model used the initial analysis of the temperature gradient to identify the fracture locations with significant temperature changes for interpretation and eliminated the rest of the fracture locations from interpretation. Thus, we obtained a prior estimation of the selected inversion parameters, which was used as an initial estimate for the inversion process. This prior estimation saved significant computation. The inversion was performed fracture by fracture using either parallel computing or sequential computing on the basis of the sensor locations. We began with a synthetic example containing multiple fractures to illustrate the approach and test the procedure accuracy and computation speed. The primary inversion parameter was flow rate, though we also interpreted either fracture length or fracture conductivity when assuming all the other parameters as additional constraints. With an adequate initial estimate, the inverted parameters matched the reference “true value” properly. The inversion process converged with reasonable iterations for each fracture (2–3 iterations). The operation time highlights the advantages of the inversion approach presented in this paper. The guided initial estimation ensured that the gradient inversion approach converged and avoided local minimization. Finally, a field application for interpreting the DTS measurement for the flow profile of the multistage-fractured horizontal well was performed using this inversion method, and it showed encouraging results. The results of our investigation illustrate the procedure feasibility for using temperature data to diagnose a multistage-fracturing treatment. Our proposed inversion model was fast and reliable and provided a promising tool that can be used to quantitatively interpret downhole temperature data.