Quantification Of Flow Rates Research Articles

Active gas camera mass flow quantification (qOGI): Application in a biogas plant and comparison to state-of-the-art gas cams.

Gas cameras are primarily used to detect gas leaks, but their use has been increasingly extended to mass flow quantification (qOGI). We employ the previously published active illuminated gas camera [Bergau etal. "Real-time active-gas imaging of small gas leaks," J. Sens. Sens. Syst. 12, 61-68 (2023) and Bergau etal. "Flow rate quantification of small methane leaks using laser spectroscopy and deep learning," Process Saf. Environ. Prot. 182, 752-759 (2024)] in a real-world application for quantification, enhancing the camera with two new features: sensitivity adaptation and camera-gas distance detection. This technology was applied to a gas leak found in the pressure swing adsorption room of a biogas plant in Germany. We compare its performance with state-of-the-art quantification gas cameras (qOGI), such as Sensia Mileva 33. Such a comparison between active and passive gas cameras is possible for the first time due to the introduced sensitivity tuning. Additionally, we enclosed the gas leak and measure the methane concentration with a flame ionization detector, providing a gold standard for comparison. Our findings revealed relative offsets to our gold standard of -57% and +319% for the DAS-camera and the Sensia, respectively, suggesting that the accuracy of mass flow quantification could be improved through the use of active gas cameras.

Measuring CSF shunt flow with MRI using flow enhancement of signal intensity (FENSI).

To develop and validate a noninvasive imaging technique for accurately assessing very slow CSF flow within shunt tubes in pediatric patients with hydrocephalus, aiming to identify obstructions that might impede CSF drainage. A simulation of shunt flow enhancement of signal intensity (shunt-FENSI) signal is used to establish the relationship between signal change and flow rate. The quantification of flow enhancement of signal intensity data involves normalization, curve fitting, and calibration to match simulated data. Additionally, a phase sweep method is introduced to accommodate the impact of magnetic field inhomogeneity on the flow measurement. The method is tested in flow phantoms, healthy adults, intensive care unit patients with external ventricular drains (EVD), and shunt patients. EVDs enable shunt-flow measurements to be acquired with a ground truth measure of CSF drainage. The flow-rate-to-signal simulation establishes signal-flow relationships and takes into account the T1 of draining fluid. The phase sweep method accurately accounts for phase accumulation due to frequency offsets at the shunt. Results in phantom and healthy human participants reveal reliable quantification of flow rates using controlled flows and agreement with the flow simulation. EVD patients display reliable measures of flow rates. Shunt patient results demonstrate feasibility of the method and consistent flow rates for functional shunts. The results demonstrate the technique's applicability, accuracy, and potential for diagnosing and noninvasively monitoring hydrocephalus. Limitations of the current approach include a high sensitivity to motion and strict requirement of imaging slice prescription.

Flow rate quantification of small methane leaks using laser spectroscopy and deep learning

To ensure safety in the transport and loading processes involving hazardous gasses, the detection of gas leaks in technical installations and the subsequent quantification of the released mass flows is of great public interest. One common approach to obtain this information is the usage of gas cameras, but they typically provide only inaccurate concentration data and are not sensitive enough to detect small gas leaks. In this work, we use a new gas camera approach that is based on laser absorption spectroscopy combined with mid-infrared imaging to solve these challenges. We gain videos of artificial gas leaks that containing more accurate concentration length information in ppm*m while visualizing small flow rates between 5 and 60 ml/min. For the ease of experimentation, we utilize methane while the camera can be adapted to other possibly hazardous gasses. On the dataset obtained, we train a deep-learning model aiming to continuously predict the flowrate. Additionally, we evaluate it on an eight-class classification task to compare accuracy metrics. We demonstrate an average difference of 1.6 ml/min from the mean predicted values to the true flow rates as well as an accuracy of (54 ± 2) % in the classification task.

Evaluation of passive acoustic methods for ambient noise baseline and gas flow rate quantification at a proposed nearshore carbon capture and storage site in Australia

Measurement, monitoring, and verification (MMV) is an integral component of carbon capture and storage (CCS) projects. Within an operational MMV equipment, hydrophone-based passive acoustic techniques are used to establish ambient noise baseline and flow rate quantification at short range, specifically to facilitate “detect-attribute-quantify” sequence of an MMV program. However, nearshore environments are acoustically complex with different soundscape components that can disproportionately dominate ambient noise levels, potentially masking acoustic signatures of bubbles used to quantify seabed gas seeps. Therefore, a robust baseline describing ambient noise variability across the range of frequencies associated with acoustic emissions of gas seeps is required, from which changes can be detected and monitored. In this context, hydrophone measurements from a proposed nearshore CCS site in Australia are analyzed to establish a temporally resolved baseline, identifying key drivers causing overall ambient noise variability. These results are compared with acoustic bubble spectrum features and flow rate estimates from a controlled in situgas release experiment to understand the likelihood of detecting bubbles and quantifying flow rate at the proposed CCS site. Despite the complexities of nearshore environment, the evaluation highlights that passive acoustic methods can provide a practical solution to complement quantification component of operational MMV programs.

The permanent temperature monitoring for flow rate quantification in production and injection wells

A technique for monitoring of a production well rate dynamics based on the results of long-term temperature measurements in the wellbore at a certain depth which is significantly higher than the productive formation in real time is presented. The proposed analytical approaches for the well rate evaluation are based on the classical temperature behavior in the intervals of liquid and gas movement along the wellbore at a relatively far from the target formations. The temperature gradient in such intervals practically does not change with time and is close to geothermal, regardless of whether the inflow or injection is stable over time, or the well is in an unstable and cyclic production. It makes possible to find a relationship between the temperature change and heat flux density on the wellbore with simple and clear analytical approach, and to associate the heat flux density dynamics with the flow rate of the fluid moving along the wellbore. The main novelty of the presented publication is the justification of temperature deconvolution application for well rate changes vs time evaluation on a substantially non-stationary well production or injection conditions. The presented approach of permanent temperature monitoring interpretation is applicable not only for cases of step well rate changes, but also for cases of gradual well rate changes vs time. A wide range of measuring sensors can be used for presented approach implementation, including permanent fiber-based distributed along the length of the wellbore systems.

Water flow rate quantification through an experimental CNT membrane: A molecular dynamics simulation approach

The comprehension of water flow rate within carbon nanostructures holds great importance in both theoretical understanding and engineering design of microscale and nanoscale devices. This study presents a comprehensive numerical model for analyzing the water flow rate in Carbon Nanotube (CNT) membranes. The outcomes of this model have particular relevance in predicting the performance and designing CNT membranes for water desalination, which offer the potential for remarkably rapid transport. By investigating the characteristics of the CNT membrane, various geometric properties that influence the overall flow rate are quantified. Apart from the diameter and length, attention is also given to non-ideal factors associated with the deformation of CNTs from their original structures. Specifically, the impact of eccentricity and bending on the flow rate through CNTs is examined, revealing limited but noteworthy effects. Additionally, a simplified model is developed to characterize the membrane using statistical data pertaining to CNT synthesis. The results of the total water flow rate demonstrate that the existing numerical model closely aligns with the reported experimental values.

Evaluation of passive acoustic methods for ambient noise baseline and gas flow rate quantification at a proposed nearshore carbon capture and storage site in Australia

Measurement, monitoring, and verification (MMV) is an integral component of carbon capture and storage (CCS) projects, providing valuable feedback for management practices and assuring integrity. Within an operational MMV equipment, hydrophone-based passive acoustic techniques are used to establish ambient noise baseline and flow rate quantification at short range, specifically to facilitate ‘detect-attribute-quantify’ sequence of an MMV program. But nearshore environments are acoustically complex with overlapping components of biophony, geophony, anthropophony, and deployment noise resulting from multiple instruments used for MMV. These soundscape components can disproportionately dominate ambient noise levels, potentially masking acoustic signatures of bubbles used to quantify seabed gas seeps. Therefore, a robust baseline describing ambient noise variability across the range of frequencies associated with acoustic emissions of gas seeps is required, from which changes can be detected and monitored. In this context, multi-year hydrophone measurements (20 Hz to 24 kHz) from a proposed nearshore CCS site in Australia are analysed to establish a temporally resolved baseline, identifying key drivers causing overall ambient noise variability. These results are compared with acoustic bubble spectrum features and flow rate estimates from a controlled in situ gas release experiment. The experiment was performed using a custom-made bubble generator at 1, 10, and 25 m range from the hydrophone to understand the likelihood of detecting bubbles and quantifying flow rate at the proposed CCS site. Despite the complexities of nearshore environment, the evaluation highlights that low-cost hydrophone-based passive acoustic methods can provide a practical solution to complement quantification component of operational MMV programs.

A novel approach to determining the hydrodynamic resistance of droplets in microchannels using active control and grey-box system identification

Inaccurate prediction of droplet hydrodynamic resistance has a profound impact on droplet chip performance and lengthens the iterative design process. Previous studies measuring droplet resistance use various approaches such as interface comparison to quantify flow rate, and pressure taps; all these methods are classified as passive. Although each study supports well their own findings, the wide variety of conditions such as channel geometry and use of surfactant in combination with the difficulty in quantifying the droplet resistance leads to poor consensus across the different studies. Overall guidelines would be broadly beneficial to the community, but are currently fairly crude, with a rule of thumb of 2 to 5 times resistance increase. The active droplet control platform previously developed enables a novel approach that is herein confirmed as promising. This proof-of-concept study focuses on verifying this approach that employs a system identification method to determine the hydrodynamic resistance of a channel containing a single droplet, from which the droplet resistance is retrieved. This method has the potential to be further applied to a large variety of conditions, and most importantly, to non-Newtonian fluids once key limitations are overcome to improve measurement resolution. The current results qualitatively agree with the literature and demonstrate the promising future for this novel active approach to quantifying droplet resistance.

Empirical Correlations for Predicting Flow Rates Using Distributed Acoustic Sensor Measurements, Validated with Wellbore and Flow Loop Data Sets

Summary Distributed acoustic sensing (DAS) is an emerging surveillance technology that is becoming increasingly popular in the oil and gas industry for real-time flow monitoring. However, there are limited studies that rigorously quantify flow rates using DAS. This work expands the existing literature by presenting a detailed workflow for accurately estimating fluid flow rates from DAS data using time- and frequency-domain signal processing. Three simple empirical correlation functions (linear, exponential, and cubic) are developed and tested to predict flow rates from DAS. The proposed correlations are demonstrated for flow rates ranging from 50 to 300 gallons per minute (GPM) in a vertical 5,163-ft-deep wellbore and from 12 to 36 GPM in a horizontal surface flow loop. Tests were performed using a single-phase flow of water as well as using synthetic oil-based drilling mud. Time-domain DAS processing using root-mean-square (RMS) value and frequency-domain processing using frequency band energy (FBE) is evaluated, followed by a statistical approach to minimize the influence of outliers. The RMS and FBE approaches are individually compared for flow prediction, and the performance of the correlations is rigorously evaluated on a blind data set that was not originally used for developing the correlations. For both the wellbore and flow loop data sets, a coefficient of determination (or R2) greater than 0.95 with an average flow rate prediction error of less than 10% was achieved for the best-performing correlation for the blind test data. The analysis procedure and workflow presented in this study can be adopted and extended to different operating conditions for quantitative flow rate prediction using DAS.

Quantifying flow rate using stage-discharge rating curve and Scs runoff equation on upland watershed of Lake Tana Sub Basin, Ethiopia

Quantifying flow rate using stage-discharge rating curve and Scs runoff equation on upland watershed of Lake Tana Sub Basin, Ethiopia

Quantification of Flow Rates and Flow Volumes in Valve Regurgitation Using 3-D High Frame-Rate Ultrasound

Valve regurgitation is a cardiac condition caused by the incomplete closure of a cardiac valve. Untreated, this condition may result in cardiac failure. Regular monitoring of this condition is essential in guiding the decision process for surgical intervention. Current guidelines recommend a multiparametric assessment of valve regurgitation using echocardiography, which is both time consuming and heavily dependent on the experience of the examiner. Several methods have been proposed to provide quantitative markers to facilitate the assessment of valve regurgitation, most notably the Proximal Isovelocity Surface Area (PISA) method and methods based on the quantification of the total Regurgitant Volume (RVol) from the power of backscattered blood signal. In this work, we propose a framework based on trans-thoracic 3-D high frame-rate acquisitions for the simultaneous estimation of the jet cross-sectional area and jet velocity directly at the jet core, which are then combined to estimate the instantaneous flow rate and RVol patients with aortic or mitral insufficiency. We compare two methods for the segmentation of the jet cross-sectional area from the power Doppler signal. Validation on simulated data indicates good segmentation accuracy for the best method (β = 0.97, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.91). Validation on recordings from a flow phantom shows good agreement (β = 1.2, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.88) with an external flow rate meter. Clinical feasibility of the method is also shown in a patient with mitral regurgitation.

Quantitatively Monitoring Bubble-Flow at a Seep Site Offshore Oregon: Field Trials and Methodological Advances for Parallel Optical and Hydroacoustical Measurements

Two lander-based devices, the Bubble-Box and GasQuant-II, were used to investigate the spatial and temporal variability and total gas flow rates of a seep area offshore Oregon, United States. The Bubble-Box is a stereo camera–equipped lander that records bubbles inside a rising corridor with 80 Hz, allowing for automated image analyses of bubble size distributions and rising speeds. GasQuant is a hydroacoustic lander using a horizontally oriented multibeam swath to record the backscatter intensity of bubble streams passing the swath plain. The experimental set up at the Astoria Canyon site at a water depth of about 500 m aimed at calibrating the hydroacoustic GasQuant data with the visual Bubble-Box data for a spatial and temporal flow rate quantification of the site. For about 90 h in total, both systems were deployed simultaneously and pressure and temperature data were recorded using a CTD as well. Detailed image analyses show a Gaussian-like bubble size distribution of bubbles with a radius of 0.6–6 mm (mean 2.5 mm, std. dev. 0.25 mm); this is very similar to other measurements reported in the literature. Rising speeds ranged from 15 to 37 cm/s between 1- and 5-mm bubble sizes and are thus, in parts, slightly faster than reported elsewhere. Bubble sizes and calculated flow rates are rather constant over time at the two monitored bubble streams. Flow rates of these individual bubble streams are in the range of 544–1,278 mm3/s. One Bubble-Box data set was used to calibrate the acoustic backscatter response of the GasQuant data, enabling us to calculate a flow rate of the ensonified seep area (∼1,700 m2) that ranged from 4.98 to 8.33 L/min (5.38 × 106 to 9.01 × 106 CH4 mol/year). Such flow rates are common for seep areas of similar size, and as such, this location is classified as a normally active seep area. For deriving these acoustically based flow rates, the detailed data pre-processing considered echogram gridding methods of the swath data and bubble responses at the respective water depth. The described method uses the inverse gas flow quantification approach and gives an in-depth example of the benefits of using acoustic and optical methods in tandem.

Simultaneous Subsea Gas Plumes Detection and Positioning Using a Transceiver of an Ultra-Short Baseline System

This paper presents an in-situ active acoustic detection system that can detect and locate the subsea gas plumes simultaneously using a transceiver of an ultra-short baseline (USBL) positioning system. Seabed gas leaks, both natural and artificial, are causing concern worldwide. Conventional detection systems, including Raman spectrometers, side-scan sonars, and multibeam sonars, suffer from some limitations such as the effective range and real-time processing problem. We use an omnidirectional USBL transceiver to illuminate surroundings and detect echoes from gas plumes. A small hydrophone array in planar circular shape is used to beam-form the received echoes. An echo identification algorithm is proposed to separate the echoes from fixed objects and gas plumes. The results are verified against various experiments. The matched filtering and phased-array beamforming are applied to determine the relative distance and angle of arrival from gas plumes. A preliminary result on gas flow rate quantification is also studied. This paper describes the system design and algorithms in detail and presents experimental results in an anechoic tank, demonstrating the great potential of this system for subsea gas plumes detection and positioning.

Influence of Spatial Resolution and Compressed SENSE Acceleration Factor on Flow Quantification with 4D Flow MRI at 3 Tesla.

Four-dimensional (4D) flow MRI allows quantifying flow in blood vessels–non invasively and in vivo. The clinical use of 4D flow MRI in small vessels, however, is hampered by long examination times and limited spatial resolution. Compressed SENSE (CS-SENSE) is a technique that can accelerate 4D flow dramatically. Here, we investigated the effect of spatial resolution and CS acceleration on flow measurements by using 4D flow MRI in small vessels in vitro at 3 T. We compared the flow in silicon tubes (inner diameters of 2, 3, 4, and 5 mm) measured with 4D flow MRI, accelerated with four CS factors (CS = 2.5, 4.5, 6.5, and 13) and three voxel sizes (0.5, 1, and 1.5 mm3) to 2D flow MRI and a flow sensor. Additionally, the velocity field in an aneurysm model acquired with 4D flow MRI was compared to the one simulated with computational fluid dynamics (CFD). A strong correlation was observed between flow sensor, 2D flow MRI, and 4D flow MRI (rho > 0.94). The use of fewer than seven voxels per vessel diameter (nROI) resulted in an overestimation of flow in more than 5% of flow measured with 2D flow MRI. A negative correlation (rho = −0.81) between flow error and nROI were found for CS = 2.5 and 4.5. No statistically significant impact of CS factor on differences in flow rates was observed. However, a trend of increased flow error with increased CS factor was observed. In an aneurysm model, the peak velocity and stagnation zone were detected by CFD and all 4D flow MRI variants. The velocity difference error in the aneurysm sac did not exceed 11% for CS = 4.5 in comparison to CS = 2.5 for all spatial resolutions. Therefore, CS factors from 2.5–4.5 can appear suitable to improve spatial or temporal resolution for accurate quantification of flow rate and velocity. We encourage reporting the number of voxels per vessel diameter to standardize 4D flow MRI protocols.

Refined protocols to mitigate user-induced uncertainty for ADCP moving-boat discharge measurement in irrigation canals

A Teledyne RD Instruments StreamPro ADCP was used to quantify flow rates between 0.5 and 8 m3/s in man-made irrigation canals with the aim of determining best practices for the method of deployment of an ADCP using a moving boat when computing mean steady discharge. Prescription for total sampling duration is refined here as the product of the duration of a single measurement transect and the total number of transects taken in reciprocal directions. The purpose of this enhancement is to lessen measurement uncertainty arising from insufficient resolution of the turbulent fluctuating velocity signal as determined by the sampling duration chosen by the user. These guidelines also estimate the point of diminishing returns for additional data collection in order to optimize time efficiency for measurement of mean steady discharge. Suggested protocols developed from field experimentation indicate that a significant reduction in the values of uncertainty metrics can be accomplished utilizing a remotely-operated tagline deployment method with a minimum transect duration of 240 s, equivalent to 240 velocity ensembles of an ADCP measuring at 1 Hz. Concurrently, at least four total transects in reciprocal directions should be measured. This expands and refines, in application to small-to-moderate sized irrigation canals, the currently held 720 s minimum total sampling duration guideline established by the USGS. These findings will equip ADCP users across a wide range of experience with further guidance to achieve more reliable direct flow quantification and hydraulic structure calibration.

KLT-IV v1.0: image velocimetry software for use with fixed and mobile platforms

Abstract. Accurately monitoring river flows can be challenging, particularly under high-flow conditions. In recent years, there has been considerable development of remote sensing techniques for the determination of river flow dynamics. Image velocimetry is one particular approach which has been shown to accurately reconstruct surface velocities under a range of hydro-geomorphic conditions. Building on these advances, a new software package, KLT-IV v1.0, has been designed to offer a user-friendly graphical interface for the determination of river flow velocity and river discharge using videos acquired from a variety of fixed and mobile platforms. Platform movement can be accounted for when ground control points and/or stable features are present or where the platform is equipped with a differential GPS device and inertial measurement unit (IMU) sensor. The application of KLT-IV v1.0 is demonstrated using two case studies at sites in the UK: (i) river Feshie and (ii) river Coquet. At these sites, footage is acquired from unmanned aerial systems (UASs) and fixed cameras. Using a combination of ground control points (GCPs) and differential GPS and IMU data to account for platform movement, image coordinates are converted to real-world distances and displacements. Flow measurements made with a UAS and fixed camera are used to generate a well-defined flow rating curve for the river Feshie. Concurrent measurements made by UAS and fixed camera are shown to deviate by &lt; 4 % under high-flow conditions where maximum velocities exceed 3 m s−1. The acquisition of footage on the river Coquet using a UAS equipped with differential GPS and IMU sensors enabled flow velocities to be precisely reconstructed along a 180 m river reach. In-channel velocities of between 0.2 and 1 m s−1 are produced. Check points indicated that unaccounted-for motion in the UAS platform is in the region of 6 cm. These examples are provided to illustrate the potential for KLT-IV to be used for quantifying flow rates using videos collected from fixed or mobile camera systems.

Fetal whole heart blood flow imaging using 4D cine MRI

Prenatal detection of congenital heart disease facilitates the opportunity for potentially life-saving care immediately after the baby is born. Echocardiography is routinely used for screening of morphological malformations, but functional measurements of blood flow are scarcely used in fetal echocardiography due to technical assumptions and issues of reliability. Magnetic resonance imaging (MRI) is readily used for quantification of abnormal blood flow in adult hearts, however, existing in utero approaches are compromised by spontaneous fetal motion. Here, we present and validate a novel method of MRI velocity-encoding combined with a motion-robust reconstruction framework for four-dimensional visualization and quantification of blood flow in the human fetal heart and major vessels. We demonstrate simultaneous 4D visualization of the anatomy and circulation, which we use to quantify flow rates through various major vessels. The framework introduced here could enable new clinical opportunities for assessment of the fetal cardiovascular system in both health and disease.

Measuring Fracture Flow Changes in a Bedrock Aquifer Due to Open Hole and Pumped Conditions Using Active Distributed Temperature Sensing

AbstractEfficiently measuring groundwater flow in bedrock aquifers is inherently challenging due to the irregular distribution and fine scale of fractures. Recent advances in Active Distributed Temperature Sensing (A‐DTS) in boreholes temporarily sealed with liners have made it possible to quantify flow rates in such aquifers at many different depths using heat as a tracer, but until now only data collected under a single hydraulic condition have been published. This paper presents the first field data from multiple A‐DTS field tests conducted under different hydraulic conditions to quantify groundwater flow redistribution within a bedrock aquifer. Three separate quasi steady state A‐DTS tests were collected in a sealed borehole: (1) natural gradient condition where all boreholes were sealed with flexible and impermeable liners, (2) cross‐connected condition where a nearby borehole was open allowing vertical flow within the borehole, and (3) forced gradient condition where the nearby open borehole was pumped at a constant rate of 54 L/min. The depth‐discrete hydraulic head responses were also measured during the three tests using a string of transducers in a sealed borehole. Results provide quantifiable insights as to how the bedrock aquifer responds, including A‐DTS‐derived measurements of flow changes in fractures at multiple depths driven by changes in gradients. The results confirm that a single open borehole or long‐screened well can significantly alter the site hydraulics and demonstrate that not all large or transmissive fractures show evidence of active flow and thus, transmissivity and aperture should not be used alone to infer active flow zones.

In Vivo Single-Molecule Detection of Nanoparticles for Multiphoton Fluorescence Correlation Spectroscopy to Quantify Cerebral Blood Flow.

We present the application of multiphoton in vivo fluorescence correlation spectroscopy (FCS) of fluorescent nanoparticles for the measurement of cerebral blood flow with excellent spatial and temporal resolution. Through the detection of single nanoparticles within the complex vessel architecture of a live mouse, this new approach enables the quantification of nanoparticle dynamics occurring within the vasculature along with simultaneous measurements of blood flow properties in the brain. In addition to providing high resolution blood flow measurements, this approach enables real-time quantification of nanoparticle concentration, degradation, and transport. This method is capable of quantifying flow rates at each pixel with submicron resolution to enable monitoring of dynamic changes in flow rates in response to changes in the animal's physiological condition. Scanning the excitation beam using FCS provides pixel by pixel mapping of flow rates with subvessel resolution across capillaries 300 μm deep in the brains of mice.

Production rates and EUR forecasts for interfering parent-parent wells and parent-child wells: Fast analytical solutions and validation with numerical reservoir simulators

Analytical expressions are given to forecast the production decline and estimated ultimate reserves (EUR) for pairs of both parent-parent wells and parent-child wells. The forecasts use physics-based flow rate quantification in elementary flow cells between hydraulic fractures sets. The intrinsic rate in the flow cells for a given shale formation can be obtained and scaled by a type curve specific for its completion and reservoir parameters. The model then can predict how changes in fracture treatment design parameters will affect the performance of new wells in the same target zone. The effect of well down-spacing and the onset of pressure interference on the performance of parent-parent wells can be forecasted with reasonable accuracy. Similarly, the equations can also predict the effect of infill drilling of child wells on the performance of both well types. The method is applied to real world examples from Eagle Ford acreage. The fast analytical model forecasts are benchmarked against the results from an independent numerical reservoir simulator, with satisfactory matches. The validated approach aims to provide a practical analytical tool for the production forecasting of multi-wells in shale formations.