Reservoir simulation

Distributed Temperature Measurements Allow Fracture Diagnostics During Flowback

In the complete paper, the authors derive a novel analytical solution to model the temperature signal associated with the shut-in during flowback and production periods.


The significant temperature difference between the fractured and nonfractured regions during the stimulation-fluid flowback period can be useful for fracture diagnosis. Recent developments in downhole temperature-monitoring systems open new possibilities to detect these temperature variations to perform production-logging analyses. In the complete paper, the authors derive a novel analytical solution to model the temperature signal associated with the shut-in during flowback and production periods. The output of this work can contribute to production-logging, warmback, and wellbore-storage analyses to achieve successful fracture diagnostic.


Information about individual fractures is critical in determining whether fracturing jobs have been successful or refracturing is required. Exploring new methods to evaluate fracture characteristics has been the focus of recent research activities. Triggered by field implementations and observations, research has been conducted to investigate temperature profiles during the early hydraulic fracturing and late production periods to characterize fractures.

Current research on the use of temperature data to evaluate hydraulic fractures and reservoirs focuses on developing forward numerical and semianalytical models to predict temperature profiles during fracturing and production. As a prelude to the production period, stimulation fluid flowback is often performed after hydraulic fracturing operations to remove the remaining fluid and loosen proppant from the wellbore. Because recording the flowback operation may be required already by regulations, the cost of collecting data from the flowback period is minimal. As a result, ongoing research on analyzing data from the flowback period has aimed to diagnose fracture design and efficiency, characterize key reservoir properties from the chemical composition of the flowback fluids, and predict long-term production. Such efforts are based on the critical timing of the flowback period—a transition between what happened during completion and what will happen during production. The potential temperature modeling on the flowback period proposed here shares the same insight. Shortly after hydraulic fracturing stimulation, the temperature in the fractured region is still lower than in the nonfractured region.

The objective of this work is to perform fracture diagnostics with the flowback temperature signal. The main objective is identifying inflow temperature from each of the fractures, critical as an input for production-logging-tool (PLT) analysis. Preliminary simulation studies found that the inflow temperature is identical to the surrounding fractured region temperature, which is masked by the heating effect introduced from wellbore fluid flow after the shut-in test (afterflow). Therefore, the authors propose analyzing this heating effect with analytical and numerical models, which are described in the complete paper. Once the heating effect is quantified, the inflow temperature for each fracture can be obtained.

Analytical Solution Verification

In this section of the complete paper, the analytical solution is modeled and verified against the wellbore-fluid-­temperature profiles obtained from numerical simulation. With a derived analytical solution, the wellbore fluid temperature associated with afterflow during the flowback period can be modeled analytically. First, the temporal temperature modeling results at various locations from the perforation are presented. To verify this analytical solution, these analytically modeled results are compared with those from a numerical simulation.

Fig. 1 presents the wellbore-­temperature-modeling results obtained from the analytical solution and numerical simulation for the base case. The temporal temperature variations at different distances from the perforation show good agreement between analytical solutions (solid curves) and numerical simulations (dotted curves) for all the cases. The ­wellbore-fluid temperature increases after shut-in. Away from the perforation, the initial reservoir temperature can increase to almost 77°C. At the perforation, the wellbore-fluid temperature should remain at 73°C if there is no afterflow. The heating effect of the wellbore-fluid temperature at the perforation is caused by the warmer fluid away from the perforation moving in. Therefore, different modeling equations can be applied for fractured and nonfractured regions.

Fig. 1—Wellbore temperature profiles obtained analytically and numerically for the base case.


Shortly after the shut-in (0.3 days for the base case), the wellbore steady-state temperature is reached. This indicates that a thermal balance has been reached between convection as a result of afterflow and conduction to surrounding rock.

When considering the wellbore-­temperature-modeling results obtained from the analytical solution and numerical simulation for the variable afterflow velocity case monitored at the toe, good agreements are achieved between analytical solutions and numerical simulations for all cases. Validation of the analytical solution on variable velocity indicates that the convolution effect of velocity variation on temperature modeling can be captured by replacement of constant velocity with variable velocity in the equation derived, assuming constant velocity.

The steady-state temperature at a late time is not established for the variable velocity case. As afterflow velocity declines over time, less warm fluid is brought into the fractured region, resulting in a continuously dropping temperature profile after the initial heating. The temperature signal obtained at the perforation indicates that it eventually will reach the surrounding region ­temperature (inflow temperature at the perforation), the speed of which depends on how fast the afterflow velocity declines and how long the shut-in test lasts. These observations will be used to develop inversion procedures to analyze temperature signals associated with variable afterflow velocity.

Parametric Analysis

Several parametric analyses are performed to identify the effects of different properties on the temperature profile. The four properties selected to perform the analyses on constant velocity cases were varying flowing temperature, after­flow velocity, wellbore radius, and boundary condition coefficient. These analyses are presented in cases of constant afterflow velocity when reaching steady state after 0.3 days of a shut-in and compared with the corresponding surrounding region temperature. Acceptable agreements are achieved between the analytical solution and numerical simulation in all 12 cases presented in the parametric analyses.

The effect of the flowing temperature variation is presented mainly during the initial heating effect. For various conditions of production-fluid temperature before the shut-in, the steady-state wellbore-fluid temperature after the shut-in test remains unchanged. Consequently, the flowing temperature does not affect the steady-state wellbore-fluid temperature profile after the shut-in.

For properties sensitive to the temperature profile, the effects of the afterflow velocity and wellbore-radius variations illustrate similar behavior. Higher velocity and larger wellbore radius result in a larger heating effect near the fracture during the shut-in period. In fact, more thermal energy is brought into the fractured region from the higher afterflow mass rate. Therefore, the afterflow mass rate is a critical factor for evaluating the heating effect.

After the parametric analyses on constant-velocity cases, the variable-velocity case is analyzed. For this analysis, another set of afterflow velocity profiles is used to model the wellbore-fluid temperature profile. It is determined that the temperature profile is sensitive to the magnitude and decline behavior of the afterflow velocity.

Inversion Procedures

After presenting the forward temperature modeling results, inflow-­temperature and afterflow-velocity characterization procedures are developed from the analytical solutions. A dedicated section of the complete paper provides temperature-interpretation techniques in terms of a semilog plot analysis applied to synthetic temperature data obtained from numerical simulation.


Stimulation-fluid flowback presents a distinct thermal signal because of the significant temperature difference between the fractured and nonfractured regions of the reservoir. This work presents the analysis of the flowback temperature profile to identify the inflow temperature of each fracture. The results from preliminary simulation studies suggest that the inflow temperature is identical to the surrounding fractured region temperature, which is masked by the heating effect induced by the wellbore fluid flow after a shut-in. By quantifying the heating effect, the inflow temperature can be obtained for each fracture. An analytical solution is presented to model the temperature signal associated with a shut-in period separating the flowback and production periods. The results of this temperature modeling can be used to evaluate the efficiency of each fracture. This analytical solution is derived using the method of characteristics applied to an existing governing equation with a newly incorporated thermal boundary condition. A wellbore-fluid simulation is built using a simplified finite-element model to serve as a validation set. The results of the simulation present good agreement with those from the analytical solution.

After the validation and analysis of the forward modeling results, inversion procedures are introduced on the basis of the derived analytical solution. By comparing the temperature profiles in the fractured and nonfractured region, the inflow-fluid temperature, surrounding temperature field, and the afterflow velocity of each fracture can be estimated. The characterization results show good accuracy against the true values. The estimations are particularly accurate for the temperature profiling of the fractured region (error of less than 3%).

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 195221, “Fracture Diagnostics Using Distributed Temperature Measurements During Stimulation-Fluid Flowback,” by Yilin Mao, SPE, and Mehdi Zeidouni, SPE, Louisiana State University, and Caroline Godefroy, Interpretive Software Products, et al., prepared for the 2019 SPE Oklahoma City Oil and Gas Symposium, Oklahoma City,  9–10 April. The paper has not been peer reviewed.