DFIT - Diagnostic Fracture Injection Tests

1. What is a DFIT and what can we get from it?

A diagnostic fracture injection test (DFIT), a term coined by Halliburton by Craig and Brown, 1999, is a small-volume, clear water injection test designed to create a hydraulic fracture. After shut-in, the pressure is monitored to estimate:

1. Minimum principal stress \((S_{h,min})\)
2. Pore pressure
3. Permeability\((k)\), and leakoff coefficient \((C_{L})\) – Estimated if the first two above have at least adequate estimates.

Key – Estimation of the Leak-off Coefficient from measured changes in pressure after injection is stopped.

More specifically, this document outlines the procedures laid out in URTeC-2019-123 which is inspired from proven classical fracture compliance modelling, an industry collaboration with field DFIT studies, statistical comparison with full-physics multiphase simulators, after the drawbacks of the ‘holistic’ DFIT procedure using the ‘tangent’ method of interpretation outlined by Barree et al., 2009. This process utilizes classical concepts of stress estimation and fracture compliance methods to prevent underestimating in-situ stress, overestimating permeability and hence improve the well spacing and overall NPV of the field.

DFITs may be conducted for high permeability and low permeability reservoirs where the fracture injection transients behave differently. There is also a difference between horizontal well and vertical well DFIT interpretation where the horizontal wells in shale present new physics and challenges like near-wellbore tortuosity.

2. Operational Procedure - from Cramer and Nguyen, 2013

1. Surface pump establishes an injection rate with water and the wellbore fluid is compressed; In low permeability reservoirs, little (if any) of the injection fluid flows into the reservoir during this time.
2. Eventually injection pressure exceeds formation breakdown or breakover pressure. Hydraulic fracturing is being propagated into the reservoir rock.
3. Water injection at the surface is continued until the wellhead pressure stabilizes.
4. Surface injection is stopped, resulting in an Instantaneous shut-in pressure (ISIP) which is net of wellbore and near-wellbore friction pressure. Net pressure at shut-in is determined as sand-face pressure – fracture closure pressure.
5. Shut-in well pressure is monitored for signs of fracture closure (indicating the minimum principal stress)
6. After-closure period is evaluated for pseudo-linear and pseudo-radial flow signatures to determine initial reservoir pressure and even transmissibility.
   

3. Important Equations and Assumptions

3.1. The G function (and g function):

Assuming validity of Carter leakoff concepts derived for fluid leakoff through the fracture when the pressure is in the fracture is constant, we can get the G function or the g function as modified time functions to interpret DFITs.
Carter leakoff is valid during injection and slightly after shut-in but not long after when the pressure drop fall off is significant.

The g-function is proportional to the cumulative volume of fluid leaked off from the beginning of injection.
The G function is proportional to the cumulative volume of fluid leaked off after shut-in.

Hence, they are calculated from Carter leakoff equations can be related to each other as well -

$$\begin{equation} \label{eq:g} g(\Delta t) = \frac{4}{3} \left[\left(1+\frac{\Delta t}{t_{e}}\right)^{1.5} - \left(\frac{\Delta t}{t_{e}}\right)^{1.5} \right] \end{equation}$$

$$\begin{equation} \label{eq:G} G(\Delta t) = \frac{4}{\pi} \left(g(\Delta t) - g(\Delta t = 0) \right) = \frac{4}{3} \left[\left(1+\frac{\Delta t}{t_{e}}\right)^{1.5} - \left(\frac{\Delta t}{t_{e}}\right)^{1.5} - 1 \right] \end{equation}$$

where \(\Delta t\) is shut-in duration, and \(t_{e}\) is the duration of injection.

Disadvantages of using G function –
1. It relies on a single ‘point-in-time’ estimate of the dP/dG for estimation of effective permeability. That pick of dP/dG might still be elevated due to residual near-wellbore tortuosity.
2. Relies on Carter leakoff which may not hold perfectly true after shut-in, since the fluid pressure decreases over time.

3.2. The H function (and h function):

Constructed in the same spirit as the G/g function plots to represent the fluid leakoff from the system from the beginning of injection and after shut in.
Time convolutional integral accounts for the deviation from Carter leakoff combining Mayerhofer et al., 1995 and Valko and Economides, 1999 and wellbore storage.

$$\begin{equation} \label{eq:Vl_writtenash} V_{L} = 4A\sqrt{\frac{k\phi c_{t}}{\pi\mu}}\int_{0}^{\Delta t+t_{e}/2} \frac{(P(\tau) - P_{res})}{d\tau} \sqrt{\Delta t +t_{e}/2 - \tau} d\tau = 4Ah(\Delta t)\sqrt{\frac{k\phi c_{t}}{\pi\mu}} \end{equation}$$

This allows the calculation of leakoff volume down to lower pressures than the G-function approach (tackling the inapplicability of the G function methods during pressure falloff as Carter leakoff becomes invalid).

$$\begin{equation} \label{eq:h} h(\Delta t_{k}) \approx (P_{0} - P_{res}) \sqrt{\Delta t_{k}+\frac{t_{e}}{2}}+\sum_{i=0}^{k} (P_{i} - P_{i-1}) \sqrt{\Delta t_{k} - \Delta t_{i}} \end{equation}$$

3.3. Mass balance equations for DFIT:

Provides an additional constraint to be used with G or H function methods for characterization using DFITs.
General Mass balance philosophy for DFITs -

\(Volume \:Injected = Wellbore \:Storage + Leakoff + Fracture \:Volume.\)

Hence,

$$\begin{equation} \label{eq:dfitmbal} V_{inj} = (P - P_{w, init})C_{w} + 4C_{L}A\sqrt{\frac{t_{e}}{2}+\Delta t}+ A\frac{(P - S_{h,min})}{S_{f}} \end{equation}$$

where \(C_{w}\) is wellbore storage coefficient, and \(C_{L}\) is the leakoff coefficient.
Fracture stiffness and area are given by \(S_{f}\) and \(A\) respectively and the volume of fluid injected is given by \(V_{inj}\).

This simplification is valid during the ideal Nolte part of the preclosure transient. Thus, only apply the equation during a period that follows the ideal behaviour.

4. What do we need for a DFIT analysis?

Fundamental data collected from the field instrumentation -

1. The Pressure data: During the sufficiently long shut in, right after injection is stopped.
2. The Rate data: The injection rate and cumulative volume prior to the shut-in.

We use the following plots to generate estimates of the leakoff coefficient and permeability -

1. Log-Log plot of P and dP/dG with respect to the G function - stress and pore pressure.
2. Log-Log plot of P and dP/dt with respect to the time - identification of impulse flow signatures and post closure transients.

We may use additional plots such as –

1. Pressure vs time inverse or square root of time inverse – for extrapolating to pore pressure.
2. Relative stiffness plot – calculated from the data and h function to get the contact pressure at closure when data does not follow Carter leakoff. When the relative stiffness increases, it indicates that the fracture walls have come into contact.

5. Typical Signatures

Typical DFIT test in a low permeability reservoir may have the following sections –

1. Near-wellbore tortuosity and frictional pressure drop.
2. Minimum dP/dG
3. Ideal Nolte period (Pre-closure transient) – Pressure in the fractures assumed constant.
4. Fracture closure signature, approximately 90% fluid leakoff at peak dP/dG
5. Post-closure transients

Fig. 1: Typical DFIT Interpretation

Good G function plot –
Typically considered good quality data if the dP/dG shows an ‘S’ shaped curve with amount of time in constant fracture pressure for a good estimate of minimum principle stress and effective ISIP.

Fig. 2: Examples of good G function plots from DFIT data

Adequate G function plots –
Typically show a very subdued ‘S’ shape with a small difference in minimum and maximum dP/dG since multiple phenomena may be overlapping in time such as near wellbore tortuosity weakening the apparent closure response, making dP/dG almost monotonic but not really.

Fig. 2: Examples of 'adequate' G function plots from DFIT data

Bad G function plots –
This may be due to severe wellbore tortuosity (horizontal wells), rapid closure due to high system permeability, leakoff into pre-existing fractures or an operational problem such as leaks. The G function looks monotonic and cannot be used for estimating anything.

Fig. 3: Examples of 'bad' G function plots from DFIT data - Cannot be used

Vertical vs Horizontal wells –
Notice the early time pressure drop. This is usually higher for horizontal wells than vertical wells since this drop is a function of wellbore frictional pressure drop. Near-wellbore tortuosity promotes a steeper drop. This is why Instantaneous shut-in pressure (ISIP) at pump off may be much higher than the effective ISIP which can be calculated as shown below.

Fig. 4: Examples of G function plots for Horizontal vs Vertical DFITs

6. Workflow for estimation of Stress

1. Plot P and dP/dG vs G function time on a linear plot.
2. A good estimate of stress would have the ideal ‘S’ shape in dP/dG. An adequate estimate would have at least a non-monotonic dP/dG with at least a reasonable difference in the minimum and maximum dP/dG. No estimation can be performed if the curve is monotonic.
3. Look for the minimum in dP/dG in the dip following the shut in. This should be the ideal Nolte period, with pressure roughly constant. We are in the period where the effect of wellbore tortuosity in pressure leakoff has decayed and the fractures are fully open, i.e. no closure response yet, indicated by the increase in dP/dG from this minimum.
4. Add 10% to this minimum dP/dG and get the corresponding Pressure at this dP/dG. This is the contact pressure or pressure at which 90 percent of the fractures can be assumed to be closed.
5. Contact pressure is heuristically 75 psi higher than the minimum principle stress, S_h,min. Hence get S_h,min from the Contact Pressure by subtracting 75 psi with an uncertainty of up to 100 psi. This accounts for the remaining ‘stress shadow’ caused by the residual aperture at contact caused by the fracture roughness.
6. Get effective ISIP by extrapolating the linear trend found in the ideal Nolte period by extrapolating the trend backward on the same plot to get the y-intercept as effective ISIP, \(P_{ISIP, eff}\).

Fig. 5: Estimating Stress from DFIT data

7. Workflow for estimation of Pore Pressure

1. Needs sufficient shut in time to see impulse flow signatures i.e. dP/dG has to peak after the minimum and decay exhibiting a signature slope for a good estimate of pore pressure. You can get an adequate estimate if you have shut in data upto the peak of dP/dG by safely extrapolating and assuming a higher tolerance on the pore pressure uncertainty. If you don’t meet at least these criteria, you cannot estimate pore pressure and hence permeability.
2. Note: Gas wells may show false radial before true linear and well may suddenly show a drop in dP/dG indicating wellbore in vacuum – in all of these cases you cannot estimate pore pressure.
3. Look for late time impulse linear or radial flow signatures in dP/dG indicated by a slope of -1/2 or -1 respectively.
4. If there is impulse linear flow, plot P vs square root time inverse for the pressure data in impulse linear flow.
5. If there is impulse radial flow, plot P vs square root time inverse for the pressure data in impulse radial flow.
6. Extrapolate these pressure plots to t=0 or y-intercept to get pore pressure.

Fig. 6: Estimating Pore Pressure from DFIT data

8. Workflow for estimation of Permeability

1. Use the G function plot, dP/dG to estimate the minimum principal stress and effective ISIP as shown above. This needs to be at least adequate to proceed.
2. Search the log-log plot of P vs time for late time impulse flow signatures (most common and reliable is the impulse linear flow with a -1/2 slope on the derivate curve, radial signatures may exist but may be unreliable). Extrapolate from the peak if data is missing for an adequate estimate of pore pressure.
3. Choose whether to use preclosure or postclosure estimates of permeability – Post closure methods might be more accurate since they need a clean and reliable impulse flow signature at late time unaffected by multiphase leakoff. Some wells may never have enough shut-in time to show a post closure transient.

8.1. Preclosure Methods

8.1.1. Using the G function

Calculate leakoff Coefficient by making an assumption about fracture geometry as -
For Radial Fractures :- $$\begin{equation} \label{eq:cl_radial_fromG} C_{L} (radial) = \frac{-P}{dG} \frac{C_{w}+\frac{16R_{f}^{3}}{3E'}}{\frac{\pi^{2}}{2}R_{f}^{2}\sqrt{t_{e}}} = \frac{-dP}{dg} \frac{C_{w}+\frac{16R_{f}^{3}}{3E'}}{2\pi R_{f}^{2}\sqrt{t_{e}}} \end{equation}$$

For PKN (fixed height) Fractures :- $$\begin{equation} \label{eq:cl_pkn_fromG} C_{L} (PKN) = -\frac{dP}{dG} \frac{\frac{2C_{w}}{\pi}+\frac{L_{f}h_{f}^{2}}{E'}}{L_{f}h_{f}\sqrt{t_{e}}} = -\frac{dP}{dg} \frac{2C_{w}+\frac{L_{f}h_{f}^{2}\pi}{E'}}{4L_{f}h_{f}\sqrt{t_{e}}} \end{equation}$$

Evaluate these at the minimum dP/dG.

The unknown parameters of fracture geometry in the above, i.e. R_f or L_f, can be determined by writing a mass balance equation for the entire system and evaluating it at effective ISIP and radial fractures, we get –

$$\begin{equation} \label{eq:mbalforcl_radial} V_{inj} = (P(\Delta t) - P_{w, init})C_{w} + 2AC_{L}\sqrt{t_{e}}g(\Delta t) + A\frac{(P(\Delta t) - S_{h,min})}{S_{f}} \end{equation}$$

$$\begin{equation} \label{eq:mbalforclandrf_radial} V_{inj} = (P - P_{w, init})C_{w} + 4C_{L}\pi R_{f}^{2}\sqrt{\frac{t_{e}}{2}+\Delta t} + R_{f}^{2}\pi\frac{16R_{f}(P - S_{h,min})}{3\pi E'} \end{equation}$$

2 equations and 2 unknowns, solve both the equations simultaneously to get Fracture radius, \(R_{f}\) and leakoff coefficient \(C_{L}\). R_f is used to calculate Fracture Area, A, if needed.
Once we have C_L, we can calculate k as -

$$\begin{equation} \label{eq:finalk_forcl} k = \left( \frac{C_{L}}{P - P_{res}} \right)^{2} \frac{\pi \mu}{\phi c_{t}} \end{equation}$$

8.1.2. Using the h function

First step is to calculate and plot P and dP/dG vs G function and calculate the h function.
Get the time and pressure at which the G*dP/dG is maximum, we assume here that 90 percent fluid has leaked off from the system.
This will be the \(\Delta t_{peak}\) and \(P_{peak}\) used in the calculations coming up.

Writing a global mass balance with that assumption at \(t= \Delta t_{peak}\), we get –

$$\begin{equation} \label{eq:ArootK_peakDeltaT} A\sqrt{k} = \frac{0.9 V_{inj} - C_{w}(P_{peak} - P_{w,init})}{4h(\Delta t_{peak})\sqrt{\frac{\phi c_{t}}{\pi \mu}}} \end{equation}$$

We can then solve for Area in the global mass balance equation. $$\begin{equation} \label{eq:A_peakDeltaT} A = \left(V_{inj} - C_{w}(P(\Delta t) - P_{w,init})- A\sqrt{k} \left( 4h(\Delta t)\sqrt{\frac{\phi c_{t}}{\pi \mu}} \right) \right)\frac{S_{f}}{P - S_{h,min}} \end{equation}$$

We can also write a global mass balance at \(\Delta t = 0 \) using effective ISIP to minimize the effect of uncertainty in S_h,min, which in this case reduces the equation to - $$\begin{equation} \label{eq:mbalatisipeff} V_{inj} = C_{w}(P_{ISIP, eff} - P_{w,init}) +4(A\sqrt k)(P_{ISIP, eff} - P_{res})\sqrt \frac{t_e}{2} \sqrt{\frac{\phi c_t}{\pi \mu}} + \frac{A}{S_f}(P_{ISIP, eff} - S_{h,min}) \end{equation}$$

Using the appropriate expressions for S_f and Area, depending on radial or PKN fracture geometry assumption, we can estimate the fracture geometry.
For radial fracture geometry - $$\begin{equation} \label{eq:mbalatisipeff_forRf} R_f = \sqrt[3]{\frac{3E'\left[ V_{inj} - C_{w}(P_{ISIP, eff} - P_{w,init}) - 4(A\sqrt k)(P_{ISIP, eff} - P_{res})\sqrt \frac{t_e}{2} \sqrt{\frac{\phi c_t}{\pi \mu}}\right]}{16(P_{ISIP, eff} - S_{h,min})}} \end{equation}$$

For PKN fracture geometry - $$\begin{equation} \label{eq:mbalatisipeff_forLf} L_f = \frac{2E'\left[ V_{inj} - C_{w}(P_{ISIP, eff} - P_{w,init}) - 4(A\sqrt k)(P_{ISIP, eff} - P_{res})\sqrt \frac{t_e}{2} \sqrt{\frac{\phi c_t}{\pi \mu}}\right]}{h_f^2 \pi(P_{ISIP, eff} - S_{h,min})} \end{equation}$$

Once you get R_f or L_f and hence fracture area, A, we can easily get the permeability from the equations shown above.

8.2. Postclosure Methods

You may have either impulse radial or impulse linear flow signatures in your DFIT post closure transient. This may appear on a log-log pressure vs time plot as a derivative slope of -1 or -0.5 respectively. In that case, we can use this data to estimate permeability using late-time analytical solutions for the appropriate flow.

8.2.1. Using Impulse Radial flow

Late time analytical solution for radial flow with constant injection – $$\begin{equation} \label{eq:analyticalradial_constinjection} P - P_{res} = \frac{Q \mu}{2\pi kh} \left[ 0.5 \left( ln \left( \frac{k\Delta t}{\phi \mu c_t r_w^2} \right) +0.80907 \right) + s \right] \end{equation}$$

Thus, we can write the impulse radial solution as a derivative of this constant rate solution as – $$\begin{equation} \label{eq:impulseradialsoln} P - P_{res} = \frac{\left( V_{inj} - C_w(P_{res} - P_{w,init})\right)\mu}{4\pi kh} \frac{1}{\Delta t} \end{equation}$$

1. Plot Pressure vs \(\Delta t^{-1}\) for the data in impulse radial flow.
2. We can get the slope of the line which can be used to calculate \(k\) assuming a fracture height, \(‘h’\). This can be assumed from well logs if payzone section is obvious or if there is strong evidence of height confinement allowing us to fix the height of the fracture.
3. If height is not known, assume radial fractures set h equal to 2R_f. Now use the kh from the slope above, but divide that by 2R_f instead to get k using this equation below -

$$\begin{equation} \label{eq:impulseradialsoln_massbalhunknown} V_{inj} = C_w (P_{ISIP, eff} - P_{w, init}) + 4 \left( \pi R_f^2 \sqrt{\frac{(kh)_{est}}{2 R_f}} \right) \left(P_{ISIP, eff} - P_{res}\right) \sqrt{\frac{t_e}{2}} \sqrt{\frac{\phi c_t}{\pi \mu}} +\frac{16R_f^3}{3E'} \left(P_{ISIP, eff} - S_{h,min} \right) \end{equation}$$

8.2.2. Using Impulse Linear flow

Late time analytical solution for linear flow with constant injection – $$\begin{equation} \label{eq:analyticallinear_constinjection} P = P_{res} + \frac{Q}{A} \sqrt{\frac{\mu}{\pi k c_t \phi}} \sqrt{\Delta t} \end{equation}$$

We can write the impulse linear solution as a derivative of this constant rate solution, taking wellbore storage into account – $$\begin{equation} \label{eq:impulselinearsoln} P = P_{res} + \frac{V_{inj} - C_w(P_{res} - P_{w,init})}{2A} \sqrt{\frac{\mu}{\pi k c_t \phi}} \frac{1}{\sqrt{\Delta t}} \end{equation}$$

1. Plot pressure vs inverse of square root time. Get the \(A\sqrt{k}\) from the slope of the data.
2. Once we have \(A\sqrt{k}\), estimate radius or length (R_f or L_f) and hence permeability using equations in the preclosure k estimate – h function method.

9. DFIT Workflow in whitson⁺

9.1 Before getting started -

9.1.1 Data, data and more data:

DFIT datasets could be far higher frequency than needed.
Datasets can vary from second by second frequency to tens of seconds for the entirety of the test. This can be harder to handle, and make the numerical derivative calculation unweildy.

Instead of uploading such high resolution data, the recommended practice -
Smooth the dataset externally by resampling the data in terms of pressure increments of 5 to 10 psi. Note that there is a further reduction using pressure increments of 30 psi in the DFIT feature to improve speed for dynamic calculations too.

9.1.2 Using Mass Upload sheets to get your DFIT data into whitson⁺ -

Add a well name to the Well Data sheet, you do not need to enter anything else in this sheet.
Use the same well name in the Production Data sheet to add DFIT data to the well -

Key information required: Pressure (bottomhole) vs time

1. Time can be in - Days or DateTime like 'YYYY-MM-DD hh:mm:ss.000'. Smallest resolution is 1 millisecond.

2. Pressure (in psia) vs time data - If only wellhead pressure is available, use the hydrostatic head of water at TVD to correct to bottomhole depth. Enter these in the p_wf or Gauge Pressure column.

3. Injection rate (in STB/d) vs time data (if available) Enter these in the q_w or Water Rate column on the mass upload Production Data sheet.

Additional required information - that cannot be uploaded via mass upload template.
Young's modulus, Poisson's ratio, reservoir fluid viscosity and compressibility.
We also need the estimated fracture height for the assumption of PKN fracture geometry.

You can enter all this information in the DFIT feature under 'Physical Assumptions'.

9.1.3 DFIT dataset example

Here's an example DFIT dataset formatted to be uploaded via the standard mass upload template -
Example DFIT Dataset
Courtesy: MCclure et. al, Resfrac

9.1.4 Choices/Assumptions that need to be made -

1. Choose the preclosure method of choice (G-function and H-function with Radial and PKN fractures) - recommended to go with H-function method with radial fracture geometry.
2. Choose the postclosure method of choice based on late time impulse flow signatures (linear/radial flow) - Note that the preclosure assumption on fracture geometry also auto-applies to the post closure analysis.

Some notes on automated selections in the software

These preliminary steps are done automatically, you may still need to review these selections -

1. Shut in is detected automatically - from zero rate - Instantaneous ISIP is identified as the pressure right after the well is shut in.
2. Initial pressure, P_w,init is chosen as the first point in the pressure data.
3. Cumulative injection volume, and maximum sustained injection rate upto the shut in time (characteristic rate), is calculated from the plot. Injection duration is autocomputed from the two above.
4. Slope in the pressure vs cumulative injection (Wellbore storage plot) is detected to calculate the wellbore storage. If rate data is unavailable, just enter the values cumulative injected volume, maximum sustained rate, and wellbore storage.
5. Pore pressure is calculated automatically by extrapolating the post closure linear transient (default) on the inverse square root time plot.
   

9.2 Key Steps to perform an analysis of a DFIT -

*GIFs to illustrate these points will be added shortly.

1. Upload the downloaded template with the DFIT dataset in the mass upload section of the project.

   
   

2. Navigate to the DFIT feature under the Well Testing section.
   

   
   

3. Review the automatic selection of parameters from the plots, i.e. Literal ISIP, initial pressure, injected volume, characteristic rate, wellbore storage coefficient, minimum dP/dG. Enter the additional parameters relevant for the calculation, i.e. Young's modulus, Poisson's ratio, reservoir fluid viscosity and compressibility.

   
   

4. Dropdowns for preclosure method and post closure methods allow you to switch between the different methods as well as fracture geometry assumption. Selection of frac geometry (Radial/PKN) in preclosure methods enforces the same geometry assumption in postclosure methods. Note that PKN fractures will need fracture height as an additional input.

   
   

5. G function plot picks - Identify point of dP/dG minimum. Identify point of G*dP/dG maximum. This automatically computes the effective ISIP, Fracture Contact Pressure and Minimum Principal Stress and are used in subsequent calculations for permeability. The resolved values could be overwritten.

   
   
   

6. Identify if the late time shut in data has post closure transients - Linear flow will have a half-slope signature and radial flow (rare, beware of false radial signatures in gas wells) will have a unit slope signature. Add the interpretation lines if needed and switch the plot (to the right) to impulse radial flow plot by clicking the 'plot radial' button. Align the slope to the pressure points near x=0 and let that extrapolate to calculate the pore pressure.

   
   

7. Calculation should dynamically run when any of the inputs are changed to compute permeability. If you have reliable post closure transients, use the permeability estimates from the postclosure analysis. Correct preclosure permeability estimates by about 1.5 since they statistically tend to overestimate the permeability.

   
   

10. Additional Resources

*Keep checking this section for more updates.
Reach out to support@whitson.com for any questions or additional information, and demos!

References

[1] Barree, R. D., S. A. Cox, J. L. Miskimins, J. V. Gilbert, and M. W. Conway. 2015. Economic optimization of horizontal well completions in unconventional reservoirs. SPE Production & Operations 3 (4): 293–311.

[2] Cramer, D. D. and D. H. Nguyen. 2013. Diagnostic fracture injection testing tactics in unconventional reservoirs. SPE 163863. Paper presented at the SPE Hydraulic Fracturing Technology Conference, Woodlands, TX.

[3] DFIT Interpretation, The URTeC-2019-123 Procedure on SAGA Wisdom - Taught by Mark McClure

[4] McClure, Mark, Vidya Bammidi, Craig Cipolla, Dave Cramer, Lucas Martin, Alexei A. Savitski, Dave Sobernheim, and Kate Voller. 2019. A collaborative study on DFIT interpretation: integrating modeling, field data, and analytical techniques. URTeC 2019-123. Paper presented at the Unconventional Resources Technology Conference, Denver, CO.

[5] McClure, Mark W., Hojung Jung, Dave D. Cramer, and Mukul M. Sharma. 2016. The fracture compliance method for picking closure pressure from diagnostic fracture injection tests. SPE Journal 21 (4): 1321–1339

[6] Mayerhofer, M. J., C. A. Ehlig-Economides, and M. J. Economides. 1995. Pressure-transient analysis of fracture-calibration tests. SPE 26527. Journal of Petroleum Technology 47 (3): 231-236

[7] Nolte, Kenneth. 1979. Determination of fracture parameters from fracturing pressure decline. SPE 8341. Paper presented at the Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers, Las Vegas, NV.

[8] Valko, P. P. and M. J. Economides. 1999. Fluid-leakoff delineation in high permeability fracturing. SPE Production & Facilities 14 (2), doi: 10.2118/56135-PA.