## Final Report Summary - HYDROFRAC (Enhancing hydraulic fracturing on the basis of numerical simulation of coupled geomechanical, hydrodynamic and microseismic processes)

PUBLISHABLE SUMMARY FOR HYDROFRAC PROJECT

(September 1, 2010 − August 31, 2014)

http://fp7.imaps.aber.ac.uk/hydrofrac.html

I. Problem

Hydraulic fracturing (HF) is a technological operation extensively used in the petroleum industry, geothermal energy exploitation, CO2 sequestration, waste deposition and others. Every year thousands of treatments are performed. Over a million treatments have been implemented for the last 60 years. The importance of HF has dramatically grown recently because huge resources of gas have been found in low permeable shales, where the classical technologies cannot be used for extraction.

A HF treatment consists in pumping a fluid (commonly water) under the pressure sufficient to create a crack (hydrofracture) in a productive layer of the rock formation. If a HF treatment is successful, it drastically increases the surface through which oil (gas, hot water) flows to the wellbore, what results in a notable growth of recovery.

As HF is a quite expensive operation, the success of a treatment is of prime economic significance. Clearly the success strongly depends on proper design and control of this technological operation, which requires understanding of the undergoing physical processes and sufficient data on the structure and properties of the rock formation. Meanwhile, the needed data is hardly available and in many cases uncertain because of inaccessibility of rock mass at the common treatment depths (hundreds and thousands of meters). Actually, there are merely two sources of information: (i) the history of pumping pressure, and (ii) microseismic observations. The first is employed in an inversion procedure based on the comparison of the recorded pressure with the pressure simulated by mathematical modeling. Still in view of mathematical difficulties and non-uniqueness of the inversion, the data obtained is often non-reliable. The second (microseismic observations), despite of high cost, has recently become an important complimentary source. However the interpretation of seismicity in terms of the HF parameters is often dubious. It is a challenge to remove, or at least decrease the uncertainty, to improve understanding and, as a result, to drastically increase the efficiency of HF.

II. Objective

The objective of the project is to meet the challenge by improving mathematical modeling of HF and by combining it with simulation of accompanying seismicity. This is of prime significance for reliable inversion of both the pressure history and observed microseismicity.

III. Breakthrough in reaching the goal

The objective has been reached as a result of four-year work on the project. The key to the advance has been found in thorough re-examination of the theoretical rationale of the HF problem. The analysis has disclosed two fundamental facts missed so far in the conventional formulation of the problem. The first consists in the advantage of using the particle velocity as the primary physical quantity rather than commonly used the flux. (The latter is the secondary quantity introduced by definitions as the product of the particle velocity by the fracture opening). It has been revealed that employing the particle velocity provides a favourable variable, avoids common confusion in formulation of boundary conditions and leads to significant analytical and computational benefits. What is of special significance, the particle velocity is directly connected with the second key element disclosed, that is the special role of the so called speed equation (SE). We have stated that the latter is the fundamental equation independent on the mass conservation law, movement equations and properties of a fluid. For more than forty years, researchers have been using the conventional formulation; although the SE has been mentioned occasionally in a few publications, it has never been used systematically for the general HF problem. This strongly hampered numerical modeling of hydraulic fracture propagation by well-established methods of the theory of propagating interfaces, such as the Level Set and Fast Marching Methods. Moreover the very possibility of using these highly efficient methods has been denied until recently.

Inclusion of the SE into the problem formulation means a breakthrough in numerical simulation of HF. It has opened extremely wide opportunities for improving simulation of HF.

IV. Results obtained on the basis of the modified formulation

Naturally the breakthrough in revealing the fundamental theoretical prerequisites (particle velocity and SE) has led to notable progress in obtaining analytical and numerical solutions and efficient computational techniques. Specifically, the main results are as follows.

(i) For the first time, simple analytical solutions have been obtained for the classical HF problems. They are applicable to both Newtonian and commonly used shear-thinning fluids. They give clear understanding of the influence of major factors on the HF propagation. In particular, the analytical solutions have given a clear answer to the question of great practical significance: if and how thinning fluids may be compared in their hydrofracturing action? They also provided benchmarks for testing numerical technologies. As such, they have been systematically employed to evaluate new computational methods developed.

(ii) It was revealed that, if the small lag between the fluid front and the fracture contour is neglected, the HF problem becomes ill-posed when trying to solve it as a boundary value problem with the fixed position of the front at a time step of calculations. This makes impossible obtaining accurate and stable numerical solutions if not overcoming this obstacle. Two highly efficient approaches have been suggested and employed for avoiding the difficulty and for accurate, stable and robust tracing the fracture propagation. One of them consists in using the specially designed epsilon - regularization. The other consists in including the SE as the additional equation with the front position as an additional unknown. The resulting dynamical system is well-posed. The both approaches employ the asymptotic 1D solutions following from the theory developed under the condition, always accepted while not explicitly, that the propagation speed is finite and non-zero.

(iii) Several highly efficient solvers, based on the theoretical findings, are developed for 1D problems. Their accuracy is four orders higher than those previously used under the same and even less time expense. They are of immediate use in both pseudo and truly 3D computational codes for solving the general HF problem.

(iv) Extremely wide options are now open for the progress in numerical simulation of HF propagation in real time on conventional laptops. They include a variety of explicit and implicit Level Set and Fast Marching Methods. The feasibility of this practically significant goal is clearly demonstrated in many numerical experiments by the comparison of their results with the obtained benchmark solutions.

V. Additional results

(v) New methods for solving the boundary integral equations, specially tailored to account for blocky structure of rock mass with a propagating HF, are developed. To decrease the memory and time expense and to increase the accuracy, new almost analytical recurrent quadrature rules are derived, implemented and successfully tested. For the first time, they are adjusted to the power-type (with an arbitrary exponent) asymptotic behavior of the solution predicted by the theory. Fast multipole method is implemented and used to solve problems with many (up to millions) degrees of freedom on a conventional laptop. It serves to account for strong inhomogeneity of rock stratum when simulating and interpreting microseismicity.

(vi) The general theory of numerical simulation of seismic and aseismic events, including microseismicity induced by HF, is developed and implemented in a computer code for modeling 3D problems. The computer program is unique in its ability to perform accurate and stable calculations of changes in local stresses and for simulation of microseismic events induced by these changes. The simulations have shown that the magnitudes, spatial and temporal distributions of the simulated events comply with those observed in HF treatments. The advantages of the synthetic seismicity (low cost of obtaining results, large amount of statistical information, well-defined mechanical state) have provided a new means for inversion of microseismic data. The comparison of the synthetic microseismicity with that observed in the course of a HF treatment provides important means to calibrate and to improve the input parameters used in modeling. Note that to the moment, only the observed seismicity and only the totality of the observed events is employed for conclusions on HF. Meanwhile, using both the synthetic and observed events, grouped in 10 minutes time intervals of the HF propagation, is much more informative. In view of scarce geometrical and mechanical data on rock mass around a borehole, this is of real value for increasing reliability of numerical simulations. These results reach the objective to join simulation of the HF propagation with simulation of the accompanying microseismicity.

(vii) For the final stage of HF treatment, when the slurry of a fracturing fluid and small stiff particles (proppant) is pumped into the fracture to prevent its closure after the pressure drop, new results are obtained on the properties of the slurry. The effective properties, although being of prime significance for transportation and placing the proppant, are difficult to be obtained in physical experiments reproducing the Poiseuille-type movement in a narrow channel (fracture). Specially designed numerical experiments, performed on a supercomputer by two complementing methods (Particle Dynamics and Smoothed Particle Hydrodynamics), have disclosed facts important for practice. Firstly, the slurry may be approximated by a Newtonian fluid with the dynamic viscosity depending on the concentration up to volumetric concentration 0.6. Secondly, the dependence of the effective viscosity on the concentration may be approximated by a simple formula obtained. Thirdly, the effective viscosity for the Couette-type movement agrees with that for the Poiseuille type movement under the parameters typical for HF. This justifies using rotational viscometers for obtaining properties of the mixture of a fluid and proppant needed to model and design HF.

VI. Dissemination of the results

The knowledge gained has been disseminated by (i) publications in peer-reviewed (38) and open access journals (16); (ii) key-note lectures (5) and presentations (74, in total) to International Symposia and Conferences; (iii) organizing and heading 5 mini-symposia on HF in frames of major international events; (iv) organizing 13 International Conferences including the major Consortium dissemination event: “International Conference on Recent Advances in Numerical Modeling of HF” with key-note lectures delivered by the leading specialists in modeling HF and in using accompanying microseismicity; (v) six PhD students working on the HYDROFRAC project participated in numerous conferences; five of them were awarded for their researches on HF in the major project dissemination event.

The results listed show that the execution of the project has reached its objectives.

(September 1, 2010 − August 31, 2014)

http://fp7.imaps.aber.ac.uk/hydrofrac.html

I. Problem

Hydraulic fracturing (HF) is a technological operation extensively used in the petroleum industry, geothermal energy exploitation, CO2 sequestration, waste deposition and others. Every year thousands of treatments are performed. Over a million treatments have been implemented for the last 60 years. The importance of HF has dramatically grown recently because huge resources of gas have been found in low permeable shales, where the classical technologies cannot be used for extraction.

A HF treatment consists in pumping a fluid (commonly water) under the pressure sufficient to create a crack (hydrofracture) in a productive layer of the rock formation. If a HF treatment is successful, it drastically increases the surface through which oil (gas, hot water) flows to the wellbore, what results in a notable growth of recovery.

As HF is a quite expensive operation, the success of a treatment is of prime economic significance. Clearly the success strongly depends on proper design and control of this technological operation, which requires understanding of the undergoing physical processes and sufficient data on the structure and properties of the rock formation. Meanwhile, the needed data is hardly available and in many cases uncertain because of inaccessibility of rock mass at the common treatment depths (hundreds and thousands of meters). Actually, there are merely two sources of information: (i) the history of pumping pressure, and (ii) microseismic observations. The first is employed in an inversion procedure based on the comparison of the recorded pressure with the pressure simulated by mathematical modeling. Still in view of mathematical difficulties and non-uniqueness of the inversion, the data obtained is often non-reliable. The second (microseismic observations), despite of high cost, has recently become an important complimentary source. However the interpretation of seismicity in terms of the HF parameters is often dubious. It is a challenge to remove, or at least decrease the uncertainty, to improve understanding and, as a result, to drastically increase the efficiency of HF.

II. Objective

The objective of the project is to meet the challenge by improving mathematical modeling of HF and by combining it with simulation of accompanying seismicity. This is of prime significance for reliable inversion of both the pressure history and observed microseismicity.

III. Breakthrough in reaching the goal

The objective has been reached as a result of four-year work on the project. The key to the advance has been found in thorough re-examination of the theoretical rationale of the HF problem. The analysis has disclosed two fundamental facts missed so far in the conventional formulation of the problem. The first consists in the advantage of using the particle velocity as the primary physical quantity rather than commonly used the flux. (The latter is the secondary quantity introduced by definitions as the product of the particle velocity by the fracture opening). It has been revealed that employing the particle velocity provides a favourable variable, avoids common confusion in formulation of boundary conditions and leads to significant analytical and computational benefits. What is of special significance, the particle velocity is directly connected with the second key element disclosed, that is the special role of the so called speed equation (SE). We have stated that the latter is the fundamental equation independent on the mass conservation law, movement equations and properties of a fluid. For more than forty years, researchers have been using the conventional formulation; although the SE has been mentioned occasionally in a few publications, it has never been used systematically for the general HF problem. This strongly hampered numerical modeling of hydraulic fracture propagation by well-established methods of the theory of propagating interfaces, such as the Level Set and Fast Marching Methods. Moreover the very possibility of using these highly efficient methods has been denied until recently.

Inclusion of the SE into the problem formulation means a breakthrough in numerical simulation of HF. It has opened extremely wide opportunities for improving simulation of HF.

IV. Results obtained on the basis of the modified formulation

Naturally the breakthrough in revealing the fundamental theoretical prerequisites (particle velocity and SE) has led to notable progress in obtaining analytical and numerical solutions and efficient computational techniques. Specifically, the main results are as follows.

(i) For the first time, simple analytical solutions have been obtained for the classical HF problems. They are applicable to both Newtonian and commonly used shear-thinning fluids. They give clear understanding of the influence of major factors on the HF propagation. In particular, the analytical solutions have given a clear answer to the question of great practical significance: if and how thinning fluids may be compared in their hydrofracturing action? They also provided benchmarks for testing numerical technologies. As such, they have been systematically employed to evaluate new computational methods developed.

(ii) It was revealed that, if the small lag between the fluid front and the fracture contour is neglected, the HF problem becomes ill-posed when trying to solve it as a boundary value problem with the fixed position of the front at a time step of calculations. This makes impossible obtaining accurate and stable numerical solutions if not overcoming this obstacle. Two highly efficient approaches have been suggested and employed for avoiding the difficulty and for accurate, stable and robust tracing the fracture propagation. One of them consists in using the specially designed epsilon - regularization. The other consists in including the SE as the additional equation with the front position as an additional unknown. The resulting dynamical system is well-posed. The both approaches employ the asymptotic 1D solutions following from the theory developed under the condition, always accepted while not explicitly, that the propagation speed is finite and non-zero.

(iii) Several highly efficient solvers, based on the theoretical findings, are developed for 1D problems. Their accuracy is four orders higher than those previously used under the same and even less time expense. They are of immediate use in both pseudo and truly 3D computational codes for solving the general HF problem.

(iv) Extremely wide options are now open for the progress in numerical simulation of HF propagation in real time on conventional laptops. They include a variety of explicit and implicit Level Set and Fast Marching Methods. The feasibility of this practically significant goal is clearly demonstrated in many numerical experiments by the comparison of their results with the obtained benchmark solutions.

V. Additional results

(v) New methods for solving the boundary integral equations, specially tailored to account for blocky structure of rock mass with a propagating HF, are developed. To decrease the memory and time expense and to increase the accuracy, new almost analytical recurrent quadrature rules are derived, implemented and successfully tested. For the first time, they are adjusted to the power-type (with an arbitrary exponent) asymptotic behavior of the solution predicted by the theory. Fast multipole method is implemented and used to solve problems with many (up to millions) degrees of freedom on a conventional laptop. It serves to account for strong inhomogeneity of rock stratum when simulating and interpreting microseismicity.

(vi) The general theory of numerical simulation of seismic and aseismic events, including microseismicity induced by HF, is developed and implemented in a computer code for modeling 3D problems. The computer program is unique in its ability to perform accurate and stable calculations of changes in local stresses and for simulation of microseismic events induced by these changes. The simulations have shown that the magnitudes, spatial and temporal distributions of the simulated events comply with those observed in HF treatments. The advantages of the synthetic seismicity (low cost of obtaining results, large amount of statistical information, well-defined mechanical state) have provided a new means for inversion of microseismic data. The comparison of the synthetic microseismicity with that observed in the course of a HF treatment provides important means to calibrate and to improve the input parameters used in modeling. Note that to the moment, only the observed seismicity and only the totality of the observed events is employed for conclusions on HF. Meanwhile, using both the synthetic and observed events, grouped in 10 minutes time intervals of the HF propagation, is much more informative. In view of scarce geometrical and mechanical data on rock mass around a borehole, this is of real value for increasing reliability of numerical simulations. These results reach the objective to join simulation of the HF propagation with simulation of the accompanying microseismicity.

(vii) For the final stage of HF treatment, when the slurry of a fracturing fluid and small stiff particles (proppant) is pumped into the fracture to prevent its closure after the pressure drop, new results are obtained on the properties of the slurry. The effective properties, although being of prime significance for transportation and placing the proppant, are difficult to be obtained in physical experiments reproducing the Poiseuille-type movement in a narrow channel (fracture). Specially designed numerical experiments, performed on a supercomputer by two complementing methods (Particle Dynamics and Smoothed Particle Hydrodynamics), have disclosed facts important for practice. Firstly, the slurry may be approximated by a Newtonian fluid with the dynamic viscosity depending on the concentration up to volumetric concentration 0.6. Secondly, the dependence of the effective viscosity on the concentration may be approximated by a simple formula obtained. Thirdly, the effective viscosity for the Couette-type movement agrees with that for the Poiseuille type movement under the parameters typical for HF. This justifies using rotational viscometers for obtaining properties of the mixture of a fluid and proppant needed to model and design HF.

VI. Dissemination of the results

The knowledge gained has been disseminated by (i) publications in peer-reviewed (38) and open access journals (16); (ii) key-note lectures (5) and presentations (74, in total) to International Symposia and Conferences; (iii) organizing and heading 5 mini-symposia on HF in frames of major international events; (iv) organizing 13 International Conferences including the major Consortium dissemination event: “International Conference on Recent Advances in Numerical Modeling of HF” with key-note lectures delivered by the leading specialists in modeling HF and in using accompanying microseismicity; (v) six PhD students working on the HYDROFRAC project participated in numerous conferences; five of them were awarded for their researches on HF in the major project dissemination event.

The results listed show that the execution of the project has reached its objectives.