Abstract:
A method for determining flow distribution in a formation having a wellbore formed therein includes the steps of positioning a sensor within the wellbore, wherein the sensor generates a feedback signal representing at least one of a temperature and a pressure measured by the sensor, injecting a fluid into the wellbore and into at least a portion of the formation adjacent the sensor, shutting-in the wellbore for a pre-determined shut-in period, generating a simulated model representing at least one of simulated temperature characteristics and simulated pressure characteristics of the formation during the shut-in period, generating a data model representing at least one of actual temperature characteristics and actual pressure characteristics of the formation during the shut-in period, wherein the data model is derived from the feedback signal, comparing the data model to the simulated model, and adjusting parameters of the simulated model to substantially match the data model.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The statements in this section merely provide background information related to the present disclosure and may not constitute prior art. 
         [0002]    The present disclosure relates generally to wellbore treatment and development of a reservoir and, in particular, to a method for determining flow distribution in a wellbore during a treatment. 
         [0003]    Hydraulic fracturing, matrix acidizing, and other types of stimulation treatments are routinely conducted in oil and gas wells to enhance hydrocarbon production. The wells being stimulated often include a large section of perforated casing or an open borehole having significant variation in rock petrophysical and mechanical properties. As a result, a treatment fluid pumped into the well may not flow to all desired hydrocarbon bearing layers that need stimulation. To achieve effective stimulation, the treatments often involve the use of diverting agents in the treating fluid, such as chemical or particulate material, to help reduce the flow into the more permeable layers that no longer need stimulation and increase the flow into the lower permeability layers. 
         [0004]    One method includes conducting the treatment through a coiled tubing, which can be positioned in the wellbore to direct the fluid immediately adjacent to layers that need to be plugged when pumping a diverter and adjacent to layers that need stimulation when pumping stimulation fluid. However, the coiled tubing technique requires an operator to know which layers need to be treated by a diverter and which layers need to be treated by a stimulation fluid. In a well with long perforated or open intervals with highly non-uniform and unknown rock properties, typical of horizontal wells, effective treatment requires knowledge of the flow distribution in the treated interval. 
         [0005]    Traditional flow measurement in a well is typically done through production logging using a flow meter to measure the hydrocarbon production rate or injection rate in the wellbore as a function of depth. Based on the logged wellbore flow rate, the production from or injection rate into each formation depth interval is determined based on a measured axial flow rate over that interval. Traditional flow measurement is valid as long as the flow distribution in the well does not change over the time period when logging is conducted. 
         [0006]    However, during a stimulation treatment, the flow distribution in a well can change quickly due to either stimulation of the formation layers to increase their flow capacity or temporary reduction in flow capacity as a result of diverting agents. To determine the effectiveness of stimulation or diversion in the well, an instantaneous measurement that gives a “snap shot” of the flow distribution in a well is desired. Unfortunately, there are few such techniques available. 
         [0007]    One technique for substantially instantaneous measurement is fiber optic Distributed Temperature Sensing (DTS) technology. DTS typical includes an optical fiber disposed in the wellbore (e.g. via a permanent fiber optic line cemented in the casing, a fiber optic line deployed using a coiled tubing, or a slickline unit). The optical fiber measures a temperature distribution along a length thereof based on an optical time-domain (e.g. optical time-domain reflectometry (OTDR), which is used extensively in the telecommunication industry). 
         [0008]    One advantage of DTS technology is the ability to acquire in a short time interval the temperature distribution along the well without having to move the sensor as in traditional well logging which can be time consuming. DTS technology effectively provides a “snap shot” of the temperature profile in the well. DTS technology has been utilized to measure temperature changes in a wellbore after a stimulation injection, from which a flow distribution of an injected fluid can be qualitatively estimated. The inference of flow distribution is typically based on magnitude of temperature “warm-back” during a shut-in period after injecting a fluid into the wellbore and surrounding portions of the formation. The injected fluid is typically colder than the formation temperature and a formation layer that receives a greater fluid flow rate during the injection has a longer “warm back” time compared to a layer or zone of the formation that receives relatively less flow of the fluid. 
         [0009]    As a non-limiting example,  FIG. 1  illustrates a graphical plot  2  of a plurality of simulated temperature profiles  4  of a laminated formation  6  during a six hour time period of “warm back”, according to the prior art. As shown, the X-axis  8  of the graphical plot  2  represents temperature in Kelvin (K) and the Y-axis  9  of the graphical plot  2  represents a depth in meters (m) measured from a pre-determined surface level. As shown, a permeability of each layer of the laminated formation  6  is estimated in units of millidarcies (mD). The layers of the formation  6  having a relatively high permeability receive more fluid during injection and a time period for “warm back” is relatively long (i.e. after a given time period, a change in temperature is less than a change in temperature of the layers having a lower permeability). The layers of the formation  6  having a relatively low permeability receive less fluid during injection and a time period for “warm back” is relatively short (i.e. after a given time period, a change in temperature is greater than a change in temperature of the layers having a higher permeability). 
         [0010]    By obtaining and analyzing multiple DTS temperature traces during the shut-in period, the injection rate distribution among different formation layers can be determined. However, current DTS interpretation techniques and methods are based on visualization of the temperature change in the DTS data log, and is qualitative in nature, at best. The current interpretation methods are further complicated in applications where a reactive fluid, such as acid, is pumped into the wellbore, wherein the reactive fluid reacts with the formation rock and can affect a temperature of the formation, leading to erroneous interpretation. In order to achieve effective stimulation, more accurate DTS interpretation methods are needed to help engineers determine the flow distribution in the well and make adjustments in the treatment accordingly. 
         [0011]    This disclosure proposes several methods for quantitatively determining the flow distribution from DTS measurement. These methods are discussed in detail below. 
       SUMMARY OF THE INVENTION 
       [0012]    An embodiment of a method for determining flow distribution in a formation having a wellbore formed therein comprises the steps of: positioning a sensor within the wellbore, wherein the sensor generates a feedback signal representing at least one of a temperature and a pressure measured by the sensor; injecting a fluid into the wellbore and into at least a portion of the formation adjacent the sensor; shutting-in the wellbore for a pre-determined shut-in period; generating a simulated model representing at least one of simulated temperature characteristics and simulated pressure characteristics of the formation during the shut-in period; generating a data model representing at least one of actual temperature characteristics and actual pressure characteristics of the formation during the shut-in period, wherein the data model is derived from the feedback signal; comparing the data model to the simulated model; and adjusting parameters of the simulated model to substantially match the data model. 
         [0013]    In an embodiment, a method for determining flow distribution in a formation having a wellbore formed therein comprises the steps of: positioning a sensor within the wellbore, wherein the sensor provides a substantially continuous temperature monitoring along a pre-determined interval, and wherein the sensor generates a feedback signal representing temperature measured by the sensor; injecting a fluid into the wellbore and into at least a portion of the formation adjacent the interval; shutting-in the wellbore for a pre-determined shut-in period; generating a simulated model representing simulated thermal characteristics of at least a sub-section of the interval during the shut-in period; generating a data model representing actual thermal characteristics of the at least a sub-section of the interval, wherein the data model is derived from the feedback signal; comparing the data model to the simulated model; and adjusting parameters of the simulated model to substantially match the data model. 
         [0014]    In an embodiment, a method for determining flow distribution in a formation having a wellbore formed therein comprises the steps of: a) positioning a distributed temperature sensor on a fiber extending along an interval within the wellbore, wherein the distributed temperature sensor provides substantially continuous temperature monitoring along the interval, and wherein the sensor generates a feedback signal representing temperature measured by the sensor; b) injecting a fluid into the wellbore and into at least a portion of the formation adjacent the interval; c) shutting-in the wellbore for a pre-determined shut-in period; d) generating a simulated model representing simulated thermal characteristics of a sub-section of the interval during the shut-in period; e) generating a data model representing actual thermal characteristics of the sub-section of the interval, wherein the data model is derived from the feedback signal; f) comparing the data model to the simulated model; g) adjusting parameters of the simulated model to substantially match the data model; and h) repeating steps d) through g) for each of a plurality of sub-sections defining the interval within the wellbore to generate a flow profile representative of the entire interval. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    These and other features and advantages of the present invention will be better understood by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein: 
           [0016]      FIG. 1  is a graphical plot of a plurality of simulated temperature profiles of a laminated formation during a six hour time period of warm back, according to the prior art; 
           [0017]      FIG. 2  is a schematic diagram of an embodiment of a wellbore treatment system; 
           [0018]      FIG. 3  is a graphical plot showing an embodiment of a simulated temperature profile and an actual measured temperature profile for a wellbore treatment at a first time period; 
           [0019]      FIG. 4  is a graphical plot showing a simulated temperature profile and an actual measured temperature profile for the wellbore treatment shown in  FIG. 3 , taken at a second time period; 
           [0020]      FIG. 5  is a schematic plot showing an embodiment of a plurality of measured temperature profiles, each of the measured temperature profiles taken at a discrete time period during a shut-in period of a wellbore treatment; 
           [0021]      FIG. 6  is a graphical representation of temperature vs. time for a sub interval of the profile represented in  FIG. 5 ; 
           [0022]      FIG. 7  is a graphical representation of an interpreted flow profile of the wellbore treatment represented in  FIG. 5 ; 
           [0023]      FIG. 8A  is a graphical plot of a measured temperature profile of the laminated formation of  FIG. 1 ; 
           [0024]      FIG. 8B  is graphical plot of an interpreted temperature of a fluid prior to injection into the laminated formation of  FIG. 1 ; 
           [0025]      FIG. 8C  is graphical plot of an interpreted temperature of the laminated formation of  FIG. 1 , prior to an injection procedure; and 
           [0026]      FIG. 8D  is graphical plot of an interpreted volume of fluid injected into the laminated formation of  FIG. 1  at various depths thereof. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0027]    Referring now to  FIG. 2 , there is shown an embodiment of a wellbore treatment system according to the invention, indicated generally at  10 . As shown, the system  10  includes a fluid injector(s)  12 , a sensor  14 , and a processor  16 . It is understood that the system  10  may include additional components. 
         [0028]    The fluid injector  12  is typically a coiled tubing, which can be positioned in a wellbore formed in a formation to selectively direct a fluid to a particular depth or layer of the formation. For example, the fluid injector  12  can direct a diverter immediately adjacent a layer of the formation to plug the layer and minimize a permeability of the layer. As a further example, the fluid injector  12  can direct a stimulation fluid adjacent a layer for stimulation. It is understood that other means for directing fluids to various depths and layers can be used, as appreciated by one skilled in the art of wellbore treatment. It is further understood that various treating fluids, diverters, and stimulation fluids can be used to treat various layers of a particular formation. 
         [0029]    The sensor  14  is typically of Distributed Temperature Sensing (DTS) technology including an optical fiber  18  disposed in the wellbore (e.g. via a permanent fiber optic line cemented in the casing, a fiber optic line deployed using a coiled tubing, or a slickline unit). The optical fiber  18  measures the temperature distribution along a length thereof based on optical time-domain (e.g. optical time-domain reflectometry). In certain embodiments, the sensor  14  includes a pressure measurement device  19  for measuring a pressure distribution in the wellbore and surrounding formation. In certain embodiments, the sensor  14  is similar to the DTS technology disclosed in U.S. Pat. No. 7,055,604 B2, hereby incorporated herein by reference in its entirety. 
         [0030]    The processor  16  is in data communication with the sensor  14  to receive data signals (e.g. a feedback signal) therefrom and analyze the signals based upon a pre-determined algorithm, mathematical process, or equation, for example. As shown in  FIG. 2 , the processor  16  analyzes and evaluates a received data based upon an instruction set  20 . The instruction set  20 , which may be embodied within any computer readable medium, includes processor executable instructions for configuring the processor  16  to perform a variety of tasks and calculations. As a non-limiting example, the instruction set  20  may include a comprehensive suite of equations governing a physical phenomena of fluid flow in the formation, a fluid flow in the wellbore, a fluid/formation (e.g. rock) interaction in the case of a reactive stimulation fluid, a fluid flow in a fracture and its deformation in the case of hydraulic fracturing, and a heat transfer in the wellbore and in the formation. As a further non-limiting example, the instruction set  20  includes a comprehensive numerical model for carbonate acidizing such as described in Society of Petroleum Engineers (SPE) Paper 107854, titled “An Experimentally Validated Wormhole Model for Self-Diverting and Conventional Acids in Carbonate Rocks Under Radial Flow Conditions,” and authored by P. Tardy, B. Lecerf and Y. Christanti, hereby incorporated herein by reference in its entirety. It is understood that any equations can be used to model a fluid flow and a heat transfer in the wellbore and adjacent formation, as appreciated by one skilled in the art of wellbore treatment. It is further understood that the processor  16  may execute a variety of functions such as controlling various settings of the sensor  14  and the fluid injector  12 , for example. 
         [0031]    As a non-limiting example, the processor  16  includes a storage device  22 . The storage device  22  may be a single storage device or may be multiple storage devices. Furthermore, the storage device  22  may be a solid state storage system, a magnetic storage system, an optical storage system or any other suitable storage system or device. It is understood that the storage device  22  is adapted to store the instruction set  20 . In certain embodiments, data retrieved from the sensor  14  is stored in the storage device  22  such as a temperature measurement and a pressure measurement, and a history of previous measurements and calculations, for example. Other data and information may be stored in the storage device  22  such as the parameters calculated by the processor  16  and a database of petrophysical and mechanical properties of various formations, for example. It is further understood that certain known parameters and numerical models for various formations and fluids may be stored in the storage device  22  to be retrieved by the processor  16 . 
         [0032]    As a further non-limiting example, the processor  16  includes a programmable device or component  24 . It is understood that the programmable device or component  24  may be in communication with any other component of the system  10  such as the fluid injector  12  and the sensor  14 , for example. In certain embodiments, the programmable component  24  is adapted to manage and control processing functions of the processor  16 . Specifically, the programmable component  24  is adapted to control the analysis of the data signals (e.g. feedback signal generated by the sensor  14 ) received by the processor  16 . It is understood that the programmable component  24  may be adapted to store data and information in the storage device  22 , and retrieve data and information from the storage device  22 . 
         [0033]    In certain embodiments, a user interface  26  is in communication, either directly or indirectly, with at least one of the fluid injector  12 , the sensor  14 , and the processor  16  to allow a user to selectively interact therewith. As a non-limiting example, the user interface  26  is a human-machine interface allowing a user to selectively and manually modify parameters of a computational model generated by the processor  16 . 
         [0034]    In use, a fluid is injected into a formation (e.g. laminated rock formation) to remove or by-pass a near well damage, which may be caused by drilling mud invasion or other mechanisms, or to create a hydraulic fracture that extends hundreds of feet into the formation to enhance well flow capacity. A temperature of the injected fluid is typically lower than a temperature of each of the layers of the formation. Throughout the injection period, the colder fluid removes thermal energy from the wellbore and surrounding areas of the formation. Typically, the higher the inflow rate into the formation, the greater the injected fluid volume (i.e. its penetration depth into the formation), and the greater the cooled region. In the case of hydraulic fracturing, the injected fluid enters the created hydraulic fracture and cools the region adjacent to the fracture surface. When pumping stops, the heat conduction from the reservoir gradually warms the fluid in the wellbore. Where a portion of the formation does not receive inflow during injection will warm back faster due to a smaller cooled region, while the formation that received greater inflow warms back more slowly. 
         [0035]      FIG. 3  illustrates a graphical plot  28  showing a simulated temperature profile  30  and an actual measured temperature profile  32  for a wellbore treatment (e.g. an acid treatment in a horizontal well in a carbonate formation) at a first time period. As a non-limiting example, the first time period is immediately after the shut-in procedure (i.e, stopping the wellbore treatment and ceasing fluid flow into the formation or the like) has been initiated. As shown, the X-axis  34  of the graphical plot  28  represents temperature in degrees Celsius (° C.) and the Y-axis  36  of the graphical plot  28  represents a depth of the formation in meters (m), measured from a pre-determined surface level. In certain embodiments, the simulated temperature profile  30  is based on at least one of estimated petrophysical, mechanical, and thermal properties of the formation, thermal properties (e.g. thermal conductivity and heat capacity) of the inject fluid, and flow properties of the inject fluid and formation. As a non-limiting example, the estimated properties of the formation can be manually provided by a user. As a further non-limiting example, the estimated properties can be generated by the processor  16  based upon stored data and known or estimated information about the formation. It is understood that a simulated pressure profile (not shown) can be generated by the processor  16  based on the estimated properties of the formation. The actual measured temperature profile  32  is based upon a data acquired by the sensor  14  during the shut-in after a period of fluid injection. 
         [0036]      FIG. 4  illustrates a graphical plot  38  showing a simulated temperature profile  40  and an actual measured temperature profile  42  for a wellbore treatment (e.g. an acid treatment in a horizontal well in a carbonate formation) at a second time period. As a non-limiting example, the second time period is approximately four hours after the first time period. It is understood that any time period can be used. As shown, the X-axis  44  of the graphical plot  38  represents temperature in degrees Celsius (° C.) and the Y-axis  46  of the graphical plot  38  represents a depth of the formation in meters (m), measured from a pre-determined surface level. In certain embodiments, the simulated temperature profile  40  is based on at least one of estimated petrophysical, mechanical, and thermal properties of the formation, thermal properties (e.g. thermal conductivity and heat capacity) of the inject fluid, and flow properties of the inject fluid and formation. As a non-limiting example, the estimated properties of the formation can be manually provided by a user. As a further non-limiting example, the estimated properties can be generated by the processor  16  based upon stored data and known information about a location of the formation. It is understood that a simulated pressure profile (not shown) can be generated by the processor  16  based on the estimated properties of the formation. The actual measured temperature  32  is based upon a data acquired by the sensor  14  during the shut-in after a period of fluid injection. 
         [0037]    As an illustrative example a layer of the formation at a particular depth is estimated to have a first set of petrophysical properties having a particular permeability and the simulated temperature profiles  30 ,  40  are generated based upon a model of the estimated properties of the formation (i.e. forward model simulation). However, where the actual measured temperatures  32 ,  42  are not aligned with the simulated temperature profiles  30 ,  40  the user modifies at least one of the estimated properties of the formation and the parameters of the model relied upon to generate the simulated temperature profiles  30 ,  40  such that the simulated temperature profiles  30 ,  40  substantially match the actual measured temperatures  32 ,  42 . In this way, the model used to generate the simulated temperature profiles  30 ,  40  is updated based upon the actual measurements of the sensor  14 . It is understood that the updated model can be used as a base model for future applications on the same or similar formation. It is further understood that the flow distribution in the formation can be quantitatively determined from the updated model. 
         [0038]      FIGS. 5-7  illustrate a method for determining a flow distribution in a formation according to another embodiment of the present invention. As a non-limiting example, the flow distribution in the formation is determined using a numerical inversion algorithm. As a further non-limiting example, a simulated temperature curve (i.e. simulated model) is generated for a given flow rate, an injection fluid temperature, and an initial formation temperature for any given depth by solving a numerical finite difference heat transfer model for modeling a convective flow of a cooler fluid into a permeable formation, as appreciated by one skilled in the art. 
         [0039]      FIG. 5  illustrates a schematic plot  47  showing a plurality of measured temperature profiles  48 , each of the measured temperature profiles  48  taken at a discrete time period t 1 , t 2 , t 3 , t 4  during the shut-in period after an injection. As shown, the X-axis  49  of the graphical plot  47  represents temperature and the Y-axis  50  of the graphical plot  47  represents a depth of the formation measured from a pre-determined surface level. In certain embodiments, a wellbore interval of interest  52  is divided into a plurality of sub sections  54  of pre-determined cross-sectional length. For each of the sub sections  54  the measured temperature profile is plotted against time, as shown in  FIG. 6 . 
         [0040]    Specifically  FIG. 6  illustrates a graphical plot  56  showing a plurality of discrete temperature measurements  58  of the sensor  14 , each of the measurements taken at the discrete time periods t 1 , t 2 , t 3 , t 4 , respectively. A theoretical temperature curve  60  (i.e. simulated model) is modeled to intersect the discrete measurements  58 . As shown, the X-axis  62  of the graphical plot  56  represents time and the Y-axis  64  of the graphical plot  56  represents a temperature. 
         [0041]    In particular, the temperature measurements  58  for a particular one of the sub sections  54  are compared to the theoretical temperature curve  60 . In certain embodiments a numerical optimization algorithm is applied to the measured temperature measurements  58  and the theoretical temperature curve  60  to find a “best match” and to minimize an error difference therebetween. For example, the numerical optimization algorithm is a sum of squares of the difference between the data values of temperature measurements  58  and corresponding points along the theoretical temperature curve  60 . As a further example, a plurality of input parameters for generating the theoretical temperature curve  60  (i.e. simulated model) are automatically modified to obtain a best match between the theoretical temperature curve  60  and the temperature measurements  58 . In certain embodiments, the input parameters include a flow rate during injection, a fluid temperature, an initial formation temperature, and a flow rate during shut-in, for example. It is understood that a number of discrete combinations of the input parameters may generate the same theoretical temperature curve. As such, an average of the input parameters can be used for the fitting procedure between the theoretical temperature curve  60  and the temperature measurements  58 . 
         [0042]    Once the theoretical temperature curve  60  is “fitted” to the temperature measurements  58 , the modified input parameters of the theoretical temperature curve  60  represent the average flow rate, the fluid temperature, and the initial formation temperature. A flow profile (i.e. the profile of the fluid volume injected during the injection period) can be obtained by repeating the comparison and fitting process described above for the remainder of the sub sections  54 . As an example,  FIG. 7  illustrates a graphical plot  65  showing a flow profile  66  (i.e. a flow distribution). As shown, the X-axis  67  of the graphical plot  65  represents a volume of injected fluid and the Y-axis  68  of the graphical plot  65  represents a depth of the formation measured from a pre-determined surface level. 
         [0043]      FIGS. 8A-8D  illustrate an example of applying a numerical inversion algorithm to the synthetic data generated by a numerical simulator, as shown in  FIG. 1 . In particular,  FIG. 8A  illustrates a graphical plot  69  showing a first measured temperature profile  70  taken at a first time period and a second measured temperature profile  72  taken at a second time period. As a non-limiting example the first time period is immediately after a shut-in procedure is initiated and the second time period is six hours after the first time period. It is understood that any time period can be used. As shown, the X-axis  74  of the graphical plot  69  represents temperature in Kelvin (K) and the Y-axis  76  of the graphical plot  69  represents a depth of the formation in meters (m), measured from a pre-determined surface level. 
         [0044]    In operation, a theoretical temperature curve (i.e. simulated model) is generated based upon a numerical finite difference heat transfer model for modeling a convective flow of a cooler fluid into a permeable formation, as appreciated by one skilled in the art. As a non-limiting example, the input parameters of the heat transfer model include estimates for a flow rate during injection, a fluid temperature, an initial formation temperature, and a flow rate during shut-in. The temperature profiles  70 ,  72  are compared to the theoretical curve in a manner similar to that shown in  FIG. 6 . In certain embodiments a numerical optimization algorithm is applied to the measured temperature profiles  70 ,  72  and the theoretical curve to automatically find a “best match” and to minimize an error difference between the temperature profiles  70 ,  72  and the theoretical curve. As a non-limiting example, the input parameters are modified so that the resultant theoretical temperature curve substantially matches an appropriate one of the temperature profiles  70 ,  72 . Once the theoretical curve is “fitted” to the appropriate one of the temperature profiles  70 ,  72 , the modified input parameters of the theoretical curve represent the average flow rate, the fluid temperature, and the initial formation temperature, as shown in  FIGS. 8B ,  8 C, and  8 D respectively. It is understood that a number of discrete combinations of the input parameters may generate the same theoretical temperature curve. As such, an average of the input parameters can be used for the fitting procedure between the theoretical temperature curve and the temperature the temperature profiles  70 ,  72 . 
         [0045]    Specifically,  FIG. 8B  is a graphical plot  78  showing an inversed (i.e. interpreted from the inversion algorithm) temperature curve  80  for the injected fluid. As shown, the X-axis  82  of the graphical plot  78  represents temperature in Kelvin (K) and the Y-axis  84  of the graphical plot  78  represents a depth of the formation in meters (m), measured from a pre-determined surface level.  FIG. 8C  is a graphical plot  86  showing an average temperature profile  88  for the formation prior to receiving the injected fluid (with a standard deviation shown as a shaded region). As shown, the X-axis  90  of the graphical plot  86  represents temperature in Kelvin (K) and the Y-axis  92  of the graphical plot  86  represents a depth of the formation in meters (m), measured from a pre-determined surface level.  FIG. 8D  is a graphical plot  94  showing a simulated average volume curve  96  for the injected fluid (with a standard deviation shown as a shaded region). As shown, the X-axis  98  of the graphical plot  94  represents volume in cubic meters of fluid injected into one meter of the formation (m 3 /m) and the Y-axis  100  of the graphical plot  94  represents a depth of the formation in meters (m), measured from a pre-determined surface level. As such, the temperature curve  80 , temperature profile  88 , and the volume curve  96  provide an accurate flow distribution profile for the formation, which can be relied upon for subsequent treatment processes. 
         [0046]    In an embodiment, a temperature data measured by the sensor  14  is compared against a set of pre-generated theoretical curves called type curves. The type curves are typically in dimensionless form, with dimensionless variables expressed as a combination of physical variables. The temperature data received from the sensor  14  is pre-processed to be presented in dimensionless form and to overlay on the theoretical type curves. By shifting the measured temperature data to find a best matched type curve, one can determine the physical parameters that correspond to the matched type curve, including the flow rate into the formation. Carrying out the same procedure for all depths, one can construct a flow profile along the wellbore as in the previous methods. An example of type curve techniques for DTS interpretation is disclosed in U.S. Pat. Appl. Pub. No. 2009/0216456, hereby incorporated herein by reference in its entirety. 
         [0047]    Several DTS interpretation methods have been discussed herein. The methods involve using a mathematical model (simulated model) to predict the expected temperature response and compare the prediction with actual measurements (measured data model). By adjusting the simulated model parameters to match the measured data model, a flow distribution in the well is deduced. For those skilled in the art, different temperature models can be used, or different techniques could be used to attain the match with the DTS measured data. However, such variations fall under the spirit of this invention. 
         [0048]    The interpreted flow profile provides stimulation field practitioners with detailed knowledge to make real time decisions to tailor the stimulation operation to maximize the stimulation effectiveness. The stimulation operations may include the following activities: position coiled tubing to a zone that has not been effectively stimulated to maximize stimulation fluid contact/inflow into that zone; position coiled tubing to a zone that has already been fully stimulated to spot a diverting agent to temporarily plug the zone so the subsequent stimulation fluid can flow into other zones that need further stimulation, rather than wasting fluid in the already stimulated zone; switch a treating fluid if it is shown ineffective; switch a diverter if it is shown ineffective; and set a temporary plug or other types of mechanical barrier in the well to isolate the already stimulated zones to allow separate treatment of the remaining zones. Other operations may rely on the flow profile generated by embodiments of the methods disclosed herein. 
         [0049]    To maximize stimulation effectiveness, a stimulation operation can be designed to consist of multiple injection cycles followed by shut-in periods in which DTS data is acquired. The DTS data is analyzed immediately to provide the field operator with the flow distribution in the well, which can be used to make adjustments of the subsequent treatment schedule if necessary to maximize stimulation effectiveness. Well production can hence be maximized as a result of the optimized stimulation. 
         [0050]    The preceding description has been presented with reference to presently preferred embodiments of the invention. Persons skilled in the art and technology to which this invention pertains will appreciate that alterations and changes in the described structures and methods of operation can be practiced without meaningfully departing from the principle, and scope of this invention. Accordingly, the foregoing description should not be read as pertaining only to the precise structures described and shown in the accompanying drawings, but rather should be read as consistent with and as support for the following claims, which are to have their fullest and fairest scope.