+45 20 21 45 25 khe.consult@gmail.com

Representative Sampling

Process Analytical Technology


Services for decision making, efficiency and sustainability:


Competence building

Public outreach

Services for decision making, efficiency and profitability:

– Consulting

– Competence building

– Public outreach

Representative Sampling

Process Analytical Technology



KHEC is a valued international resource providing state-of-the-art sampling, process analytical technology (PAT) and chemometric consulting for reliable decision making in science, technology, industry, business and regulating authorities.


Representative sampling, process analytical technologies (PAT) and chemometrics constitute a complement of necessary scientific competences for reliable process monitoring and decision making.
The theory of sampling (TOS) is of critical importance.

why sampling?

Analytical results forming the basis for decision making in science, technology, industry, society must be relevant, valid and reliable.
Materials and process are heterogeneous. Heterogeneity is the arch enemy of all sampling.


KHEC offers consulting, courses and advanced educational outreach in:

  • Theory and Practise of Representative Sampling
  • Process Analytical Technology
  • Multivariate Data Analysis
  • Acoustics Chemometrics

theory of sampling (tos)

The Theory of Sampling provides a complete description of heterogeneity and all types of errors involved in sampling of materials and processes, as well as the necessary tools for their evaluation, elimination and/or minimization.


The impact of KHEC’s activities are:
  • Reduced economic loss
  • Improvements in process efficiency
  • Reduction of raw materials waste
  • Increased, documented ROI
  • Increased scientific credibilty


consulting & outreach

KHE offers on-site audits and consulting combined with TOS training, according to individual client requests (in-person or remote).

KHE is an experienced speaker and lecturer offering presentations, courses and educational outreach: 

  • Theory and Practice of Representative Sampling (TOS)
  • Process Analytical Technology
  • Chemometrics


get in touch


Theory and Practice of Sampling of Heterogeneous Materials & Processes (TOS)

(3-day comprehensive course; introductory formats also available for 1, or 2 days)

Course objective:

This course provides a comprehensive introduction to the Theory of and Practice of Sampling (TOS) for stationary as well as dynamic lots (process sampling). TOS is presented as a framework set of six Governing Principles (GP) and four Sampling Unit Operations (SUO) with which to secure representative samples and analytical results in all of science, industry, society, business and for regulatory oversight. The goal is to make all attendees able to design, implement and use fully only representative procedures and equipment.

Virtual 1:1 session included with sampling textbook

Since the book “Introduction to the Theory and Practice of Sampling” was published in February 2020, there has been overwhelmingly positive reaction from many readers.

During the corona pandemic, most in-person meetings, seminars and courses have been impossible. As a consequence, many readers reached out by phone and e-mail, asking for clarification of certain topics in the book, in order to take full advantage of its benefits for their specific industry and business. These encounters, via phone, Skype, Teams, Zoom have been very instructive and valuable for all stakeholders.


Introduction to the Theory and Practice of Sampling

This book presents the Theory of Sampling (TOS) for all readers and audiences starting from level zero. The TOS is presented in a novel didactic framework without excessive background mathematics and statistics that often scare newcomers away. The overall objective is to present a unifying conceptual framework within which all the TOS’ principles, unit operations and sampling error management rules can be understood in the easiest manner possible.

Multivariate Data Analysis

This long-anticipated textbook is currently the most up-to-date resource on chemometrics and Multivariate Data Analysis (MVA). The field of chemometrics is the application of multivariate data analysis methodology to solve chemistry-based problems. It explains not only how to understand experimental outputs, but also to put this newfound knowledge into use for deeper scientific understanding or business gains.


Kim H. Esbensen
is an internationally recognised expert and consultant in sampling, chemometrics and PAT (Process Analytical Technology). Through an extensive academic career he has conducted R&D across a wide range of application fields, primarily process industries (minerals, bio-fuel, recycling, environmental monitoring).

Esbensen has been responsible for a university educational program straddling 30+ years in chemometrics, PAT, TOS, instrumental analysis, Multivariate Image Analysis (MIA), process technology and Philosophy of Science and has subsequently developed a widely recognised continuing education concept today offered via KHE Consulting. His CV lists ~250 publications, ~400 lectures/presentations. He is a recipient of the Pierre Gy Sampling Gold Medal (2013), and the Russian Chemometrics Society Gold Medal (2012). In 2003 he inaugurated the biannual series of World Conferences on Sampling and Blending (WCSB), now in its 8.th edition.

  • Adjunct professor, Aalborg University (AAU), Denmark
  • Adjunct professor, Geological Survey of Denmark and Greenland (GEUS)
  • Assoc. Professor, Université du Québec à Chicoutimi (UQAC)
  • Guest professor (2017) ÉTS – École de Technologie Supérieure, Montreal
  • Guest professor (2018) Recinto Universitario de Mayaguez, Puerto Rico
  • Guest professor (2017) University College of SE Norway (HSN)