Ralph disentangled himself cautiously and stole away through the branches. In a few seconds the fat boy's grunts were behind him and he was hurrying toward the screen that still lay between him and the lagoon. (Lord of the Flies)What type of process is “were” in “the fat boy’s grunts were …”? Is it relational: circumstantial, with “behind him” as Attribute? It looks like a verb that denotes transformation in Location and could therefore be a material process with “behind him” as a circumstance construing movement in space. …
As you can clearly see, transitivity is insufficient to interpret what is going on in the field here
First, grammatically: “were” is not a type of process. Process type is a clause rank system, not a verb classification. The whole clause instantiates a relational process, as you have analysed. By definition it is a relation between Carrier and Attribute.
Second, you want to re-interpret it as a material process, because it realises a step in a sequence of movements. But this is not a grammatical meaning, it is discourse semantic, as follows.
Ralph disentangled himself cautiously^stole away through the branches^In a few seconds the fat boy's grunts were behind him^he was hurrying toward the screen
This sequence of figures at the level of discourse realises an activity sequence at the level of field. In principle, the sequence could be realised at the level of grammar in many ways, with the same or similar lexical items, e.g...Following cautious disentanglement and escape through the branches, Ralph ran quickly away from the grunting fat boy, and the screen grew rapidly nearer.Classifying clauses is only one step towards understanding text
 Instantiation is the relation between potential and instance, not function and form. It is, for example, the relation between relational process as potential, and an instance of a relational process; it is the relation between a clause as potential and an instance of a clause. The relation between a clause and a relational process, in the sense of a figure, is realisation — the relation between different levels of symbolic abstraction.
 In terms of ideational semantics, the text involves two sequences, the first a sequence of happening figures, the second a sequence of a being figure and a happening figure.
 This misunderstands stratification. The content plane is stratified into meaning (semantics) and wording (lexicogrammar). The grammar realises meaning; the meaning that grammar realises is semantics.
 It is misleading to refer to the model of sequences and figures (Halliday & Matthiessen 1999) as discourse semantics.
 In SFL theory, field is the ideational dimension of context, and context is the culture construed as a semiotic system that is realised by language; that is, context and language are distinct levels of symbolic abstraction. The field that is realised by the ideational meaning of a text is 'what is going on' in a situation, as an instance of the culture. The misunderstanding of field as 'activity sequence' can be traced back to Martin (1992).
This misunderstanding is compounded by Martin's (1992) misconstrual of context as register, which in SFL theory, is a point of variation on the cline of instantiation (of language, not context). See other posts for why this creates inconsistencies that make the model internally incoherent, and thus untenable. See also Discourse Semantic Theory.